{"appState":{"pageLoadApiCallsStatus":true},"categoryState":{"relatedCategories":{"headers":{"timestamp":"2023-02-17T08:01:05+00:00"},"categoryId":33722,"data":{"title":"Basic Math","slug":"basic-math","image":{"src":null,"width":0,"height":0},"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"parentCategory":{"categoryId":33720,"title":"Math","slug":"math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"}},"childCategories":[],"description":"Add and subtract negative numbers, calculate how much to tip, make sense of exponents, and generally get mathy, with our easy-to-read articles.","relatedArticles":{"self":"https://dummies-api.dummies.com/v2/articles?category=33722&offset=0&size=5"},"hasArticle":true,"hasBook":true,"articleCount":151,"bookCount":4},"_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"relatedCategoriesLoadedStatus":"success"},"listState":{"list":{"count":10,"total":154,"items":[{"headers":{"creationTime":"2016-03-27T16:46:41+00:00","modifiedTime":"2023-02-16T21:04:02+00:00","timestamp":"2023-02-17T00:01:03+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"AS and A-Level Maths For Dummies Cheat Sheet","strippedTitle":"as and a-level maths for dummies cheat sheet","slug":"as-a-level-maths-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"Some of the most important things to remember in AS-level and A-level maths are the rules for differentiating and integrating expressions. This cheat sheet is a","noIndex":0,"noFollow":0},"content":"Some of the most important things to remember in AS-level and A-level maths are the rules for differentiating and integrating expressions. This cheat sheet is a handy reference for what happens when you differentiate or integrate powers of <i>x</i>, trigonometric functions, exponentials or logarithms – as well as the rules you need for what to do when they’re combined!","description":"Some of the most important things to remember in AS-level and A-level maths are the rules for differentiating and integrating expressions. This cheat sheet is a handy reference for what happens when you differentiate or integrate powers of <i>x</i>, trigonometric functions, exponentials or logarithms – as well as the rules you need for what to do when they’re combined!","blurb":"","authors":[],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/253710"}},{"articleId":249996,"title":"Pre-Algebra Practice Questions: Solving Simple Algebraic Equations","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra Practice Questions: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249986"}},{"articleId":249980,"title":"Pre-Algebra Practice Questions: Rearranging Equations to Isolate x","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":0,"slug":null,"isbn":null,"categoryList":null,"amazon":null,"image":null,"title":null,"testBankPinActivationLink":null,"bookOutOfPrint":false,"authorsInfo":null,"authors":null,"_links":null},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[null]}]\" id=\"du-slot-63eec3bf119bb\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[null]}]\" id=\"du-slot-63eec3bf1240f\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":138462,"title":"Differentiating Simple Terms and Functions for AS & A-Level Maths","slug":"differentiating-simple-terms-and-functions-for-as-a-level-maths","categoryList":[],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/138462"}},{"articleId":138464,"title":"Differentiating Combinations for AS & A-Level Maths","slug":"differentiating-combinations-for-as-a-level-maths","categoryList":[],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/138464"}},{"articleId":138461,"title":"Integrating Simple Terms and Functions for AS & A Level Maths","slug":"integrating-simple-terms-and-functions-for-as-a-level-maths","categoryList":[],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/138461"}},{"articleId":138463,"title":"Integrating Combinations for AS & A-Level Maths","slug":"integrating-combinations-for-as-a-level-maths","categoryList":[],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/138463"}}],"content":[{"title":"Differentiating simple terms and functions","thumb":null,"image":null,"content":"<p>This is a handy guide to the building blocks of differentiation for A-level maths: it gives you all of the things you’re expected to know to differentiate (powers of <i>x</i>, exponentials, logarithms and trigonometric functions) and what you get when you do the calculus!</p>\n<p>In the following table, <i>a</i> represents any constant.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/503353.image0.jpg\" alt=\"image0.jpg\" width=\"535\" height=\"168\" /></p>\n<p class=\"Tip\">Note that ln(<i>ax</i>) differentiates to <i>a</i> / <i>ax</i>, and after you cancel the <i>a</i>s you’re left with 1/<i>x</i>.</p>\n"},{"title":"Differentiating combinations","thumb":null,"image":null,"content":"<p>Once you’ve mastered the building blocks of differentiation for A-level maths, the next step is to get comfortable with the various rules – what happens when you have a function with something complicated inside the brackets? How about if you have expressions involving addition, subtraction, multiplication or division? This table reminds you what to do in these situations, including the dreaded chain rule, quotient rule and product rule from Core 3.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/503355.image0.jpg\" alt=\"image0.jpg\" width=\"535\" height=\"168\" /></p>\n<p class=\"Remember\">If you’re doing <i>p</i><i>arametric differentiation</i><i> </i>in Core 4, then <i>d</i><i>y</i>/<i>d</i><i>x</i> = (<i>d</i><i>y</i>/<i>d</i><i>t</i>)/(<i>d</i><i>x</i>/<i>d</i><i>t</i>).</p>\n"},{"title":"Integrating simple terms and functions","thumb":null,"image":null,"content":"<p>If you want to get a good grade in A-level maths, one of the skills you need is the integration of simple terms – powers of <i>x</i>, exponentials and trigonometric functions.</p>\n<p class=\"Remember\">Any time you integrate, you have to remember to add a constant! If you are working with limits, this cancels out, and if you have additional information, you may be able to work the constant out.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/503357.image0.jpg\" alt=\"image0.jpg\" width=\"535\" height=\"144\" /></p>\n"},{"title":"Integrating combinations","thumb":null,"image":null,"content":"<p>When you have to integrate something more complicated than a simple expression for A-level maths, the chances are you’ll need to use one of the rules in this table, which shows you how to deal with a function when it has a linear argument, two terms added to or subtracted from each other, and the formula for integration by parts. In this table, a capital letter means “the integral of the lower-case letter” – so <i>F</i> is the integral of <i>f</i>, <i>U</i> is the integral of <i>u</i>, and <i>V</i> is the integral of <i>v</i>.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/503359.image0.jpg\" alt=\"image0.jpg\" width=\"535\" height=\"120\" /></p>\n<p>You also need to know about calculating a volume of revolution: Rotating the curve <i>y</i>=<i>f</i>(<i>x</i>) around the <i>x</i>-axis between limits of <i>a</i> and <i>b</i> gives you a volume of</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/503360.image1.png\" alt=\"image1.png\" width=\"69\" height=\"33\" /></p>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2023-02-16T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":207393},{"headers":{"creationTime":"2017-05-25T18:45:56+00:00","modifiedTime":"2022-11-04T15:50:20+00:00","timestamp":"2022-11-04T18:01:02+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"How to Calculate Percentages","strippedTitle":"how to calculate percentages","slug":"how-to-calculate-percentages","canonicalUrl":"","seo":{"metaDescription":"Figure out how much to tip or how good that sale price actually is by learning how to calculate percentages.","noIndex":0,"noFollow":0},"content":"<figure style=\"margin: 0;\"><figcaption style=\"margin-bottom: 10px;\">Listen to the article:</figcaption><audio src=\"/wp-content/uploads/how-to-calculate-percentages.mp3\" controls=\"controls\"><a href=\"/wp-content/uploads/how-to-calculate-percentages.mp3\">Download audio</a></audio></figure>\r\n\r\nWhether you're leaving a tip at a restaurant or figuring out just how much those stylish shoes are <a href=\"https://www.dummies.com/article/academics-the-arts/math/pre-algebra/how-to-calculate-a-percentage-discount-191241/\">on sale</a>, you can't get away from percentages. While there are numerous percentage calculators online, it's helpful to be able to do some quick math in your head to calculate percentages without any digital assistance.\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/percentages.jpg\"><img class=\"aligncenter wp-image-240019 size-full\" src=\"https://www.dummies.com/wp-content/uploads/percentages.jpg\" alt=\"calculating percentages\" width=\"535\" height=\"267\" /></a>\r\n<h2 id=\"tab1\" >What is percentage?</h2>\r\nThe word percentage comes from the word percent. If you split the word percent into its root words, you see “per” and “cent.” Cent is an old European word with French, Latin, and Italian origins meaning “hundred.\" So, percent is translated directly to “per hundred.” If you have 87 percent, you literally have 87 per 100. If it snowed 13 times in the last 100 days, it snowed 13 percent of the time.\r\n<h2 id=\"tab2\" >How to find percentage</h2>\r\nThe numbers that you will be converting into percentages can be given to you in two different formats: decimal and fraction. Decimal format is easier to calculate into a percentage. Converting a decimal to a percentage is as simple as multiplying it by 100. To convert .87 to a percent, simply multiply .87 by 100.\r\n\r\n.87 × 100=87, which gives us 87 percent.\r\n<p class=\"article-tips tip\">Percent is often abbreviated with the % symbol. You can present your answer as 87% or 87 percent — either way is acceptable.</p>\r\nIf you are given a fraction, convert it to a percentage by dividing the top number by the bottom number. If you are given 13/100, you would divide 13 by 100.\r\n\r\n13 ÷ 100 = .13\r\n\r\nThen, follow the steps above for converting a decimal to a percent.\r\n\r\n.13 × 100 = 13, thus giving you 13%.\r\n\r\nThe more difficult task comes when you need to know a percentage when you are given numbers that don’t fit so neatly into 100.\r\n\r\nMost of the time, you will be given a percentage of a specific number. For example, you may know that 40 percent of your paycheck will go to taxes and you want to find out how much money that is.\r\n\r\n \r\n<h2 id=\"tab3\" >How to calculate percentage of a specific number</h2>\r\nThis process is the reverse of what you did earlier. First convert the percentage number to a decimal. Then, you divide your percentage by 100. So, 40 percent would be 40 divided by 100.\r\n\r\n40 ÷ 100 = .40\r\n\r\nNext, once you have the decimal version of your percentage, simply multiply it by the given number (in this case, the amount of your paycheck). If your paycheck is $750, you would multiply 750 by .40.\r\n\r\n750 × .40 = 300\r\n\r\nYour answer would be 300. You are paying $300 in taxes.\r\n\r\nLet’s try another example. You need to save 25 percent of your paycheck for the next 6 months to pay for an upcoming vacation. If your paycheck is $1,500, how much should you save?\r\n\r\nStart by converting 25 percent to a decimal.\r\n\r\n25 ÷ 100 = .25\r\n\r\nNow, multiply the decimal by the amount of your paycheck, or 1500.\r\n\r\n1500 × .25 = 375\r\n\r\nThis means you need to save $375 from each paycheck.","description":"<figure style=\"margin: 0;\"><figcaption style=\"margin-bottom: 10px;\">Listen to the article:</figcaption><audio src=\"/wp-content/uploads/how-to-calculate-percentages.mp3\" controls=\"controls\"><a href=\"/wp-content/uploads/how-to-calculate-percentages.mp3\">Download audio</a></audio></figure>\r\n\r\nWhether you're leaving a tip at a restaurant or figuring out just how much those stylish shoes are <a href=\"https://www.dummies.com/article/academics-the-arts/math/pre-algebra/how-to-calculate-a-percentage-discount-191241/\">on sale</a>, you can't get away from percentages. While there are numerous percentage calculators online, it's helpful to be able to do some quick math in your head to calculate percentages without any digital assistance.\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/percentages.jpg\"><img class=\"aligncenter wp-image-240019 size-full\" src=\"https://www.dummies.com/wp-content/uploads/percentages.jpg\" alt=\"calculating percentages\" width=\"535\" height=\"267\" /></a>\r\n<h2 id=\"tab1\" >What is percentage?</h2>\r\nThe word percentage comes from the word percent. If you split the word percent into its root words, you see “per” and “cent.” Cent is an old European word with French, Latin, and Italian origins meaning “hundred.\" So, percent is translated directly to “per hundred.” If you have 87 percent, you literally have 87 per 100. If it snowed 13 times in the last 100 days, it snowed 13 percent of the time.\r\n<h2 id=\"tab2\" >How to find percentage</h2>\r\nThe numbers that you will be converting into percentages can be given to you in two different formats: decimal and fraction. Decimal format is easier to calculate into a percentage. Converting a decimal to a percentage is as simple as multiplying it by 100. To convert .87 to a percent, simply multiply .87 by 100.\r\n\r\n.87 × 100=87, which gives us 87 percent.\r\n<p class=\"article-tips tip\">Percent is often abbreviated with the % symbol. You can present your answer as 87% or 87 percent — either way is acceptable.</p>\r\nIf you are given a fraction, convert it to a percentage by dividing the top number by the bottom number. If you are given 13/100, you would divide 13 by 100.\r\n\r\n13 ÷ 100 = .13\r\n\r\nThen, follow the steps above for converting a decimal to a percent.\r\n\r\n.13 × 100 = 13, thus giving you 13%.\r\n\r\nThe more difficult task comes when you need to know a percentage when you are given numbers that don’t fit so neatly into 100.\r\n\r\nMost of the time, you will be given a percentage of a specific number. For example, you may know that 40 percent of your paycheck will go to taxes and you want to find out how much money that is.\r\n\r\n \r\n<h2 id=\"tab3\" >How to calculate percentage of a specific number</h2>\r\nThis process is the reverse of what you did earlier. First convert the percentage number to a decimal. Then, you divide your percentage by 100. So, 40 percent would be 40 divided by 100.\r\n\r\n40 ÷ 100 = .40\r\n\r\nNext, once you have the decimal version of your percentage, simply multiply it by the given number (in this case, the amount of your paycheck). If your paycheck is $750, you would multiply 750 by .40.\r\n\r\n750 × .40 = 300\r\n\r\nYour answer would be 300. You are paying $300 in taxes.\r\n\r\nLet’s try another example. You need to save 25 percent of your paycheck for the next 6 months to pay for an upcoming vacation. If your paycheck is $1,500, how much should you save?\r\n\r\nStart by converting 25 percent to a decimal.\r\n\r\n25 ÷ 100 = .25\r\n\r\nNow, multiply the decimal by the amount of your paycheck, or 1500.\r\n\r\n1500 × .25 = 375\r\n\r\nThis means you need to save $375 from each paycheck.","blurb":"","authors":[{"authorId":8941,"name":"Ashley Watters, Abshier House","slug":"ashley-watters-abshier-house","description":"","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8941"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"What is percentage?","target":"#tab1"},{"label":"How to find percentage","target":"#tab2"},{"label":"How to calculate percentage of a specific number","target":"#tab3"}],"relatedArticles":{"fromBook":[],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/253710"}},{"articleId":249996,"title":"Pre-Algebra Practice Questions: Solving Simple Algebraic Equations","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra Practice Questions: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249986"}},{"articleId":249980,"title":"Pre-Algebra Practice Questions: Rearranging Equations to Isolate x","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":0,"slug":null,"isbn":null,"categoryList":null,"amazon":null,"image":null,"title":null,"testBankPinActivationLink":null,"bookOutOfPrint":false,"authorsInfo":null,"authors":null,"_links":null},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[null]}]\" id=\"du-slot-6365535e91185\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[null]}]\" id=\"du-slot-6365535e920ec\"></div></div>"},"articleType":{"articleType":"Articles","articleList":null,"content":null,"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Solve","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2021-07-07T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":240018},{"headers":{"creationTime":"2016-03-26T11:06:08+00:00","modifiedTime":"2022-10-03T13:20:12+00:00","timestamp":"2022-10-03T15:01:03+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Applying Order of Operations to Expressions with Only Multiplication and Division","strippedTitle":"applying order of operations to expressions with only multiplication and division","slug":"applying-order-of-operations-to-expressions-with-only-multiplication-and-division","canonicalUrl":"","seo":{"metaDescription":"Some expressions contain only multiplication and division. When this is the case, the rule for evaluating the expression is pretty straightforward. When an expr","noIndex":0,"noFollow":0},"content":"Some expressions contain only multiplication and division. When this is the case, the rule for evaluating the expression is pretty straightforward. When an expression contains only multiplication and division, evaluate it step by step from left to right.