{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"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 — and fun — for average readers. He is the author of <i>Logic For Dummies</i> and <i>Basic Math & 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 — and fun — for average readers. 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Applying Order of Operations to Expressions with Only Multiplication and Division

By: Mark Zegarelli and

Updated: 10-03-2022

From The Book: Basic Math & Pre-Algebra For Dummies

Basic Math & Pre-Algebra For Dummies

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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,

About This Article

This article is from the book:

Basic Math & Pre-Algebra For Dummies ,

About the book author:

Mark Zegarelli, a math tutor and writer with 25 years of professional experience, delights in making technical information crystal clear — and fun — for average readers. He is the author of Logic For Dummies and Basic Math & Pre-Algebra For Dummies.

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Basic Math ,