{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T11:06:08+00:00","modifiedTime":"2023-07-10T19:00:07+00:00","timestamp":"2023-07-10T21:01:03+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":"Evaluating an Expression with Only Multiplication & Division","strippedTitle":"evaluating an expression with only multiplication & 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\r\n<blockquote>9 × 2 ÷ 6 ÷ 3 × 2</blockquote>\r\nAgain, the expression contains only multiplication and division, so you can move from left to right, starting with 9 x 2:\r\n<blockquote>= 18 ÷ 6 ÷ 3 × 2\r\n= 3 ÷ 3 × 2\r\n= 1 × 2\r\n= 2</blockquote>\r\nNotice that the expression shrinks one number at a time until all that’s left is 2. So\r\n<blockquote>9 × 2 ÷ 6 ÷ 3 × 2 = 2</blockquote>\r\nHere’s another quick example:\r\n<blockquote>−2 × 6 ÷ −4</blockquote>\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<blockquote>= −2 × 6 ÷ −4\r\n= −12 ÷ −4\r\n= 3</blockquote>\r\nThus,\r\n<blockquote>−2 × 6 ÷ −4 = 3</blockquote>","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\r\n<blockquote>9 × 2 ÷ 6 ÷ 3 × 2</blockquote>\r\nAgain, the expression contains only multiplication and division, so you can move from left to right, starting with 9 x 2:\r\n<blockquote>= 18 ÷ 6 ÷ 3 × 2\r\n= 3 ÷ 3 × 2\r\n= 1 × 2\r\n= 2</blockquote>\r\nNotice that the expression shrinks one number at a time until all that’s left is 2. So\r\n<blockquote>9 × 2 ÷ 6 ÷ 3 × 2 = 2</blockquote>\r\nHere’s another quick example:\r\n<blockquote>−2 × 6 ÷ −4</blockquote>\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<blockquote>= −2 × 6 ÷ −4\r\n= −12 ÷ −4\r\n= 3</blockquote>\r\nThus,\r\n<blockquote>−2 × 6 ÷ −4 = 3</blockquote>","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","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":"Important Operations that Make Math Problems Easier","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":"Working with Exponents, Radicals, & 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: 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":"Solving Simple Equations in Pre-Algebra Problems","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: 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":"Rearranging Algebraic 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><p><b><b data-author-id=\"9399\">Mark Zegarelli</b></b> is a math teacher and tutor with degrees in math and English from Rutgers University. 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Evaluating an Expression with Only Multiplication & Division

By: Mark Zegarelli and

Updated: 07-10-2023

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:

9 × 2 ÷ 6 ÷ 3 × 2

Again, the expression contains only multiplication and division, so you can move from left to right, starting with 9 x 2:

= 18 ÷ 6 ÷ 3 × 2 = 3 ÷ 3 × 2 = 1 × 2 = 2

Notice that the expression shrinks one number at a time until all that’s left is 2. So

9 × 2 ÷ 6 ÷ 3 × 2 = 2

Here’s another quick example:

−2 × 6 ÷ −4

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):

= −2 × 6 ÷ −4 = −12 ÷ −4 = 3

Thus,

−2 × 6 ÷ −4 = 3

About This Article

This article is from the book:

Basic Math & Pre-Algebra For Dummies ,

About the book author:

Mark Zegarelli is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com.

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