\r\n<h2 id=\"tab1\" >The Three Types of Big Four Expressions</h2>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>Expression</th>\r\n<th>Example</th>\r\n<th>Rule</th>\r\n</tr>\r\n<tr>\r\n<td>Contains only addition and subtraction</td>\r\n<td>12 + 7 – 6 – 3 + 8</td>\r\n<td>Evaluate left to right.</td>\r\n</tr>\r\n<tr>\r\n<td>Contains only multiplication and division</td>\r\n<td>18 ÷ 3 x 7 ÷ 14</td>\r\n<td>Evaluate left to right.</td>\r\n</tr>\r\n<tr>\r\n<td>Mixed-operator expression: contains a combination of\r\naddition/subtraction and multiplication/division</td>\r\n<td>9 + 6 ÷ 3</td>\r\n<td>1. Evaluate multiplication and division left to right.\r\n2. Evaluate addition and subtraction left to right.</td>\r\n</tr>\r\n</tbody>\r\n</table>\r\n<p class=\"Remember\">Suppose you want to evaluate this expression:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435640.image0.jpg\" alt=\"image0.jpg\" width=\"161\" height=\"31\" />\r\n\r\nAgain, the expression contains only multiplication and division, so you can move from left to right, starting with 9 x 2:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435641.image1.jpg\" alt=\"image1.jpg\" width=\"156\" height=\"150\" />\r\n\r\nNotice that the expression shrinks one number at a time until all that’s left is 2. So\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435642.image2.jpg\" alt=\"image2.jpg\" width=\"198\" height=\"31\" />\r\n\r\nHere’s another quick example:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435643.image3.jpg\" alt=\"image3.jpg\" width=\"115\" height=\"31\" />\r\n\r\nEven though this expression has some negative numbers, the only operations it contains are multiplication and division. So you can evaluate it in two steps from left to right (remembering the rules for multiplying and dividing with negative numbers):\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435644.image4.jpg\" alt=\"image4.jpg\" width=\"137\" height=\"111\" />\r\n\r\nThus,\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435645.image5.jpg\" alt=\"image5.jpg\" width=\"157\" height=\"31\" />","description":"Some expressions contain only multiplication and division. When this is the case, the rule for evaluating the expression is pretty straightforward. When an expression contains only multiplication and division, evaluate it step by step from left to right.\r\n<h2 id=\"tab1\" >The Three Types of Big Four Expressions</h2>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>Expression</th>\r\n<th>Example</th>\r\n<th>Rule</th>\r\n</tr>\r\n<tr>\r\n<td>Contains only addition and subtraction</td>\r\n<td>12 + 7 – 6 – 3 + 8</td>\r\n<td>Evaluate left to right.</td>\r\n</tr>\r\n<tr>\r\n<td>Contains only multiplication and division</td>\r\n<td>18 ÷ 3 x 7 ÷ 14</td>\r\n<td>Evaluate left to right.</td>\r\n</tr>\r\n<tr>\r\n<td>Mixed-operator expression: contains a combination of\r\naddition/subtraction and multiplication/division</td>\r\n<td>9 + 6 ÷ 3</td>\r\n<td>1. Evaluate multiplication and division left to right.\r\n2. Evaluate addition and subtraction left to right.</td>\r\n</tr>\r\n</tbody>\r\n</table>\r\n<p class=\"Remember\">Suppose you want to evaluate this expression:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435640.image0.jpg\" alt=\"image0.jpg\" width=\"161\" height=\"31\" />\r\n\r\nAgain, the expression contains only multiplication and division, so you can move from left to right, starting with 9 x 2:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435641.image1.jpg\" alt=\"image1.jpg\" width=\"156\" height=\"150\" />\r\n\r\nNotice that the expression shrinks one number at a time until all that’s left is 2. So\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435642.image2.jpg\" alt=\"image2.jpg\" width=\"198\" height=\"31\" />\r\n\r\nHere’s another quick example:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435643.image3.jpg\" alt=\"image3.jpg\" width=\"115\" height=\"31\" />\r\n\r\nEven though this expression has some negative numbers, the only operations it contains are multiplication and division. So you can evaluate it in two steps from left to right (remembering the rules for multiplying and dividing with negative numbers):\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435644.image4.jpg\" alt=\"image4.jpg\" width=\"137\" height=\"111\" />\r\n\r\nThus,\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/435645.image5.jpg\" alt=\"image5.jpg\" width=\"157\" height=\"31\" />","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <b>Mark Zegarelli</b>, a math tutor and writer with 25 years of professional experience, delights in making technical information crystal clear &#8212; and fun &#8212; for average readers. He is the author of <i>Logic For Dummies</i> and <i>Basic Math &amp; Pre-Algebra For Dummies</i>.","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":33726,"title":"Pre-Algebra","slug":"pre-algebra","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33726"}},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"The Three Types of Big Four Expressions","target":"#tab1"}],"relatedArticles":{"fromBook":[{"articleId":207780,"title":"Basic Math & Pre-Algebra For Dummies Cheat Sheet","slug":"basic-math-pre-algebra-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207780"}},{"articleId":194384,"title":"How to Write Numbers in Scientific Notation","slug":"how-to-write-numbers-in-scientific-notation","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/194384"}},{"articleId":158569,"title":"Inverse Operations and Commutative, Associative, and Distributive Properties","slug":"inverse-operations-and-commutative-associative-and-distributive-properties","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158569"}},{"articleId":158567,"title":"Converting Metric Units to English Units","slug":"converting-metric-units-to-english-units","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158567"}},{"articleId":158560,"title":"A Guide to Working with Exponents, Radicals, and Absolute Value","slug":"a-guide-to-working-with-exponents-radicals-and-absolute-value","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158560"}}],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/253710"}},{"articleId":249996,"title":"Pre-Algebra Practice Questions: Solving Simple Algebraic Equations","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra Practice Questions: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249986"}},{"articleId":249980,"title":"Pre-Algebra Practice Questions: Rearranging Equations to Isolate x","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281978,"slug":"basic-math-pre-algebra-for-dummies-2nd-edition","isbn":"9781119293637","categoryList":["academics-the-arts","math","basic-math"],"amazon":{"default":"https://www.amazon.com/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119293634-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/basic-math-and-pre-algebra-for-dummies-2nd-edition-cover-9781119293637-203x255.jpg","width":203,"height":255},"title":"Basic Math & Pre-Algebra For Dummies","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"<p><b><b data-author-id=\"9399\">Mark Zegarelli</b></b>, a math tutor and writer with 25 years of professional experience, delights in making technical information crystal clear &#8212; and fun &#8212; for average readers. 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Some math concepts may seem complicated at first, but after you work with them for a little bit, you may wonder what all the fuss is about.\r\n\r\nYou'll find easy-to-understand explanations and clear examples in these articles that cover basic math concepts — like order of operations; the commutative, associative, and distributive properties; radicals, exponents, and absolute values — that you may remember (or not) from your early math and pre-algebra classes.\r\n\r\nYou'll also find handy and easy-to-understand conversion guides for converting between metric and English units and between fractions, percents, and decimals.","description":"A little understanding can go a long way toward helping master math. Some math concepts may seem complicated at first, but after you work with them for a little bit, you may wonder what all the fuss is about.\r\n\r\nYou'll find easy-to-understand explanations and clear examples in these articles that cover basic math concepts — like order of operations; the commutative, associative, and distributive properties; radicals, exponents, and absolute values — that you may remember (or not) from your early math and pre-algebra classes.\r\n\r\nYou'll also find handy and easy-to-understand conversion guides for converting between metric and English units and between fractions, percents, and decimals.","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <b>Mark Zegarelli</b>, a math tutor and writer with 25 years of professional experience, delights in making technical information crystal clear &#8212; and fun &#8212; for average readers. He is the author of <i>Logic For Dummies</i> and <i>Basic Math &amp; Pre-Algebra For Dummies</i>.","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":33726,"title":"Pre-Algebra","slug":"pre-algebra","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33726"}},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":194384,"title":"How to Write Numbers in Scientific Notation","slug":"how-to-write-numbers-in-scientific-notation","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/194384"}},{"articleId":158569,"title":"Inverse Operations and Commutative, Associative, and Distributive Properties","slug":"inverse-operations-and-commutative-associative-and-distributive-properties","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158569"}},{"articleId":158567,"title":"Converting Metric Units to English Units","slug":"converting-metric-units-to-english-units","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158567"}},{"articleId":158560,"title":"A Guide to Working with Exponents, Radicals, and Absolute Value","slug":"a-guide-to-working-with-exponents-radicals-and-absolute-value","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158560"}},{"articleId":158557,"title":"A Quick Conversion Guide for Fractions, Decimals, and Percents","slug":"a-quick-conversion-guide-for-fractions-decimals-and-percents","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158557"}}],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/253710"}},{"articleId":249996,"title":"Pre-Algebra Practice Questions: Solving Simple Algebraic Equations","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra Practice Questions: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249986"}},{"articleId":249980,"title":"Pre-Algebra Practice Questions: Rearranging Equations to Isolate x","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281978,"slug":"basic-math-pre-algebra-for-dummies-2nd-edition","isbn":"9781119293637","categoryList":["academics-the-arts","math","basic-math"],"amazon":{"default":"https://www.amazon.com/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119293634-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/basic-math-and-pre-algebra-for-dummies-2nd-edition-cover-9781119293637-203x255.jpg","width":203,"height":255},"title":"Basic Math & Pre-Algebra For Dummies","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"<p><b><b data-author-id=\"9399\">Mark Zegarelli</b></b>, a math tutor and writer with 25 years of professional experience, delights in making technical information crystal clear &#8212; and fun &#8212; for average readers. He is the author of <i>Logic For Dummies</i> and <i>Basic Math &amp; Pre-Algebra For Dummies</i>.</p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <b>Mark Zegarelli</b>, a math tutor and writer with 25 years of professional experience, delights in making technical information crystal clear &#8212; and fun &#8212; for average readers. He is the author of <i>Logic For Dummies</i> and <i>Basic Math &amp; Pre-Algebra For Dummies</i>.","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119293637&quot;]}]\" id=\"du-slot-633af92ec81e5\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119293637&quot;]}]\" id=\"du-slot-633af92ec92eb\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":158567,"title":"Converting Metric Units to English Units","slug":"converting-metric-units-to-english-units","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158567"}},{"articleId":158554,"title":"Following the Order of Operations","slug":"following-the-order-of-operations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158554"}},{"articleId":158569,"title":"Inverse Operations and Commutative, Associative, and Distributive Properties","slug":"inverse-operations-and-commutative-associative-and-distributive-properties","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158569"}},{"articleId":158560,"title":"A Guide to Working with Exponents, Radicals, and Absolute Value","slug":"a-guide-to-working-with-exponents-radicals-and-absolute-value","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158560"}},{"articleId":158557,"title":"A Quick Conversion Guide for Fractions, Decimals, and Percents","slug":"a-quick-conversion-guide-for-fractions-decimals-and-percents","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/158557"}}],"content":[{"title":"Converting metric units to English units","thumb":null,"image":null,"content":"<p>The English system of measurements is most commonly used in the United States. In contrast, the metric system is used throughout most of the rest of the world. Converting measurements between the English and metric systems is a common everyday reason to know math. This article gives you some precise metric-to-English conversions, as well as some easy-to-remember conversions that are good enough for most situations.</p>\n<table border=\"0\">\n<caption>Metric-to-English Conversion Table</caption>\n<tbody>\n<tr>\n<th>Metric-to-English Conversions</th>\n<th>Metric Units in Plain English</th>\n</tr>\n<tr>\n<td>1 meter ≈ 3.28 feet</td>\n<td>A meter is about 3 feet (1 yard).</td>\n</tr>\n<tr>\n<td>1 kilometer ≈ 0.62 miles</td>\n<td>A kilometer is about 1/2 mile.</td>\n</tr>\n<tr>\n<td>1 liter ≈ 0.26 gallons</td>\n<td>A liter is about 1 quart (1/4 gallon).</td>\n</tr>\n<tr>\n<td>1 kilogram ≈ 2.20 pounds</td>\n<td>A kilo is about 2 pounds.</td>\n</tr>\n<tr>\n<td>0°C = 32°F</td>\n<td>0°C is cold.</td>\n</tr>\n<tr>\n<td>10°C = 50°F</td>\n<td>10°C is cool.</td>\n</tr>\n<tr>\n<td>20°C = 68°F</td>\n<td>20°C is warm.</td>\n</tr>\n<tr>\n<td>30°C = 86°</td>\n<td>30°C is hot.</td>\n</tr>\n</tbody>\n</table>\n<p class=\"Tip\">Here&#8217;s an easy temperature conversion to remember: 16°C = 61°F.</p>\n"},{"title":"Following the order of operations","thumb":null,"image":null,"content":"<p>When arithmetic expressions get complex, use the order of operations (also called the <i>order of precedence)</i> to simplify them. Complex math problems require you to perform a combination of operations — addition, subtraction, multiplication, and division — to find the solution. The order of operations simply tells you what operations to do first, second, third, and so on.</p>\n<p>Evaluate arithmetic expressions from left to right, according to the following order of precedence:</p>\n<ol class=\"level-one\">\n<li>\n<p class=\"first-para\">Parentheses</p>\n</li>\n<li>\n<p class=\"first-para\">Exponents</p>\n</li>\n<li>\n<p class=\"first-para\">Multiplication and division</p>\n</li>\n<li>\n<p class=\"first-para\">Addition and subtraction</p>\n</li>\n</ol>\n<p class=\"Remember\">Following the order of operation is important; otherwise, you&#8217;ll end up with the wrong answer. Suppose you have the problem 9 + 5 × 7. If you follow the order of operations, you see that the answer is 44. If you ignore the order of operations and just work left to right, you get a completely different — and wrong — answer:</p>\n<blockquote><p>9 + 5 × 7 = 9 + 35 = 44    RIGHT</p></blockquote>\n<blockquote><p>9 + 5 × 7 = 14 × 7 = 98     WRONG!</p></blockquote>\n"},{"title":"Inverse operations and commutative, associative, and distributive properties","thumb":null,"image":null,"content":"<p>The Big Four math operations — addition, subtraction, multiplication, and division — let you combine numbers and perform calculations. Certain operations possess properties that enable you to manipulate the numbers in the problem, which comes in handy, especially when you get into higher math like algebra. The important properties you need to know are the commutative property, the associative property, and the distributive property. Understanding what an inverse operation is is also helpful.</p>\n<h2>Inverse operations</h2>\n<p><i>Inverse operations</i> are pairs of operations that you can work &#8220;backward&#8221; to cancel each other out. Two pairs of the Big Four operations — addition, subtraction, multiplication, and division —are inverses of each other:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>Addition and subtraction are inverse operations of each other.</b> When you start with any value, then add a number to it and subtract the same number from the result, the value you started with remains unchanged. For example:</p>\n<blockquote><p>2 + 3 = 5    so    5 – 3 = 2</p></blockquote>\n<blockquote><p>7 – 1 = 6    so    6 + 1 = 7</p></blockquote>\n</li>\n<li>\n<p class=\"first-para\"><b>Multiplication and division are inverse operations of each other. </b>When you start with any value, then multiply it by a number and divide the result by the same number (except zero), the value you started with remains unchanged. For example:</p>\n<blockquote><p>3 × 4 = 12    so    12 ÷ 4 = 3</p></blockquote>\n<blockquote><p>10 ÷ 2 = 5    so    5 × 2 = 10</p></blockquote>\n</li>\n</ul>\n<h2>The commutative property</h2>\n<p>An operation is <i>commutative</i> when you apply it to a pair of numbers either forwards or backwards and expect the same result. The two Big Four that are commutative are addition and subtraction.</p>\n<p>Addition is commutative because, for example, 3 + 5 is the same as 5 + 3. In other words</p>\n<blockquote><p>3 + 5 = 5 + 3</p></blockquote>\n<p>Multiplication is <i>commutative</i> because 2 × 7 is the same as 7 × 2. In other words</p>\n<blockquote><p>2 × 7 = 7 × 2</p></blockquote>\n<h2>The associative property</h2>\n<p>An operation is <i>associative</i> when you can apply it, using parentheses, in different groupings of numbers and still expect the same result. The two Big Four operations that are associative are addition and multiplication.</p>\n<p>Addition is associative because, for example, the problem (2 + 4) + 7 produces the same result as does the problem 2 + (4 + 7). In other words,</p>\n<blockquote><p>(2 + 4) + 7 = 2 + (4 + 7)</p></blockquote>\n<p>No matter which pair of numbers you add together first, the answer is the same: 13.</p>\n<p>Multiplication is associative because, for example, the problem 3 × (4 × 5) produces the same result as the problem (3 × 4) × 5. In other words,</p>\n<blockquote><p>3 × (4 × 5) = (3 × 4) × 5</p></blockquote>\n<p>Again, no matter which pair of numbers you multiply first, both problems yield the same answer: 60.</p>\n<h2>The distributive property</h2>\n<p>The <i>distributive property</i> connects the operations of multiplication and addition. When multiplication is described as &#8220;distributive over addition,&#8221; you can split a multiplication problem into two smaller problems and then add the results.</p>\n<p>For example, suppose you want to multiply 27 × 6. You know that 27 equals 20 + 7, so you can do this multiplication in two steps:</p>\n<ol class=\"level-one\">\n<li>\n<p class=\"first-para\">First multiply 20 × 6; then multiply 7 × 6.</p>\n<p class=\"child-para\">20 × 6 = 1207 × 6 = 42</p>\n</li>\n<li>\n<p class=\"first-para\">Then add the results.</p>\n<p class=\"child-para\">120 + 42 = 162</p>\n</li>\n</ol>\n<p>Therefore, 27 × 6 = 162.</p>\n"},{"title":"A guide to working with exponents, radicals, and absolute value","thumb":null,"image":null,"content":"<p>Exponents, radicals, and absolute value are mathematical operations that go beyond addition, subtraction, multiplication, and division. They are useful in more advanced math, such as algebra, but they also have real-world applications, especially in geometry and measurement.</p>\n<p><i>Exponents </i>(powers) are repeated multiplication: When you raise a number to the power of an exponent, you multiply that number by itself the number of times indicated by the exponent. For example:</p>\n<blockquote><p>7<sup>2</sup> = 7 × 7 = 49</p></blockquote>\n<blockquote><p>2<sup>5</sup> = 2 × 2 × 2 × 2 × 2 = 32</p></blockquote>\n<p><i>Square roots </i>(radicals) are the inverse of exponent 2 — that is, the number that, when multiplied by itself, gives you the indicated value.</p>\n<p><i>Absolute value </i>is the positive value of a number — that is, the value of a negative number when you drop the minus sign. For example:</p>\n<p>Absolute value is used to describe numbers that are always positive, such as the distance between two points or the area inside a polygon.</p>\n"},{"title":"A quick conversion guide for fractions, decimals, and percents","thumb":null,"image":null,"content":"<p>Fractions, decimals, and percents are the three most common ways to give a mathematical description of parts of a whole object. <i>Fractions </i>are common in baking and carpentry when you&#8217;re using English measurement units (such as cups, gallons, feet, and inches). <i>Decimals </i>are used with dollars and cents, the metric system, and in scientific notation. <i>Percents </i>are used in business when figuring profit and interest rates, as well as in statistics.</p>\n<p>Use the following table as a handy guide when you need to make basic conversions among the three.</p>\n<table>\n<tbody>\n<tr>\n<th>Fraction</th>\n<th>Decimal</th>\n<th>Percent</th>\n</tr>\n<tr>\n<td>1/100</td>\n<td>0.01</td>\n<td>1%</td>\n</tr>\n<tr>\n<td>1/20</td>\n<td>0.05</td>\n<td>5%</td>\n</tr>\n<tr>\n<td>1/10</td>\n<td>0.1</td>\n<td>10%</td>\n</tr>\n<tr>\n<td>1/5</td>\n<td>0.2</td>\n<td>20%</td>\n</tr>\n<tr>\n<td>1/4</td>\n<td>0.25</td>\n<td>25%</td>\n</tr>\n<tr>\n<td>3/10</td>\n<td>0.3</td>\n<td>30%</td>\n</tr>\n<tr>\n<td>2/5</td>\n<td>0.4</td>\n<td>40%</td>\n</tr>\n<tr>\n<td>1/2</td>\n<td>0.5</td>\n<td>50%</td>\n</tr>\n<tr>\n<td>3/5</td>\n<td>0.6</td>\n<td>60%</td>\n</tr>\n<tr>\n<td>7/10</td>\n<td>0.7</td>\n<td>70%</td>\n</tr>\n<tr>\n<td>3/4</td>\n<td>0.75</td>\n<td>75%</td>\n</tr>\n<tr>\n<td>4/5</td>\n<td>0.8</td>\n<td>80%</td>\n</tr>\n<tr>\n<td>9/10</td>\n<td>0.9</td>\n<td>90%</td>\n</tr>\n<tr>\n<td>1</td>\n<td>1.0</td>\n<td>100%</td>\n</tr>\n<tr>\n<td>2</td>\n<td>2.0</td>\n<td>200%</td>\n</tr>\n<tr>\n<td>10</td>\n<td>10.0</td>\n<td>1,000%</td>\n</tr>\n</tbody>\n</table>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2022-02-22T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":207780},{"headers":{"creationTime":"2016-03-26T10:59:26+00:00","modifiedTime":"2022-09-27T17:18:50+00:00","timestamp":"2022-09-27T18:01:02+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"How to Divide Decimals","strippedTitle":"how to divide decimals","slug":"how-to-divide-decimals","canonicalUrl":"","seo":{"metaDescription":"Use this quick guide on dividing decimals to get ahead in your math class and take your next test with confidence.","noIndex":0,"noFollow":0},"content":"Dividing decimals is similar to dividing whole numbers, except you have to handle the decimal point before you start dividing. Here’s how to divide decimals step by step:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Move the decimal point in the divisor and dividend.</p>\r\n<p class=\"child-para\">Turn the <i>divisor</i> (the number you’re dividing by) into a whole number by moving the decimal point all the way to the right. At the same time, move the decimal point in the <i>dividend</i> (the number you’re dividing) the same number of places to the right.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Place a decimal point in the <i>quotient</i> (the answer) directly above where the decimal point now appears in the dividend.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Divide as usual, being careful to line up the quotient properly so that the decimal point falls into place.</p>\r\n<p class=\"child-para\">Line up each digit in the quotient just over the last digit in the dividend used in that cycle.</p>\r\n</li>\r\n</ol>\r\n<p class=\"Remember\">As with whole-number division, sometimes decimal division doesn’t work out evenly at the end. With decimals, however, you never write a remainder. Instead, attach enough trailing zeros to round the quotient to a certain number of decimal places. The digit to the right of the digit you’re rounding to tells you whether to round up or down, so you always have to figure out the division to one extra place.</p>\r\nSee the following chart:\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>To Round a Decimal to</th>\r\n<th>Fill Out the Dividend with Trailing Zeros to</th>\r\n</tr>\r\n<tr>\r\n<td>A whole number</td>\r\n<td>One decimal place</td>\r\n</tr>\r\n<tr>\r\n<td>One decimal place</td>\r\n<td>Two decimal places</td>\r\n</tr>\r\n<tr>\r\n<td>Two decimal places</td>\r\n<td>Three decimal places</td>\r\n</tr>\r\n</tbody>\r\n</table>\r\n<h2 id=\"tab1\" >Sample questions</h2>\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Divide the following: 9.152 / 0.8 = ?</p>\r\n<p class=\"child-para\"><b>11.44</b>. To start out, write the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438411.image0.jpg\" alt=\"image0.jpg\" width=\"106\" height=\"35\" />\r\n<p class=\"child-para\">Turn 0.8 into the whole number 8 by moving the decimal point one place to the right. At the same time, move the decimal point in 9.1526 one place to the right. Put your decimal point in the quotient directly above where it falls in 91.25:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438412.image1.jpg\" alt=\"image1.jpg\" width=\"94\" height=\"48\" />\r\n<p class=\"child-para\">Now you’re ready to divide. Just be careful to line up the quotient properly so that the decimal point falls into place.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438413.image2.jpg\" alt=\"image2.jpg\" width=\"97\" height=\"367\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">Divide the following: 21.9 / 0.015 = ?</p>\r\n<p class=\"child-para\"><b>1,460.</b> Set up the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438414.image3.jpg\" alt=\"image3.jpg\" width=\"146\" height=\"35\" />\r\n<p class=\"child-para\">Notice that two trailing zeros are attached to the dividend because you need to move the decimal points in each number three places to the right. Again, place the decimal point in the quotient directly above where it now appears in the dividend, 21900:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438415.image4.jpg\" alt=\"image4.jpg\" width=\"115\" height=\"35\" />\r\n<p class=\"child-para\">Now you’re ready to divide. Line up the quotient carefully so the decimal point falls into place:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438416.image5.jpg\" alt=\"image5.jpg\" width=\"115\" height=\"253\" />\r\n<p class=\"child-para\">Even though the division comes out even after you write the digit 6 in the quotient, you still need to add a placeholding zero so that the decimal point appears in the correct place.</p>\r\n</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Practice questions</h2>\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Divide these two decimals: 9.345 / 0.05 = ?</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Solve the following division: 3.15 / 0.021 = ?</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Perform the following decimal division, rounding to one decimal place: 6.7 / 10.1.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Find the solution, rounding to the nearest hundredth: 9.13 <b>/</b> 4.25.</p>\r\n</li>\r\n</ol>\r\nFollowing are answers to the practice questions:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">9.345 / 0.05 = 186.9. To start out, write the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438417.image6.jpg\" alt=\"image6.jpg\" width=\"119\" height=\"35\" />\r\n<p class=\"child-para\">Turn the divisor (0.05) into a whole number by moving the decimal point two places to the right. At the same time, move the decimal point in the dividend (9.345) two places to the right. Place the decimal point in the quotient directly above where it now appears in the dividend:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438418.image7.jpg\" alt=\"image7.jpg\" width=\"94\" height=\"43\" />\r\n<p class=\"child-para\">Now you’re ready to divide. Be careful to line up the quotient properly so that the decimal point falls into place.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438419.image8.jpg\" alt=\"image8.jpg\" width=\"91\" height=\"389\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">3.15 / 0.021 = 150. Write the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438420.image9.jpg\" alt=\"image9.jpg\" width=\"118\" height=\"35\" />\r\n<p class=\"child-para\">You need to move the decimal point in the divisor (0.021) three places to the right, so attach an additional trailing zero to the dividend (3.15) to extend it to three decimal places:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438421.image10.jpg\" alt=\"image10.jpg\" width=\"131\" height=\"35\" />\r\n<p class=\"child-para\">Now you can move both decimal points three places to the right. Place the decimal point in the quotient above the decimal point in the dividend:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438422.image11.jpg\" alt=\"image11.jpg\" width=\"107\" height=\"43\" />\r\n<p class=\"child-para\">Divide, being careful to line up the quotient properly:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438423.image12.jpg\" alt=\"image12.jpg\" width=\"96\" height=\"220\" />\r\n<p class=\"child-para\">Remember to insert a placeholding zero in the quotient so that the decimal point ends up in the correct place.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">6.7 / 10.1 = 0.7. To start out, write the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438424.image13.jpg\" alt=\"image13.jpg\" width=\"88\" height=\"35\" />\r\n<p class=\"child-para\">Turn the divisor (10.1) into a whole number by moving the decimal point one place to the right. At the same time, move the decimal point in the dividend (6.7) one place to the right:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438425.image14.jpg\" alt=\"image14.jpg\" width=\"91\" height=\"43\" />\r\n<p class=\"child-para\">The problem asks you to round the quotient to one decimal place, so fill out the dividend with trailing zeros to two decimal places:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438426.image15.jpg\" alt=\"image15.jpg\" width=\"119\" height=\"43\" />\r\n<p class=\"child-para\">Now you’re ready to divide:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438427.image16.jpg\" alt=\"image16.jpg\" width=\"116\" height=\"209\" />\r\n<p class=\"child-para\">Round the quotient to one decimal place:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438428.image17.jpg\" alt=\"image17.jpg\" width=\"118\" height=\"25\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">9.13 / 4.25 = 2.15. First, write the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438429.image18.jpg\" alt=\"image18.jpg\" width=\"106\" height=\"35\" />\r\n<p class=\"child-para\">Turn the divisor (4.25) into a whole number by moving the decimal point two places to the right. At the same time, move the decimal point in the dividend (9.13) two places to the right:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438430.image19.jpg\" alt=\"image19.jpg\" width=\"101\" height=\"43\" />\r\n<p class=\"child-para\">The problem asks you to round the quotient to the nearest hundredth, so fill out the dividend with trailing zeros to three decimal places:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438431.image20.jpg\" alt=\"image20.jpg\" width=\"148\" height=\"40\" />\r\n<p class=\"child-para\">Now divide, carefully lining up the quotient:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438432.image21.jpg\" alt=\"image21.jpg\" width=\"154\" height=\"389\" />\r\n<p class=\"child-para\">Round the quotient to the nearest hundredth:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438433.image22.jpg\" alt=\"image22.jpg\" width=\"145\" height=\"26\" /></li>\r\n</ol>","description":"Dividing decimals is similar to dividing whole numbers, except you have to handle the decimal point before you start dividing. Here’s how to divide decimals step by step:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Move the decimal point in the divisor and dividend.</p>\r\n<p class=\"child-para\">Turn the <i>divisor</i> (the number you’re dividing by) into a whole number by moving the decimal point all the way to the right. At the same time, move the decimal point in the <i>dividend</i> (the number you’re dividing) the same number of places to the right.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Place a decimal point in the <i>quotient</i> (the answer) directly above where the decimal point now appears in the dividend.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Divide as usual, being careful to line up the quotient properly so that the decimal point falls into place.</p>\r\n<p class=\"child-para\">Line up each digit in the quotient just over the last digit in the dividend used in that cycle.</p>\r\n</li>\r\n</ol>\r\n<p class=\"Remember\">As with whole-number division, sometimes decimal division doesn’t work out evenly at the end. With decimals, however, you never write a remainder. Instead, attach enough trailing zeros to round the quotient to a certain number of decimal places. The digit to the right of the digit you’re rounding to tells you whether to round up or down, so you always have to figure out the division to one extra place.</p>\r\nSee the following chart:\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>To Round a Decimal to</th>\r\n<th>Fill Out the Dividend with Trailing Zeros to</th>\r\n</tr>\r\n<tr>\r\n<td>A whole number</td>\r\n<td>One decimal place</td>\r\n</tr>\r\n<tr>\r\n<td>One decimal place</td>\r\n<td>Two decimal places</td>\r\n</tr>\r\n<tr>\r\n<td>Two decimal places</td>\r\n<td>Three decimal places</td>\r\n</tr>\r\n</tbody>\r\n</table>\r\n<h2 id=\"tab1\" >Sample questions</h2>\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Divide the following: 9.152 / 0.8 = ?</p>\r\n<p class=\"child-para\"><b>11.44</b>. To start out, write the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438411.image0.jpg\" alt=\"image0.jpg\" width=\"106\" height=\"35\" />\r\n<p class=\"child-para\">Turn 0.8 into the whole number 8 by moving the decimal point one place to the right. At the same time, move the decimal point in 9.1526 one place to the right. Put your decimal point in the quotient directly above where it falls in 91.25:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438412.image1.jpg\" alt=\"image1.jpg\" width=\"94\" height=\"48\" />\r\n<p class=\"child-para\">Now you’re ready to divide. Just be careful to line up the quotient properly so that the decimal point falls into place.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438413.image2.jpg\" alt=\"image2.jpg\" width=\"97\" height=\"367\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">Divide the following: 21.9 / 0.015 = ?</p>\r\n<p class=\"child-para\"><b>1,460.</b> Set up the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438414.image3.jpg\" alt=\"image3.jpg\" width=\"146\" height=\"35\" />\r\n<p class=\"child-para\">Notice that two trailing zeros are attached to the dividend because you need to move the decimal points in each number three places to the right. Again, place the decimal point in the quotient directly above where it now appears in the dividend, 21900:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438415.image4.jpg\" alt=\"image4.jpg\" width=\"115\" height=\"35\" />\r\n<p class=\"child-para\">Now you’re ready to divide. Line up the quotient carefully so the decimal point falls into place:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438416.image5.jpg\" alt=\"image5.jpg\" width=\"115\" height=\"253\" />\r\n<p class=\"child-para\">Even though the division comes out even after you write the digit 6 in the quotient, you still need to add a placeholding zero so that the decimal point appears in the correct place.</p>\r\n</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Practice questions</h2>\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Divide these two decimals: 9.345 / 0.05 = ?</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Solve the following division: 3.15 / 0.021 = ?</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Perform the following decimal division, rounding to one decimal place: 6.7 / 10.1.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Find the solution, rounding to the nearest hundredth: 9.13 <b>/</b> 4.25.</p>\r\n</li>\r\n</ol>\r\nFollowing are answers to the practice questions:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">9.345 / 0.05 = 186.9. To start out, write the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438417.image6.jpg\" alt=\"image6.jpg\" width=\"119\" height=\"35\" />\r\n<p class=\"child-para\">Turn the divisor (0.05) into a whole number by moving the decimal point two places to the right. At the same time, move the decimal point in the dividend (9.345) two places to the right. Place the decimal point in the quotient directly above where it now appears in the dividend:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438418.image7.jpg\" alt=\"image7.jpg\" width=\"94\" height=\"43\" />\r\n<p class=\"child-para\">Now you’re ready to divide. Be careful to line up the quotient properly so that the decimal point falls into place.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438419.image8.jpg\" alt=\"image8.jpg\" width=\"91\" height=\"389\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">3.15 / 0.021 = 150. Write the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438420.image9.jpg\" alt=\"image9.jpg\" width=\"118\" height=\"35\" />\r\n<p class=\"child-para\">You need to move the decimal point in the divisor (0.021) three places to the right, so attach an additional trailing zero to the dividend (3.15) to extend it to three decimal places:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438421.image10.jpg\" alt=\"image10.jpg\" width=\"131\" height=\"35\" />\r\n<p class=\"child-para\">Now you can move both decimal points three places to the right. Place the decimal point in the quotient above the decimal point in the dividend:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438422.image11.jpg\" alt=\"image11.jpg\" width=\"107\" height=\"43\" />\r\n<p class=\"child-para\">Divide, being careful to line up the quotient properly:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438423.image12.jpg\" alt=\"image12.jpg\" width=\"96\" height=\"220\" />\r\n<p class=\"child-para\">Remember to insert a placeholding zero in the quotient so that the decimal point ends up in the correct place.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">6.7 / 10.1 = 0.7. To start out, write the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438424.image13.jpg\" alt=\"image13.jpg\" width=\"88\" height=\"35\" />\r\n<p class=\"child-para\">Turn the divisor (10.1) into a whole number by moving the decimal point one place to the right. At the same time, move the decimal point in the dividend (6.7) one place to the right:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438425.image14.jpg\" alt=\"image14.jpg\" width=\"91\" height=\"43\" />\r\n<p class=\"child-para\">The problem asks you to round the quotient to one decimal place, so fill out the dividend with trailing zeros to two decimal places:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438426.image15.jpg\" alt=\"image15.jpg\" width=\"119\" height=\"43\" />\r\n<p class=\"child-para\">Now you’re ready to divide:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438427.image16.jpg\" alt=\"image16.jpg\" width=\"116\" height=\"209\" />\r\n<p class=\"child-para\">Round the quotient to one decimal place:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438428.image17.jpg\" alt=\"image17.jpg\" width=\"118\" height=\"25\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">9.13 / 4.25 = 2.15. First, write the problem as usual:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438429.image18.jpg\" alt=\"image18.jpg\" width=\"106\" height=\"35\" />\r\n<p class=\"child-para\">Turn the divisor (4.25) into a whole number by moving the decimal point two places to the right. At the same time, move the decimal point in the dividend (9.13) two places to the right:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438430.image19.jpg\" alt=\"image19.jpg\" width=\"101\" height=\"43\" />\r\n<p class=\"child-para\">The problem asks you to round the quotient to the nearest hundredth, so fill out the dividend with trailing zeros to three decimal places:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438431.image20.jpg\" alt=\"image20.jpg\" width=\"148\" height=\"40\" />\r\n<p class=\"child-para\">Now divide, carefully lining up the quotient:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438432.image21.jpg\" alt=\"image21.jpg\" width=\"154\" height=\"389\" />\r\n<p class=\"child-para\">Round the quotient to the nearest hundredth:</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/438433.image22.jpg\" alt=\"image22.jpg\" width=\"145\" height=\"26\" /></li>\r\n</ol>","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is an instructor and math and test prep tutor in New Jersey. He is the author of <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, ACT Math For Dummies, Logic For Dummies,</i> and <i>Calculus II For Dummies</i>. In his spare time, he enjoys traveling and learning foreign languages.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Sample questions","target":"#tab1"},{"label":"Practice questions","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using 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Math & Pre-Algebra Workbook For Dummies with Online Practice","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"9399\">Mark Zegarelli</b> is a math and test prep teacher who has written a wide variety of basic math and pre-algebra books in the <i>For Dummies</i> series. </p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is an instructor and math and test prep tutor in New Jersey. He is the author of <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, ACT Math For Dummies, Logic For Dummies,</i> and <i>Calculus II For Dummies</i>. In his spare time, he enjoys traveling and learning foreign languages.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119357513&quot;]}]\" id=\"du-slot-63333a5e8a12b\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119357513&quot;]}]\" id=\"du-slot-63333a5e8b65a\"></div></div>"},"articleType":{"articleType":"Articles","articleList":null,"content":null,"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2021-07-24T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":149586},{"headers":{"creationTime":"2022-03-17T18:13:41+00:00","modifiedTime":"2022-05-04T19:00:18+00:00","timestamp":"2022-09-14T18:19:42+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","strippedTitle":"teaching your kids new math (k-5) for dummies cheat sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"When you're helping your K-5 child learn math skills, this Cheat Sheet can provide some handy reminders for various problem types.","noIndex":0,"noFollow":0},"content":"When you’re working with your K–5 child to practice math skills, it can help to have a tool to remind you of some of the basics related to addition, subtraction, multiplication, division, and fractions. For those times, this Cheat Sheet can come in handy.","description":"When you’re working with your K–5 child to practice math skills, it can help to have a tool to remind you of some of the basics related to addition, subtraction, multiplication, division, and fractions. For those times, this Cheat Sheet can come in handy.","blurb":"","authors":[],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":34197,"title":"Parenting","slug":"parenting","_links":{"self":"https://dummies-api.dummies.com/v2/categories/34197"}},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[],"fromCategory":[{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/253710"}},{"articleId":249996,"title":"Pre-Algebra Practice Questions: Solving Simple Algebraic Equations","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra Practice Questions: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249986"}},{"articleId":249980,"title":"Pre-Algebra Practice Questions: Rearranging Equations to Isolate x","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249980"}},{"articleId":249971,"title":"Pre-Algebra Practice Questions: Cross-Multiply to Solve Equations","slug":"pre-algebra-practice-questions-cross-multiply-solve-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249971"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":291192,"slug":"teaching-your-kids-new-math-k-5-for-dummies","isbn":"9781119867098","categoryList":["academics-the-arts","teaching","homeschooling"],"amazon":{"default":"https://www.amazon.com/gp/product/1119867096/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119867096/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119867096-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119867096/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119867096/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/9781119867098-203x255.jpg","width":203,"height":255},"title":"Teaching Your Kids New Math, K-5 For Dummies","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"<p><b>Dr. <b data-author-id=\"34734\">Kris Jamsa</b></b> is the author of 115 books on computing and education. He holds eight college degrees, which include a PhD in Computer Science, a PhD in Education, and a Masters in Education with a focus on multiple intelligences. Jamsa was the founder of the Head of the Class series, an e-learning portal for kindergarten through fifth grade.</p>","authors":[{"authorId":34734,"name":"Kris Jamsa","slug":"kris-jamsa","description":" <p><b>Dr. Kris Jamsa</b> is the author of 115 books on computing and education. He holds eight college degrees, which include a PhD in Computer Science, a PhD in Education, and a Masters in Education with a focus on multiple intelligences. Jamsa was the founder of the Head of the Class series, an e-learning portal for kindergarten through fifth grade.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/34734"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[{"title":"Be a Rad Dad","slug":"be-the-best-dad","collectionId":293237}],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119867098&quot;]}]\" id=\"du-slot-63221b3ed0cc6\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119867098&quot;]}]\" id=\"du-slot-63221b3ed1703\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":0,"title":"","slug":null,"categoryList":[],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/"}}],"content":[{"title":"Addition and subtraction","thumb":null,"image":null,"content":"<p>Practice daily with your addition and subtraction flash cards until your child can successfully complete timed addition or subtraction tests, which you can find online.</p>\n<h3>Using a number line</h3>\n<p>For children just learning addition, both of small and large numbers, a visual aid, such as a number line, can be helpful. Your child should know that numbers on the number line increase from left to right. For younger grade levels, the number line will normally start at 0 or 1 and have an ending number at the far right.</p>\n<p>Using a number line is similar to counting. For addition, you have a starting location and then you move right as you add a number. Again, for lower grades, you will typically move right one number at a time. For subtraction, you move left along the number line</p>\n<p>For higher grades, however, the number line may not have starting and ending numbers. Instead, as your child performs addition or subtraction, they indicate a starting number to which they then add or subtract another number. In addition, depending on the numbers they are adding or subtracting, your child may move right or left by units of 100, 10, and finally 1.</p>\n<p>The following figure illustrates using the number line for addition.</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291579\" src=\"https://www.dummies.com/wp-content/uploads/9781119867098-cs0101.jpg\" alt=\"example of using a number line to learn addition\" width=\"535\" height=\"265\" /></p>\n<p>The following illustrates the use of a number line for subtraction of small and large numbers.</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291580\" src=\"https://www.dummies.com/wp-content/uploads/9781119867098-cs0102.jpg\" alt=\"example of using a number line to learn subtraction\" width=\"535\" height=\"320\" /></p>\n<h3>Adding with regrouping (carrying)</h3>\n<p>Some time ago, students learned to add numbers using regrouping — a fancy term to describe carrying for addition and borrowing for subtraction. As your child begins to add numbers that require regrouping, you should draw a small box above the tens (or hundreds) digits into which your child will write the number they are carrying. The box will help your child better visualize the process of carrying a ten and will help them align the numbers they must add, as shown here:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291601\" src=\"https://www.dummies.com/wp-content/uploads/Adding-with-regrouping.jpg\" alt=\"equation showing adding with regrouping\" width=\"124\" height=\"244\" /></p>\n<h3>Adding with decomposition</h3>\n<p>A common new-math addition technique is to decompose large numbers into their hundreds, tens, and ones components and then separately add each. The following example illustrates how to use decomposition when adding large numbers:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291602\" src=\"https://www.dummies.com/wp-content/uploads/Adding-with-decomposition.jpg\" alt=\"equation showing adding with decomposition\" width=\"496\" height=\"196\" /></p>\n<h3>Subtracting with regrouping (borrowing)</h3>\n<p>Use a box to help your child with borrowing:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291603\" src=\"https://www.dummies.com/wp-content/uploads/Subtracting-with-regrouping.jpg\" alt=\"equation showing subtracting with regrouping\" width=\"137\" height=\"245\" /></p>\n<h3>Checking results</h3>\n<p>When we use math, it’s like that we’ll eventually make a mistake. Fortunately, we can often detect mistakes if we take time to double-check our work.</p>\n<p>One way to check work is by performing the complementary operation. For example, if your child is solving an addition problem, they can check their work using subtraction, as shown here:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291604\" src=\"https://www.dummies.com/wp-content/uploads/Checking-results.jpg\" alt=\"math problem showing how to check results\" width=\"281\" height=\"161\" /></p>\n<p>If your child is working on a subtraction problem, they can check their work using addition, like so:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291605\" src=\"https://www.dummies.com/wp-content/uploads/Checking-results-subtraction.jpg\" alt=\"checking results with subtraction\" width=\"287\" height=\"164\" /></p>\n"},{"title":"Multiplication and division","thumb":null,"image":null,"content":"<p>Practice daily with your multiplication and division flash cards until your child can successfully complete a timed multiplication or division test, which you can find online.</p>\n<h3>Doing old school multiplication</h3>\n<p>To increase your child’s understanding and skills, have them practice multiplication problems using the old school approach, as shown here:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291606\" src=\"https://www.dummies.com/wp-content/uploads/Old-school-multipl.jpg\" alt=\"old school multiplication\" width=\"103\" height=\"259\" /></p>\n<h3>Doing Box Method multiplication</h3>\n<p>Another way to solve multiplication problems is with the Box Method, as shown in this example:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291607\" src=\"https://www.dummies.com/wp-content/uploads/Box-method-multipli.jpg\" alt=\"box method multiplication\" width=\"254\" height=\"565\" /></p>\n<h3>Long division example</h3>\n<p>Division problems with larger numbers require long division, as shown here:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291608\" src=\"https://www.dummies.com/wp-content/uploads/Long-division-example.jpg\" alt=\"long division\" width=\"175\" height=\"347\" /></p>\n<h3>Checking results</h3>\n<p>Although this method is not often used, your child can check their work on a multiplication problem by using division, as in this example:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291609\" src=\"https://www.dummies.com/wp-content/uploads/Checking-results-using-division.jpg\" alt=\"check results using division\" width=\"410\" height=\"350\" /></p>\n<p>They can check work on a division problem, by using multiplication, like so:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291610\" src=\"https://www.dummies.com/wp-content/uploads/Checking-results-using-multipli.jpg\" alt=\"check results using multiplication\" width=\"308\" height=\"365\" /></p>\n<p>&nbsp;</p>\n"},{"title":"Fractions","thumb":null,"image":null,"content":"<p>Use the following examples as quick reminders for common fraction operations.</p>\n<h3>Adding like fractions</h3>\n<p>When adding like fractions (fractions in which the denominator, or bottom number, is the same), add the numerators (the top number). The denominator does not change, as shown here:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291611\" src=\"https://www.dummies.com/wp-content/uploads/Adding-fractions.jpg\" alt=\"adding like fractions\" width=\"190\" height=\"109\" /></p>\n<h3>Adding unlike fractions</h3>\n<p>When two fractions are unlike — the denominators are different — adding them is a slightly more involved process. Here are the steps for the following expression:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291612\" src=\"https://www.dummies.com/wp-content/uploads/Adding-unlike-fractions.jpg\" alt=\"adding unlike fractions\" width=\"184\" height=\"131\" /></p>\n<ol>\n<li><strong> Identify the common denominator by multiplying each fraction’s numerator and denominator by the denominator of the second fraction.</strong></li>\n</ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291613\" src=\"https://www.dummies.com/wp-content/uploads/Identify-common-denominator.jpg\" alt=\"identify common denominator\" width=\"433\" height=\"125\" /></p>\n<ol start=\"2\">\n<li><strong> Add the numerator (top number). The denominator does not change.</strong></li>\n</ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291614\" src=\"https://www.dummies.com/wp-content/uploads/Add-the-numerator.jpg\" alt=\"add the numerator\" width=\"203\" height=\"119\" /></p>\n<h3>Subtracting like fractions</h3>\n<p>When subtracting like fractions (fractions in which the denominator, or bottom number, is the same), subtract the numerators (the top number). The denominator does not change, as shown here:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291615\" src=\"https://www.dummies.com/wp-content/uploads/Subtracting-like-fractions.jpg\" alt=\"subtracting like fractions\" width=\"199\" height=\"127\" /></p>\n<h3>Subtracting unlike Fractions</h3>\n<p>When two fractions are unlike, you have to make the denominators the same before you can subtract the fractions:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291617\" src=\"https://www.dummies.com/wp-content/uploads/Subtracting-unlike-fractions.jpg\" alt=\"subtracting unlike fractions\" width=\"167\" height=\"131\" /></p>\n<ol>\n<li><strong> Identify the common denominator by multiplying each fraction’s numerator and denominator by the denominator of the second fraction.</strong></li>\n</ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291618\" src=\"https://www.dummies.com/wp-content/uploads/ID-common-denominator-in-subbing-unlike-fractions.jpg\" alt=\"identify common denominator in subtracting fractions\" width=\"418\" height=\"128\" /></p>\n<ol start=\"2\">\n<li><strong> Subtract the numerator (top number). The denominator does not change.</strong></li>\n</ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291619\" src=\"https://www.dummies.com/wp-content/uploads/Subtract-numerator-with-unlike-fractions.jpg\" alt=\"subtract numerator in subtracting unlike fractions\" width=\"196\" height=\"128\" /></p>\n<h3>Multiplying fractions</h3>\n<p>When you multiply two fractions, you simply multiply the two numerators (top numbers) and also multiply the two denominators (bottom numbers), as shown here:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291620\" src=\"https://www.dummies.com/wp-content/uploads/Multiplying-fractions.jpg\" alt=\"multiplying fractions\" width=\"217\" height=\"131\" /></p>\n<h3>Dividing fractions</h3>\n<p>To divide fractions, flip the second fraction (to create its reciprocal) and then multiply:</p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-291621\" src=\"https://www.dummies.com/wp-content/uploads/Dividing-fractions.jpg\" alt=\"dividing fractions\" width=\"223\" height=\"259\" /></p>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Solve","lifeExpectancy":"One year","lifeExpectancySetFrom":"2022-03-17T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":291491},{"headers":{"creationTime":"2016-03-27T16:49:34+00:00","modifiedTime":"2022-04-27T18:24:06+00:00","timestamp":"2022-09-14T18:19:41+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Basic Math and Pre-Algebra: 1001 Practice Problems For Dummies Cheat Sheet","strippedTitle":"basic math and pre-algebra: 1001 practice problems for dummies cheat sheet","slug":"1001-basic-math-pre-algebra-practice-problems-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"Keep this helpful refresher on fractions, decimals, and percents handy as you're honing your basic math skills.","noIndex":0,"noFollow":0},"content":"To successfully master basic math, you need to practice addition, subtraction, multiplication, and division problems. You also need to understand order of operations, fractions, decimals, percents, ratios, weights and measures, and even a little geometry.\r\n\r\nAfter you've become proficient in these and other basic math concepts, you can begin to tackle pre-algebra, which involves variables, expressions, and equations.","description":"To successfully master basic math, you need to practice addition, subtraction, multiplication, and division problems. You also need to understand order of operations, fractions, decimals, percents, ratios, weights and measures, and even a little geometry.\r\n\r\nAfter you've become proficient in these and other basic math concepts, you can begin to tackle pre-algebra, which involves variables, expressions, and equations.","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <b>Mark Zegarelli</b> is a professional writer with degrees in both English and Math from Rutgers University. He has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software documentation, and the occasional book or film review. Along the way, he&#8217;s also paid a few bills doing housecleaning, decorative painting, and (for ten hours) retail sales. He likes writing best, though.","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":33726,"title":"Pre-Algebra","slug":"pre-algebra","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33726"}},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":167535,"title":"Basic Math Tips: Percents","slug":"basic-math-tips-percents","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/167535"}},{"articleId":167536,"title":"Basic Math Tips: Fractions","slug":"basic-math-tips-fractions","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/167536"}},{"articleId":167521,"title":"Basic Math Tips: Decimals","slug":"basic-math-tips-decimals","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/167521"}}],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/253710"}},{"articleId":249996,"title":"Pre-Algebra Practice Questions: Solving Simple Algebraic Equations","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra Practice Questions: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249986"}},{"articleId":249980,"title":"Pre-Algebra Practice Questions: Rearranging Equations to Isolate x","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281915,"slug":"basic-math-and-pre-algebra-1001-practice-problems-for-dummies-free-online-practice","isbn":"9781119883500","categoryList":["academics-the-arts","math","basic-math"],"amazon":{"default":"https://www.amazon.com/gp/product/1119883504/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119883504/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119883504-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119883504/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119883504/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/9781119883500-204x255.jpg","width":204,"height":255},"title":"Basic Math & Pre-Algebra","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"<p><b><b data-author-id=\"9399\">Mark Zegarelli</b></b> is a professional writer with degrees in both English and Math from Rutgers University. He has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software documentation, and the occasional book or film review. Along the way, he&#8217;s also paid a few bills doing housecleaning, decorative painting, and (for ten hours) retail sales. He likes writing best, though.</p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <b>Mark Zegarelli</b> is a professional writer with degrees in both English and Math from Rutgers University. He has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software documentation, and the occasional book or film review. Along the way, he&#8217;s also paid a few bills doing housecleaning, decorative painting, and (for ten hours) retail sales. He likes writing best, though.","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119883500&quot;]}]\" id=\"du-slot-63221b3da179e\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119883500&quot;]}]\" id=\"du-slot-63221b3da2119\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":167536,"title":"Basic Math Tips: Fractions","slug":"basic-math-tips-fractions","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/167536"}},{"articleId":167521,"title":"Basic Math Tips: Decimals","slug":"basic-math-tips-decimals","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/167521"}},{"articleId":167535,"title":"Basic Math Tips: Percents","slug":"basic-math-tips-percents","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/167535"}}],"content":[{"title":"How to deal with fractions","thumb":null,"image":null,"content":"<p>Fractions are a common way of describing parts of a whole. They&#8217;re commonly used for English weights and measures, especially for small measurements in cooking and carpentry. If you want to be proficient in basic math, and if you want to prepare for pre-algebra, you need to know the ins and outs of fractions.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">Remember that the <i>numerator</i> of a fraction is the top number and the <i>denominator</i> is the bottom number.</p>\n</li>\n<li>\n<p class=\"first-para\">The <i>reciprocal </i>of a fraction is that fraction turned upside-down.</p>\n</li>\n<li>\n<p class=\"first-para\">To increase the terms of a fraction, multiply the numerator and denominator by the same number.</p>\n</li>\n<li>\n<p class=\"first-para\">To reduce the terms of a fraction to lowest terms, divide both the numerator and denominator by the greatest possible number.</p>\n</li>\n<li>\n<p class=\"first-para\">To simplify complex fractions, first simplify the numerator and denominator to two separate fractions; then change the problem to division.</p>\n</li>\n</ul>\n"},{"title":"Working with decimals","thumb":null,"image":null,"content":"<p>Decimals are commonly used for money, as well as for weights and measures, especially when using the metric system. As you practice basic math and pre-algebra problems, you&#8217;ll find that decimals are easier to work with than fractions.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">To change a decimal to a fraction, put the decimal in the numerator of a fraction with a denominator of 1. Then, continue to multiply both the numerator and denominator by 10 until the numerator is a whole number. If necessary, reduce the fraction.</p>\n</li>\n<li>\n<p class=\"first-para\">To change a fraction to a decimal, divide the numerator by the denominator until the division either terminates or repeats.</p>\n</li>\n<li>\n<p class=\"first-para\">To change a repeating decimal to a fraction, put the repeating portion of the decimal (without the decimal point) into the numerator of a fraction. Use as a denominator a number composed only of 9s with the same number of digits as the numerator. If necessary, reduce the fraction.</p>\n</li>\n<li>\n<p class=\"first-para\">To add or subtract decimals, line up the decimal points.</p>\n</li>\n<li>\n<p class=\"first-para\">To multiply decimals, begin by multiplying without worrying about the decimal points. When you&#8217;re done, count the number of digits to the right of the decimal point in each factor and add the result. Place the decimal point in your answer so that your answer has the same number of digits after the decimal point.</p>\n</li>\n<li>\n<p class=\"first-para\">To divide decimals, turn the <i>divisor</i> (the number you&#8217;re dividing by) into a whole number by moving the decimal point all the way to the right. At the same time, move the decimal point in the <i>dividend</i> (the number you&#8217;re dividing) the same number of places to the right. Then place a decimal point in the <i>quotient</i> (the answer) directly above where the decimal point now appears in the dividend.</p>\n</li>\n<li>\n<p class=\"first-para\">When dividing decimals, continue until the answer either terminates or repeats.</p>\n</li>\n</ul>\n"},{"title":"Figuring percents","thumb":null,"image":null,"content":"<p>Percents are commonly used in business to represent partial amounts of money. They&#8217;re also used in statistics to indicate a portion of a data set. As you practice basic math problems, you&#8217;ll discover that percents are closely related to decimals, which means that they&#8217;re easier to work with than fractions.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">To change a percent to a decimal, move the decimal point two places to the left and drop the percent sign.</p>\n</li>\n<li>\n<p class=\"first-para\">To change a decimal to a percent, move the decimal point two places to the right and attach a percent sign.</p>\n</li>\n<li>\n<p class=\"first-para\">To change a percent to a fraction, drop the percent sign and put the number of the percent in the numerator of a fraction with a denominator of 100. If necessary, reduce the fraction.</p>\n</li>\n<li>\n<p class=\"first-para\">To change a fraction to a percent, first change the fraction to a decimal by dividing. Then change the decimal to a percent by moving the decimal point two places to the right and attaching a percent sign.</p>\n</li>\n<li>\n<p class=\"first-para\">Calculate simple percents by dividing. For example, to find 50% of a number, divide by 2; to find 25%, divide by 4; to find 20%, divide by 5; and so forth.</p>\n</li>\n<li>\n<p class=\"first-para\">You can calculate some percents by reversing the numbers. For example 14% of 50 is the same as 50% of 14, which equals 7.</p>\n</li>\n</ul>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2022-01-28T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":207993},{"headers":{"creationTime":"2016-03-27T16:56:07+00:00","modifiedTime":"2022-04-27T15:33:42+00:00","timestamp":"2022-09-14T18:19:41+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Technical Math For Dummies Cheat Sheet","strippedTitle":"technical math for dummies cheat sheet","slug":"technical-math-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"Make everyday situations easier by grasping some technical math basics, like calculating a tip or converting to the metric system.","noIndex":0,"noFollow":0},"content":"Grasping some technical math basics can simplify everyday situations faced by many professionals and even non-professionals, including having to solve word problems, calculate tips, make change, or match American and metric measurements.","description":"Grasping some technical math basics can simplify everyday situations faced by many professionals and even non-professionals, including having to solve word problems, calculate tips, make change, or match American and metric measurements.","blurb":"","authors":[{"authorId":9795,"name":"Barry Schoenborn","slug":"barry-schoenborn","description":" <p><b>Barry Schoenborn</b>, a longtime math, science, and technical writer, is the coauthor of <i>Technical Math For Dummies, Medical Dosage Calculations For Dummies, </i>and<i> Physician Assistant Exam For Dummies.</i></p>","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9795"}},{"authorId":10348,"name":"Bradley Simkins","slug":"bradley-simkins","description":" <b>Dr. Richard W. Snyder</b>, DO is an osteopathic physician, board certified in both internal medicine and nephrology. He has authored and coauthored several articles in peer-reviewed journals. <p><b>Barry Schoenborn</b> is a longtime technical writer and is the coauthor of <i>Technical Math For Dummies</i>.</p>","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/10348"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":192334,"title":"Simple Steps for Solving Word Problems","slug":"simple-steps-for-solving-word-problems","categoryList":["business-careers-money","careers","trades-tech-engineering-careers"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192334"}},{"articleId":192335,"title":"Matching American and Metric Units of Measurement","slug":"matching-american-and-metric-units-of-measurement","categoryList":["business-careers-money","careers","trades-tech-engineering-careers"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192335"}},{"articleId":192330,"title":"Counting Change for Customers the Old-Fashioned Way","slug":"counting-change-for-customers-the-old-fashioned-way","categoryList":["business-careers-money","careers","trades-tech-engineering-careers"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192330"}},{"articleId":192318,"title":"Calculating a Standard 15-Percent Tip","slug":"calculating-a-standard-15-percent-tip","categoryList":["business-careers-money","careers","trades-tech-engineering-careers"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192318"}}],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/253710"}},{"articleId":249996,"title":"Pre-Algebra Practice Questions: Solving Simple Algebraic Equations","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra Practice Questions: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249986"}},{"articleId":249980,"title":"Pre-Algebra Practice Questions: Rearranging Equations to Isolate x","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282627,"slug":"technical-math-for-dummies","isbn":"9780470598740","categoryList":["business-careers-money","careers","trades-tech-engineering-careers"],"amazon":{"default":"https://www.amazon.com/gp/product/0470598743/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/0470598743/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/0470598743-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/0470598743/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/0470598743/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/technical-math-for-dummies-cover-9780470598740-203x255.jpg","width":203,"height":255},"title":"Technical Math For Dummies","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<b data-author-id=\"9795\">Barry Schoenborn</b> is a technical writer who has worked in many of the trades described in the book. <p><b data-author-id=\"10348\">Bradley Simkins</b> has taught numerous classes and tutored at the Multimedia Math Learning Center at American River College in Sacramento.</p>","authors":[{"authorId":9795,"name":"Barry Schoenborn","slug":"barry-schoenborn","description":" <p><b>Barry Schoenborn</b>, a longtime math, science, and technical writer, is the coauthor of <i>Technical Math For Dummies, Medical Dosage Calculations For Dummies, </i>and<i> Physician Assistant Exam For Dummies.</i></p>","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9795"}},{"authorId":10348,"name":"Bradley Simkins","slug":"bradley-simkins","description":" <b>Dr. Richard W. Snyder</b>, DO is an osteopathic physician, board certified in both internal medicine and nephrology. He has authored and coauthored several articles in peer-reviewed journals. <p><b>Barry Schoenborn</b> is a longtime technical writer and is the coauthor of <i>Technical Math For Dummies</i>.</p>","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/10348"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9780470598740&quot;]}]\" id=\"du-slot-63221b3d3f684\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9780470598740&quot;]}]\" id=\"du-slot-63221b3d4010b\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":192334,"title":"Simple Steps for Solving Word Problems","slug":"simple-steps-for-solving-word-problems","categoryList":["business-careers-money","careers","trades-tech-engineering-careers"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192334"}},{"articleId":192318,"title":"Calculating a Standard 15-Percent Tip","slug":"calculating-a-standard-15-percent-tip","categoryList":["business-careers-money","careers","trades-tech-engineering-careers"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192318"}},{"articleId":192330,"title":"Counting Change for Customers the Old-Fashioned Way","slug":"counting-change-for-customers-the-old-fashioned-way","categoryList":["business-careers-money","careers","trades-tech-engineering-careers"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192330"}},{"articleId":192335,"title":"Matching American and Metric Units of Measurement","slug":"matching-american-and-metric-units-of-measurement","categoryList":["business-careers-money","careers","trades-tech-engineering-careers"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192335"}}],"content":[{"title":"Simple steps for solving word problems","thumb":null,"image":null,"content":"<p>Word problems aren’t just on school tests. You solve word problems every day in your work or even while you’re just out and about. Don’t worry — these steps make solving word problems easier than you think. Just follow these easy steps to take away the mystery:</p>\n<ol class=\"level-one\">\n<li>\n<p class=\"first-para\">Read the problem.</p>\n<p class=\"child-para\">Begin by reading the problem carefully. Don’t jump to any conclusions about the answer until you understand the problem.</p>\n</li>\n<li>\n<p class=\"first-para\">Identify and list the facts.</p>\n<p class=\"child-para\">Look at all the information given in the story problem and make a list of what you know.</p>\n</li>\n<li>\n<p class=\"first-para\">Figure out exactly what the problem is asking for.</p>\n<p class=\"child-para\">Know what you’re trying to find. The problem often states the required answer, but sometimes you have to ferret it out from the information given. If an important fact isn’t there, you can often convert some piece of the given information.</p>\n</li>\n<li>\n<p class=\"first-para\">Eliminate excess information.</p>\n<p class=\"child-para\">The problem may include facts that don’t help you find the solution, so clear them out of the way.</p>\n</li>\n<li>\n<p class=\"first-para\">Pay attention to units of measurement.</p>\n<p class=\"child-para\">For example, if dimensions are given in inches, but the answer must be in square feet, you need to convert units. You can use a table of conversions, an online calculator, or your own memory to get the conversion factors.</p>\n</li>\n<li>\n<p class=\"first-para\">Draw a diagram.</p>\n<p class=\"child-para\">Sometimes a diagram helps you visualize the problem (but not always).</p>\n</li>\n<li>\n<p class=\"first-para\">Find or develop a formula.</p>\n<p class=\"child-para\">When you see the math that needs to be done, you probably know a common math formula to use for the computation. You will find that you use some special formulas again and again.</p>\n</li>\n<li>\n<p class=\"first-para\">Consult a reference.</p>\n<p class=\"child-para\">If you’re stuck, look for a reference of some kind, such as a conversion chart or even a blog where someone has encountered the same problem you’re having (although as always, consider Internet sources carefully).</p>\n</li>\n<li>\n<p class=\"first-para\">Do the math and check your answer.</p>\n<p class=\"child-para\">After you have an answer, be sure to test it. If the result is outrageously high or low, verify whether you made a mistake.</p>\n</li>\n</ol>\n"},{"title":"Calculating a standard 20-percent tip","thumb":null,"image":null,"content":"<p>Calculating a 20-percent tip in your head may seem tricky, but here’s a, well, <em>tip</em> for those situations when you need to calculate that standard tip amount. And it works 100 percent of the time. In order to determine a 20-percent tip, follow these steps:</p>\n<ol class=\"level-one\">\n<li>\n<p class=\"first-para\">Take the bill and figure 10 percent in your head.</p>\n<p class=\"child-para\">Just move the decimal point one place to the left. For a $50.00 dinner, that’s $5.00.</p>\n</li>\n<li>\n<p class=\"first-para\">Double the amount created in Step 1.</p>\n<p class=\"child-para\">10 percent x 2 = 20 percent! In this case, it&#8217;s $5.00 x 2, which equals $10.00.</p>\n</li>\n</ol>\n<p class=\"Remember\">Many cellphones and smartphones have tip calculators, but the steps provided here can help you out in a pinch if you don’t have access to your phone for some reason.</p>\n"},{"title":"Counting change for customers the old-fashioned way","thumb":null,"image":null,"content":"<p>Although many cashiers simply dump all your change in your hand at once, counting change the old-fashioned way ensures that customers get the proper amount. Here’s an easy way to make a customer’s change, using counting and simple addition:</p>\n<ol class=\"level-one\">\n<li>\n<p class=\"first-para\">Leave the payment in plain sight on top of the cash drawer.</p>\n<p class=\"child-para\">Say your customer gives you a $10.00 bill for a $9.56 purchase. Put it on the cash drawer while you gather the change.</p>\n</li>\n<li>\n<p class=\"first-para\">Count the change out and give it back to the customer, starting with the smallest coins and describing what you’re giving.</p>\n<p class=\"child-para\">For the example of $9.56, say</p>\n<p class=\"child-para\">“Your purchase was $9.56, out of $10.00. That’s $9.56,</p>\n<p class=\"child-para\">plus 4 cents (4 pennies) makes $9.60,</p>\n<p class=\"child-para\">plus 5 cents (a nickel) makes $9.65,</p>\n<p class=\"child-para\">plus 10 cents (a dime) makes $9.75,</p>\n<p class=\"child-para\">plus 25 cents (a quarter) makes $10.00.”</p>\n</li>\n</ol>\n"},{"title":"Matching American and Metric units of measurement","thumb":null,"image":null,"content":"<p>If you’ve ever had to match American and metric measurement units, you know direct comparisons of these unit systems can be tricky. If you need to know the metric equivalent of an inch, for example, or the American equivalent of a kilometer, use the following table to help you make a proper comparison between the two systems of measurement.</p>\n<table style=\"height: 148px;\" border=\"0\" width=\"391\">\n<tbody>\n<tr>\n<td width=\"150\"><strong>American Length</strong></td>\n<td><strong>Metric Length</strong></td>\n</tr>\n<tr>\n<td>*</td>\n<td>millimeter</td>\n</tr>\n<tr>\n<td>inch</td>\n<td>centimeter (0.4 inches)</td>\n</tr>\n<tr>\n<td>foot (12 inches)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>yard (3 feet)</td>\n<td>meter (39.37 inches)</td>\n</tr>\n<tr>\n<td>rod (16.5 feet)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>furlong (1/8 mile)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>mile (5,280 feet)</td>\n<td>kilometer (0.6214 miles)</td>\n</tr>\n</tbody>\n</table>\n<table style=\"height: 136px;\" border=\"0\" width=\"391\">\n<tbody>\n<tr>\n<td width=\"150\"><strong>American Area</strong></td>\n<td><strong>Metric Area</strong></td>\n</tr>\n<tr>\n<td>square inch</td>\n<td>square centimeter (0.1550 square inches)</td>\n</tr>\n<tr>\n<td>square foot (144 square inches)</td>\n<td>square decimeter (0.1076 square feet)</td>\n</tr>\n<tr>\n<td>square yard (9 square feet)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>acre (43,560 square feet)</td>\n<td>hectare (10,000 square meters, 0.01 square kilometers, 0.4047 acres)</td>\n</tr>\n<tr>\n<td>square mile (640 acres)</td>\n<td>square kilometer (0.3861 square miles)</td>\n</tr>\n</tbody>\n</table>\n<table style=\"height: 106px;\" border=\"0\" width=\"390\">\n<tbody>\n<tr>\n<td width=\"150\"><strong>American Volume</strong></td>\n<td><strong>Metric Volume</strong></td>\n</tr>\n<tr>\n<td>*</td>\n<td>cubic millimeter</td>\n</tr>\n<tr>\n<td>cubic inch</td>\n<td>cubic centimeter (0.0610 cubic inches)</td>\n</tr>\n<tr>\n<td>cubic foot (1,728 cubic inches)</td>\n<td>cubic meter (0.0283 cubic feet)</td>\n</tr>\n<tr>\n<td>cubic yard (27 cubic feet)</td>\n<td>cubic meter (0.7645 cubic yards)</td>\n</tr>\n</tbody>\n</table>\n<table style=\"height: 274px;\" border=\"0\" width=\"391\">\n<tbody>\n<tr>\n<td width=\"150\"><strong>American Weight</strong></td>\n<td><strong>Metric Weight</strong></td>\n</tr>\n<tr>\n<td>*</td>\n<td>gram</td>\n</tr>\n<tr>\n<td>grain</td>\n<td>*</td>\n</tr>\n<tr>\n<td>dram (27.3438 grains)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>ounce (437.5 grains)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>pound (16 ounces, 7,000 grains)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>*</td>\n<td>kilogram (1,000 grams)</td>\n</tr>\n<tr>\n<td>hundredweight (100 pounds)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>ton (20 hundred weight, 2,000 pounds)</td>\n<td>tonne (1,000 kilograms, 1.1023 tons)</td>\n</tr>\n<tr>\n<td>long hundredweight (112 pounds)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>long ton (20 long hundredweight, 2,240 pounds)</td>\n<td>*</td>\n</tr>\n</tbody>\n</table>\n<table border=\"0\">\n<tbody>\n<tr>\n<td width=\"150\"><strong>American liquid volume</strong></td>\n<td><strong>Metric liquid volume</strong></td>\n</tr>\n<tr>\n<td>*</td>\n<td>milliliter</td>\n</tr>\n<tr>\n<td>fluid ounce (29.5735 milliliters)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>cup (8 fluid ounces)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>pint (16 fluid ounces)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>*</td>\n<td>liter (1,000 milliliters, 1.0567 quarts)</td>\n</tr>\n<tr>\n<td>quart (32 fluid ounces, 2 pints)</td>\n<td>*</td>\n</tr>\n<tr>\n<td>gallon (4 quarts)</td>\n<td>*</td>\n</tr>\n</tbody>\n</table>\n<table style=\"height: 40px;\" border=\"0\" width=\"391\">\n<tbody>\n<tr>\n<td width=\"150\"><strong>American Temperature</strong></td>\n<td><strong>Metric temperature</strong></td>\n</tr>\n<tr>\n<td>degrees Fahrenheit</td>\n<td>degrees Kelvin</td>\n</tr>\n</tbody>\n</table>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Solve","lifeExpectancy":"Two years","lifeExpectancySetFrom":"2022-04-27T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":208987},{"headers":{"creationTime":"2016-03-27T16:57:54+00:00","modifiedTime":"2022-04-14T20:31:26+00:00","timestamp":"2022-09-14T18:19:37+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Everyday Math For Dummies Cheat Sheet","strippedTitle":"everyday math for dummies cheat sheet","slug":"everyday-math-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"Whether you're looking to manage your mortgage, cover your credit card, or just leave a tip, basic math comes in handy.","noIndex":0,"noFollow":0},"content":"Everyday math comes in handy when you’re dealing with finances like credit cards and mortgages, and even helps when you’re trying to figure out how much to leave for a tip. Knowing some basic math formulas, the Pythagoras theorem, and a simpler way to add are key to everyday math.","description":"Everyday math comes in handy when you’re dealing with finances like credit cards and mortgages, and even helps when you’re trying to figure out how much to leave for a tip. Knowing some basic math formulas, the Pythagoras theorem, and a simpler way to add are key to everyday math.","blurb":"","authors":[],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/253710"}},{"articleId":249996,"title":"Pre-Algebra Practice Questions: Solving Simple Algebraic Equations","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra Practice Questions: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249986"}},{"articleId":249980,"title":"Pre-Algebra Practice Questions: Rearranging Equations to Isolate x","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":0,"slug":null,"isbn":null,"categoryList":null,"amazon":null,"image":null,"title":null,"testBankPinActivationLink":null,"bookOutOfPrint":false,"authorsInfo":null,"authors":null,"_links":null},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[null]}]\" id=\"du-slot-63221b39c9d74\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[null]}]\" id=\"du-slot-63221b39ca7f9\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":194824,"title":"Grouping Numbers for Easy Addition","slug":"grouping-numbers-for-easy-addition","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/194824"}},{"articleId":194793,"title":"Using Basic Math for Tipping","slug":"using-basic-math-for-tipping","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/194793"}},{"articleId":194787,"title":"Getting to Know Pythagoras’ Theorem","slug":"getting-to-know-pythagoras-theorem","categoryList":[],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/194787"}},{"articleId":194796,"title":"Using Everyday Math in Everyday Life","slug":"using-everyday-math-in-everyday-life","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/194796"}},{"articleId":194788,"title":"Basic Math Formulas","slug":"basic-math-formulas","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/194788"}}],"content":[{"title":"Using basic math for tipping","thumb":null,"image":null,"content":"<p>These basic tipping rules apply to meals in the $20 to $100 price range, which covers almost 90 percent of restaurant meals for two in the U.S. Apply these simple math rules to your check total:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">Basic Rule (total between $30 and $100): Multiply the first digit by 2. That’s the tip.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">Example: $43.75. The first digit is 4. Leave 4 x 2 = $8.</p>\n</li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\">Lower-cost rule (total between $6 and $30): Divide by 5 and round off. That’s the tip.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">Example: $26.90. Five goes into this about 5 times. Leave $5.</p>\n</li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\">Party of four (total between $40 and $100): Round to the nearest 10. Multiply the first digit by 3. Everyone kicks in that amount.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><i></i>Example: $52.50. Rounds to $50. Everyone pays $15.</p>\n</li>\n</ul>\n</li>\n</ul>\n<p>If you’re not up for doing the math, use this handy tip chart. The tip range is 15 to 18 percent but if you’re feeling generous, feel free to tip more.</p>\n<table>\n<tbody>\n<tr>\n<th>Total on Check</th>\n<th>Tip</th>\n<th>Total on Check</th>\n<th>Tip</th>\n</tr>\n<tr>\n<td>$10 and below</td>\n<td>Be nice.</td>\n<td>$84 to $95</td>\n<td>$16.00</td>\n</tr>\n<tr>\n<td>$11 to $16</td>\n<td>$2.50</td>\n<td>$96 to $110</td>\n<td>$18.00</td>\n</tr>\n<tr>\n<td>$17 to $23</td>\n<td>$3.00</td>\n<td>$110 to $130</td>\n<td>$20</td>\n</tr>\n<tr>\n<td>$24 to $30</td>\n<td>$4.50</td>\n<td>$131 to $160</td>\n<td>$25</td>\n</tr>\n<tr>\n<td>$31 to $37</td>\n<td>$5.00</td>\n<td>$161 to $200</td>\n<td>$30</td>\n</tr>\n<tr>\n<td>$38 to $44</td>\n<td>$6.00</td>\n<td>$201 to $250</td>\n<td>$40</td>\n</tr>\n<tr>\n<td>$45 to $52</td>\n<td>$7.50</td>\n<td>$251 to $300</td>\n<td>$50</td>\n</tr>\n<tr>\n<td>$53 to $60</td>\n<td>$9.00</td>\n<td>$301 to $400</td>\n<td>$60</td>\n</tr>\n<tr>\n<td>$61 to $70</td>\n<td>$10.00</td>\n<td>$401 to $500</td>\n<td>$80</td>\n</tr>\n<tr>\n<td>$71 to $83</td>\n<td>$12.00</td>\n<td></td>\n<td></td>\n</tr>\n</tbody>\n</table>\n"},{"title":"Getting to know Pythagoras' Theorem","thumb":null,"image":null,"content":"<p>An earlier version of Pythagoras’ theory existed in ancient civilizations, but only for particular triangles. The Pythagoras’ theorem expanded this earlier version, try the proof for yourself:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/157255.image0.jpg\" alt=\"image0.jpg\" width=\"535\" height=\"370\" /></p>\n"},{"title":"Using everyday math in everyday life","thumb":null,"image":null,"content":"<p>Whether you’re dealing with your everyday finances, or getting together for a neighborhood card game, you need to know basic math to help you simplify and stay on top of your money matters.</p>\n<h2>Playing poker</h2>\n<p>Here are a few crucial rules that you can memorize easily. Spend your time in a real game watching people tap their feet or blink a lot.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">In a four-person game, you need to have a hand with at least a pair of tens to have a 50 percent chance of winning.</p>\n</li>\n<li>\n<p class=\"first-para\">If you really like to have things nailed down, you should have at least two pair, kings high to have a 90 percent chance of winning.</p>\n</li>\n</ul>\n<h2>Using credit cards</h2>\n<p><i>Warning:</i> If you make a purchase on a credit card with an interest rate near 20 percent and then make payments at twice the monthly minimum, the purchase will cost 50 percent more than the price in the store.</p>\n<h2>Dealing with mortgages</h2>\n<p>Here’s a simple mortgage table for a $100,000 loan. To calculate a different loan amount, multiply the payment by the new amount and divide by 100,000. For fractional interest rates, take the fraction of the step up to the next whole-number rate.</p>\n<table>\n<tbody>\n<tr>\n<th>Interest Rate</th>\n<th>Monthly Payment, 30 years</th>\n<th>Monthly Payment, 15 years</th>\n</tr>\n<tr>\n<td>4%</td>\n<td>$477.42</td>\n<td>$739.69</td>\n</tr>\n<tr>\n<td>5%</td>\n<td>$536.82</td>\n<td>$790.79</td>\n</tr>\n<tr>\n<td>6%</td>\n<td>$599.55</td>\n<td>$843.86</td>\n</tr>\n<tr>\n<td>7%</td>\n<td>$665.30</td>\n<td>$898.83</td>\n</tr>\n<tr>\n<td>8%</td>\n<td>$733.76</td>\n<td>$955.65</td>\n</tr>\n</tbody>\n</table>\n"},{"title":"Basic math formulas","thumb":null,"image":null,"content":"<p>If you’re looking to find the area or volumes of basic shapes like rectangles, triangles, or circles, keep this diagram handy for the simple math formulas:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/157258.image0.jpg\" alt=\"image0.jpg\" width=\"535\" height=\"242\" /></p>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Solve","lifeExpectancy":"One year","lifeExpectancySetFrom":"2022-04-14T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":209346},{"headers":{"creationTime":"2016-03-27T16:49:53+00:00","modifiedTime":"2022-02-28T17:10:19+00:00","timestamp":"2022-09-14T18:19:18+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Math For Real Life For Dummies Cheat Sheet","strippedTitle":"math for real life for dummies cheat sheet","slug":"math-for-real-life-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"Here's a handy guide to some of the most common and practical math calculations we tend to make in our everyday lives.","noIndex":0,"noFollow":0},"content":"Using real-life math can simplify everyday situations. Math comes in handy every time you take a trip, go shopping, or do projects around the house.","description":"Using real-life math can simplify everyday situations. Math comes in handy every time you take a trip, go shopping, or do projects around the house.","blurb":"","authors":[{"authorId":9795,"name":"Barry Schoenborn","slug":"barry-schoenborn","description":" <p><b>Barry Schoenborn</b>, a longtime math, science, and technical writer, is the coauthor of <i>Technical Math For Dummies, Medical Dosage Calculations For Dummies, </i>and<i> Physician Assistant Exam For Dummies.</i></p>","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9795"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":170371,"title":"Calculating Area and Volume for Household Projects","slug":"calculating-area-and-volume-for-household-projects","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/170371"}},{"articleId":170367,"title":"Calculating GPA","slug":"calculating-gpa","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/170367"}},{"articleId":170366,"title":"Estimating Taxes and Discounts When Shopping","slug":"estimating-taxes-and-discounts-when-shopping","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/170366"}},{"articleId":170143,"title":"Using Your Body to Estimate Length","slug":"using-your-body-to-estimate-length","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/170143"}},{"articleId":170134,"title":"Calculating Speed, Time, and Distance","slug":"calculating-speed-time-and-distance","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/170134"}}],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/253710"}},{"articleId":249996,"title":"Pre-Algebra Practice Questions: Solving Simple Algebraic Equations","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra Practice Questions: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249986"}},{"articleId":249980,"title":"Pre-Algebra Practice Questions: Rearranging Equations to Isolate x","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282384,"slug":"math-for-real-life-for-dummies","isbn":"9781118453308","categoryList":["academics-the-arts","math","basic-math"],"amazon":{"default":"https://www.amazon.com/gp/product/1118453301/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1118453301/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1118453301-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1118453301/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1118453301/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/math-for-real-life-for-dummies-cover-9781118453308-168x255.jpg","width":168,"height":255},"title":"Math For Real Life For Dummies","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"9795\">Barry Schoenborn</b>, a longtime math, science, and technical writer, is the coauthor of <i>Technical Math For Dummies, Medical Dosage Calculations For Dummies, </i>and<i> Physician Assistant Exam For Dummies.</i></p>","authors":[{"authorId":9795,"name":"Barry Schoenborn","slug":"barry-schoenborn","description":" <p><b>Barry Schoenborn</b>, a longtime math, science, and technical writer, is the coauthor of <i>Technical Math For Dummies, Medical Dosage Calculations For Dummies, </i>and<i> Physician Assistant Exam For Dummies.</i></p>","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9795"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781118453308&quot;]}]\" id=\"du-slot-63221b265793d\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781118453308&quot;]}]\" id=\"du-slot-63221b2658388\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":170366,"title":"Estimating Taxes and Discounts When Shopping","slug":"estimating-taxes-and-discounts-when-shopping","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/170366"}},{"articleId":170371,"title":"Calculating Area and Volume for Household Projects","slug":"calculating-area-and-volume-for-household-projects","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/170371"}},{"articleId":170143,"title":"Using Your Body to Estimate Length","slug":"using-your-body-to-estimate-length","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/170143"}},{"articleId":170134,"title":"Calculating Speed, Time, and Distance","slug":"calculating-speed-time-and-distance","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/170134"}},{"articleId":170367,"title":"Calculating GPA","slug":"calculating-gpa","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/170367"}}],"content":[{"title":"Estimating taxes and discounts when shopping","thumb":null,"image":null,"content":"<p>When you go shopping, you often encounter discounts and sales offers that change the price of an item. In addition, many states in the United States charge sales tax, and if you&#8217;re shopping abroad, you may face a value added tax.</p>\n<p>To determine how much the total will be (and whether it fits into your budget or whether you have enough cash on hand to make the purchase), you need to be able to calculate the discounted price as well as determine the sales and any other taxes.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>Estimating sales tax: </b>In the U.S., state sales taxes often end up being over 8 percent when you add in applicable local taxes. Therefore, a safe estimate is to allow for a 10 percent sales tax. A quick way to figure 10 percent of an item&#8217;s purchase price is to move the decimal point one place to the left. For example, if you buy a $70 item at the hardware store, the tax will be approximately $7, making the purchase price in the neighborhood of $77.</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Estimating VAT: </b>Many European Union and non-EU countries have a value added tax (VAT) that hovers around 20 percent. To estimate VAT, follow the same approach as you would to calculate a sales tax: Determine 10 percent by moving the decimal one place to the left. Then, double that amount. Using the $70 purchase at the hardware store example, the VAT will be approximately $14.</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Calculating a discount: </b>Discounts can be for any amount: 5 percent, 10 percent, 30 percent, and so on. To do the calculations in your head, first determine what a 10 percent discount is (because that&#8217;s the easiest one to calculate) and then do a little multiplication or division to get closer to the actual discount amount.</p>\n<p class=\"child-para\">For example, if an item is being offered at a 40 percent discount, figure 10 percent and then multiply that amount by 4. A 40 percent discount on an $80 dress, for example, works out to be $32 off (10 percent of $80 is $8, and $8 multiplied by 4 is $32). If the discount is 15 percent, figure the 10 percent discount, divide that number in half to determine what a 5 percent discount, and then add the two together. For the $80 dress, you&#8217;d end up with a $12 discount: $8 (10 percent) + $4 (5 percent) = $12 (15 percent).</p>\n</li>\n</ul>\n"},{"title":"Calculating area and volume for household projects","thumb":null,"image":null,"content":"<p>Many household projects require that you be able to calculate area or volume. Whether you&#8217;re painting your kid&#8217;s room, mulching your flowerbed for the winter, planting grass seed in the spring, or tackling any other project for which you need to find out how much of something you need to cover, knowing how to figure area and volume is a time- and money-saver.</p>\n<h2>Calculating area</h2>\n<p>To calculate area, you simply use this formula:</p>\n<p>area = length × width<br />\n<i>a = lw</i></p>\n<p>From there, you can get the other information you need:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>Figuring how much seed you need: </b>Use the area formula to calculate the area you want to cover and then calculate the number of pounds of seed you need. Seed companies indicate how much coverage a pound of seed gives you. Simply divide the area you need to cover by the amount of area that 1 pound of seed covers. For example, if you want to cover an area of 1,625 square feet, and 1 pound of seed covers 600 square feet, you need about 3 pounds of seed (1,625 divided by 600 is 2.7).</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Calculating area to be painted:</b> You can calculate the area of each wall and then add the values together, or you can determine the perimeter of the room (add the length of each wall) and multiply that value by the room&#8217;s height. A room that has a 42-foot perimeter and 8-foot ceilings has an area of 336 feet.</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Calculating how many square yards of carpeting you need: </b>First calculate the area of the room and then convert that number from square feet to square yards by dividing the area by 9 (a square yard is 3 feet wide and 3 feet long).</p>\n</li>\n</ul>\n<h2>Calculating volume</h2>\n<p>When the area you want to cover has depth as well as height and width, you need to determine volume rather than area. Mulching a flowerbed is one such project: To protect your flowers, you need to spread a few inches of mulch over the whole bed.</p>\n<p>To calculate volume, you use this formula:</p>\n<p>volume = length × width × height<br />\n<i>v = lwh</i></p>\n<p>With that info, you can then do additional calculations to figure out how many bags of mulch to buy.</p>\n<p>Say, for example, that you want to cover 6.68 cubic feet with mulch (that&#8217;s the volume you need for a small bed, mulching to a depth of 3 inches). Simply divide the volume you need by the number of cubic feet in a bag of mulch. If each bag holds 3 cubic feet, you need 2.23 bags. So buy 3 to be safe.</p>\n"},{"title":"Using your body to estimate length","thumb":null,"image":null,"content":"<p>Many real-life math problems don&#8217;t require exact solutions or precise calculations. When you need an approximate idea of length, you have a handy-dandy &#8220;ruler&#8221; always nearby: your body. Yes, your body — and its various parts — can serve as a quick length estimator.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>Your hand: </b>The width of your palm is about 4 inches (10 centimeters).</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Your foot: </b>An average foot is about 12 inches long.</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Your forearm from elbow to fingertip: </b>Your forearm is about 1.5 feet (46 centimeters).</p>\n</li>\n<li>\n<p class=\"first-para\"><b>From nose to finger tip: </b>The distance between your nose and your fingertip when your arm is extended is about a yard (36 inches). If you haven&#8217;t used this method yourself, ask your mother or grandmother: It&#8217;s the traditional way of measuring cloth.</p>\n</li>\n<li>\n<p class=\"first-para\"><b>The distance of one full stride: </b>Called a <i>pace, </i>it&#8217;s about 58 inches, just short of 6 feet. The Romans used this measurement, and so can you!</p>\n</li>\n</ul>\n<p>These estimates are just that: estimates. A more accurate way use your body parts to estimate length is to know your own measurements: the width of your own palm, the length of your own foot, and so on. Then, wherever you are, you&#8217;ll have a pretty accurate ruler very close by.</p>\n"},{"title":"Calculating speed, time, and distance","thumb":null,"image":null,"content":"<p>If you drive a car or have ever flown in an airplane, you&#8217;ve probably noticed that time, speed, and distance are related. Here&#8217;s the basic formula for distance (<em>d</em>), which equals speed (called <em>velocity</em> in science and represented by <em>v</em>) multiplied by time (<em>t</em>):</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/358137.distance.jpg\" alt=\"distance.jpg\" width=\"152\" height=\"30\" /></p>\n<p>From this simple formula, you can derive these other formulas as well:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/358138.distance_time.jpg\" alt=\"distance_time.jpg\" width=\"114\" height=\"115\" /></p>\n<p>By knowing any two of the components, you can use these formulas to figure out the third. If you know how far you&#8217;ve traveled and the time the journey has taken, you can calculate your average speed. If you know the distance and the average speed, you can calculate the time you&#8217;ve been driving.</p>\n<p class=\"Tip\">This &#8220;know two to get all three&#8221; trick applies to many day-to-day math activities: buying lumber (length needed/price per board foot/total cost), buying cases of motor oil (price per can/number of cans in a case/total cost), or buying meat at the grocery store (weight of cut/price per pound/total cost).</p>\n"},{"title":"Calculating GPA","thumb":null,"image":null,"content":"<p>Nowadays, grade point averages are a big deal, especially for college-bound students and their anxious parents. GPA is easy to calculate if you understand that it&#8217;s simply an average.</p>\n<p>To determine an average, you add up all of the values in the group and then divide that total by the number of values in the group.</p>\n<p>The tricky part about GPAs, however, is that you&#8217;re working with letter grades rather than numbers. For that reason, before you can calculate a GPA, you have to do a little conversion work first.</p>\n<p>Follow these steps to calculate a GPA:</p>\n<ol class=\"level-one\">\n<li>\n<p class=\"first-para\">Convert the grades to numbers, using this scale:</p>\n<table>\n<tbody>\n<tr>\n<th>Letter Grade</th>\n<th>Number Value</th>\n</tr>\n<tr>\n<td>A</td>\n<td>4</td>\n</tr>\n<tr>\n<td>B</td>\n<td>3</td>\n</tr>\n<tr>\n<td>C</td>\n<td>2</td>\n</tr>\n<tr>\n<td>D</td>\n<td>1</td>\n</tr>\n<tr>\n<td>F</td>\n<td>0</td>\n</tr>\n</tbody>\n</table>\n<p class=\"child-para\">Say you&#8217;re taking four courses and your grades are A, A, C, and D. The numeric equivalents are 4, 4, 2, and 1.</p>\n</li>\n<li>\n<p class=\"first-para\">Add the numbers up.</p>\n<p class=\"child-para\">When you&#8217;re calculating your GPA for a semester or quarter, the task is pretty easy because people don&#8217;t usually take a lot of courses. In the example, the total is 11. The task gets a bit more challenging when you&#8217;re calculating GPA for a larger number of classes.</p>\n</li>\n<li>\n<p class=\"first-para\">Divide by the number of courses.</p>\n<p class=\"child-para\">In this example, divide by 4 (the number of courses). The result is a number greater than 2 and less than 3. (Actually, it&#8217;s 2 with a remainder of 3, which works out to be 0.75.) Your GPA is 2.75, or about a C+.</p>\n</li>\n</ol>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Solve","lifeExpectancy":"Five 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Basic Math Articles

Add and subtract negative numbers, calculate how much to tip, make sense of exponents, and generally get mathy, with our easy-to-read articles.

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Basic Math AS and A-Level Maths For Dummies Cheat Sheet

Cheat Sheet / Updated 02-16-2023

Some of the most important things to remember in AS-level and A-level maths are the rules for differentiating and integrating expressions. This cheat sheet is a handy reference for what happens when you differentiate or integrate powers of x, trigonometric functions, exponentials or logarithms – as well as the rules you need for what to do when they’re combined!

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Basic Math How to Calculate Percentages

Article / Updated 11-04-2022

Listen to the article:Download audio Whether you're leaving a tip at a restaurant or figuring out just how much those stylish shoes are on sale, you can't get away from percentages. While there are numerous percentage calculators online, it's helpful to be able to do some quick math in your head to calculate percentages without any digital assistance. What is percentage? The word percentage comes from the word percent. If you split the word percent into its root words, you see “per” and “cent.” Cent is an old European word with French, Latin, and Italian origins meaning “hundred." So, percent is translated directly to “per hundred.” If you have 87 percent, you literally have 87 per 100. If it snowed 13 times in the last 100 days, it snowed 13 percent of the time. How to find percentage The numbers that you will be converting into percentages can be given to you in two different formats: decimal and fraction. Decimal format is easier to calculate into a percentage. Converting a decimal to a percentage is as simple as multiplying it by 100. To convert .87 to a percent, simply multiply .87 by 100. .87 × 100=87, which gives us 87 percent. Percent is often abbreviated with the % symbol. You can present your answer as 87% or 87 percent — either way is acceptable. If you are given a fraction, convert it to a percentage by dividing the top number by the bottom number. If you are given 13/100, you would divide 13 by 100. 13 ÷ 100 = .13 Then, follow the steps above for converting a decimal to a percent. .13 × 100 = 13, thus giving you 13%. The more difficult task comes when you need to know a percentage when you are given numbers that don’t fit so neatly into 100. Most of the time, you will be given a percentage of a specific number. For example, you may know that 40 percent of your paycheck will go to taxes and you want to find out how much money that is. How to calculate percentage of a specific number This process is the reverse of what you did earlier. First convert the percentage number to a decimal. Then, you divide your percentage by 100. So, 40 percent would be 40 divided by 100. 40 ÷ 100 = .40 Next, once you have the decimal version of your percentage, simply multiply it by the given number (in this case, the amount of your paycheck). If your paycheck is $750, you would multiply 750 by .40. 750 × .40 = 300 Your answer would be 300. You are paying $300 in taxes. Let’s try another example. You need to save 25 percent of your paycheck for the next 6 months to pay for an upcoming vacation. If your paycheck is $1,500, how much should you save? Start by converting 25 percent to a decimal. 25 ÷ 100 = .25 Now, multiply the decimal by the amount of your paycheck, or 1500. 1500 × .25 = 375 This means you need to save $375 from each paycheck.

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Basic Math Applying Order of Operations to Expressions with Only Multiplication and Division

Article / Updated 10-03-2022

Some expressions contain only multiplication and division. When this is the case, the rule for evaluating the expression is pretty straightforward. When an expression contains only multiplication and division, evaluate it step by step from left to right. The Three Types of Big Four Expressions Expression Example Rule Contains only addition and subtraction 12 + 7 – 6 – 3 + 8 Evaluate left to right. Contains only multiplication and division 18 ÷ 3 x 7 ÷ 14 Evaluate left to right. Mixed-operator expression: contains a combination of addition/subtraction and multiplication/division 9 + 6 ÷ 3 1. Evaluate multiplication and division left to right. 2. Evaluate addition and subtraction left to right. Suppose you want to evaluate this expression: Again, the expression contains only multiplication and division, so you can move from left to right, starting with 9 x 2: Notice that the expression shrinks one number at a time until all that’s left is 2. So Here’s another quick example: Even though this expression has some negative numbers, the only operations it contains are multiplication and division. So you can evaluate it in two steps from left to right (remembering the rules for multiplying and dividing with negative numbers): Thus,

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Basic Math Basic Math & Pre-Algebra For Dummies Cheat Sheet

Cheat Sheet / Updated 10-03-2022

A little understanding can go a long way toward helping master math. Some math concepts may seem complicated at first, but after you work with them for a little bit, you may wonder what all the fuss is about. You'll find easy-to-understand explanations and clear examples in these articles that cover basic math concepts — like order of operations; the commutative, associative, and distributive properties; radicals, exponents, and absolute values — that you may remember (or not) from your early math and pre-algebra classes. You'll also find handy and easy-to-understand conversion guides for converting between metric and English units and between fractions, percents, and decimals.

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Basic Math How to Divide Decimals

Article / Updated 09-27-2022

Dividing decimals is similar to dividing whole numbers, except you have to handle the decimal point before you start dividing. Here’s how to divide decimals step by step: Move the decimal point in the divisor and dividend. Turn the divisor (the number you’re dividing by) into a whole number by moving the decimal point all the way to the right. At the same time, move the decimal point in the dividend (the number you’re dividing) the same number of places to the right. Place a decimal point in the quotient (the answer) directly above where the decimal point now appears in the dividend. Divide as usual, being careful to line up the quotient properly so that the decimal point falls into place. Line up each digit in the quotient just over the last digit in the dividend used in that cycle. As with whole-number division, sometimes decimal division doesn’t work out evenly at the end. With decimals, however, you never write a remainder. Instead, attach enough trailing zeros to round the quotient to a certain number of decimal places. The digit to the right of the digit you’re rounding to tells you whether to round up or down, so you always have to figure out the division to one extra place. See the following chart: To Round a Decimal to Fill Out the Dividend with Trailing Zeros to A whole number One decimal place One decimal place Two decimal places Two decimal places Three decimal places Sample questions Divide the following: 9.152 / 0.8 = ? 11.44. To start out, write the problem as usual: Turn 0.8 into the whole number 8 by moving the decimal point one place to the right. At the same time, move the decimal point in 9.1526 one place to the right. Put your decimal point in the quotient directly above where it falls in 91.25: Now you’re ready to divide. Just be careful to line up the quotient properly so that the decimal point falls into place. Divide the following: 21.9 / 0.015 = ? 1,460. Set up the problem as usual: Notice that two trailing zeros are attached to the dividend because you need to move the decimal points in each number three places to the right. Again, place the decimal point in the quotient directly above where it now appears in the dividend, 21900: Now you’re ready to divide. Line up the quotient carefully so the decimal point falls into place: Even though the division comes out even after you write the digit 6 in the quotient, you still need to add a placeholding zero so that the decimal point appears in the correct place. Practice questions Divide these two decimals: 9.345 / 0.05 = ? Solve the following division: 3.15 / 0.021 = ? Perform the following decimal division, rounding to one decimal place: 6.7 / 10.1. Find the solution, rounding to the nearest hundredth: 9.13 / 4.25. Following are answers to the practice questions: 9.345 / 0.05 = 186.9. To start out, write the problem as usual: Turn the divisor (0.05) into a whole number by moving the decimal point two places to the right. At the same time, move the decimal point in the dividend (9.345) two places to the right. Place the decimal point in the quotient directly above where it now appears in the dividend: Now you’re ready to divide. Be careful to line up the quotient properly so that the decimal point falls into place. 3.15 / 0.021 = 150. Write the problem as usual: You need to move the decimal point in the divisor (0.021) three places to the right, so attach an additional trailing zero to the dividend (3.15) to extend it to three decimal places: Now you can move both decimal points three places to the right. Place the decimal point in the quotient above the decimal point in the dividend: Divide, being careful to line up the quotient properly: Remember to insert a placeholding zero in the quotient so that the decimal point ends up in the correct place. 6.7 / 10.1 = 0.7. To start out, write the problem as usual: Turn the divisor (10.1) into a whole number by moving the decimal point one place to the right. At the same time, move the decimal point in the dividend (6.7) one place to the right: The problem asks you to round the quotient to one decimal place, so fill out the dividend with trailing zeros to two decimal places: Now you’re ready to divide: Round the quotient to one decimal place: 9.13 / 4.25 = 2.15. First, write the problem as usual: Turn the divisor (4.25) into a whole number by moving the decimal point two places to the right. At the same time, move the decimal point in the dividend (9.13) two places to the right: The problem asks you to round the quotient to the nearest hundredth, so fill out the dividend with trailing zeros to three decimal places: Now divide, carefully lining up the quotient: Round the quotient to the nearest hundredth:

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Basic Math Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet

Cheat Sheet / Updated 05-04-2022

When you’re working with your K–5 child to practice math skills, it can help to have a tool to remind you of some of the basics related to addition, subtraction, multiplication, division, and fractions. For those times, this Cheat Sheet can come in handy.

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Basic Math Basic Math and Pre-Algebra: 1001 Practice Problems For Dummies Cheat Sheet

Cheat Sheet / Updated 04-27-2022

To successfully master basic math, you need to practice addition, subtraction, multiplication, and division problems. You also need to understand order of operations, fractions, decimals, percents, ratios, weights and measures, and even a little geometry. After you've become proficient in these and other basic math concepts, you can begin to tackle pre-algebra, which involves variables, expressions, and equations.

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Basic Math Technical Math For Dummies Cheat Sheet

Cheat Sheet / Updated 04-27-2022

Grasping some technical math basics can simplify everyday situations faced by many professionals and even non-professionals, including having to solve word problems, calculate tips, make change, or match American and metric measurements.

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Basic Math Everyday Math For Dummies Cheat Sheet

Cheat Sheet / Updated 04-14-2022

Everyday math comes in handy when you’re dealing with finances like credit cards and mortgages, and even helps when you’re trying to figure out how much to leave for a tip. Knowing some basic math formulas, the Pythagoras theorem, and a simpler way to add are key to everyday math.

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Basic Math Math For Real Life For Dummies Cheat Sheet

Cheat Sheet / Updated 02-28-2022

Using real-life math can simplify everyday situations. Math comes in handy every time you take a trip, go shopping, or do projects around the house.

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