{"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":[{"articleId":172026,"title":"Repurposing Items for Beautiful Holiday Decorating","slug":"decorating-for-the-holidays-with-what-you-already-have","categoryList":["home-auto-hobbies","crafts","gifts-holidays"],"_links":{"self":"/articles/172026"}},{"articleId":192609,"title":"How to Pray the Rosary: A Comprehensive Guide","slug":"how-to-pray-the-rosary","categoryList":["body-mind-spirit","religion-spirituality","christianity","catholicism"],"_links":{"self":"/articles/192609"}},{"articleId":193770,"title":"How to Play Rummy: All You Need to Know","slug":"rummy-understanding-the-rules-and-starting-a-game","categoryList":["home-auto-hobbies","games","card-games","general-card-games"],"_links":{"self":"/articles/193770"}},{"articleId":153792,"title":"Format Numbers in Thousands and Millions in Excel Reports","slug":"format-numbers-in-thousands-and-millions-in-excel-reports","categoryList":["technology","software","microsoft-products","excel"],"_links":{"self":"/articles/153792"}},{"articleId":147241,"title":"How to Use the Z-Table","slug":"how-to-use-the-z-table","categoryList":["academics-the-arts","math","statistics"],"_links":{"self":"/articles/147241"}}],"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. 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.</p>","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"}}],"_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 = \"[{"key":"cat","values":["academics-the-arts","math","basic-math"]},{"key":"isbn","values":["9781119293637"]}]\" id=\"du-slot-64ac718f5cb21\"></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 = \"[{"key":"cat","values":["academics-the-arts","math","basic-math"]},{"key":"isbn","values":["9781119293637"]}]\" id=\"du-slot-64ac718f5ddb5\"></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":"2022-10-03T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":150507},"articleLoadedStatus":"success"},"listState":{"list":{},"objectTitle":"","status":"initial","pageType":null,"objectId":null,"page":1,"sortField":"time","sortOrder":1,"categoriesIds":[],"articleTypes":[],"filterData":{},"filterDataLoadedStatus":"initial","pageSize":10},"adsState":{"pageScripts":{"headers":{"timestamp":"2024-11-22T05:50:01+00:00"},"adsId":0,"data":{"scripts":[{"pages":["all"],"location":"header","script":"\r\n<script src=\"https://cdn.optimizely.com/js/10563184655.js\"></script>","enabled":false},{"pages":["all"],"location":"header","script":"\r\n<script>var _comscore = _comscore || [];_comscore.push({ c1: \"2\", c2: \"15097263\" });(function() {var s = document.createElement(\"script\"), el = document.getElementsByTagName(\"script\")[0]; s.async = true;s.src = (document.location.protocol == \"https:\" ? \"https://sb\" : \"http://b\") + \".scorecardresearch.com/beacon.js\";el.parentNode.insertBefore(s, el);})();</script><noscript><img src=\"https://sb.scorecardresearch.com/p?c1=2&c2=15097263&cv=2.0&cj=1\" /></noscript>\r\n","enabled":true},{"pages":["all"],"location":"footer","script":"\r\n<script type='text/javascript'>\r\n(function(){var g=function(e,h,f,g){\r\nthis.get=function(a){for(var a=a+\"=\",c=document.cookie.split(\";\"),b=0,e=c.length;b<e;b++){for(var d=c[b];\" \"==d.charAt(0);)d=d.substring(1,d.length);if(0==d.indexOf(a))return d.substring(a.length,d.length)}return null};\r\nthis.set=function(a,c){var b=\"\",b=new Date;b.setTime(b.getTime()+6048E5);b=\"; expires=\"+b.toGMTString();document.cookie=a+\"=\"+c+b+\"; path=/; \"};\r\nthis.check=function(){var a=this.get(f);if(a)a=a.split(\":\");else if(100!=e)\"v\"==h&&(e=Math.random()>=e/100?0:100),a=[h,e,0],this.set(f,a.join(\":\"));else return!0;var c=a[1];if(100==c)return!0;switch(a[0]){case \"v\":return!1;case \"r\":return c=a[2]%Math.floor(100/c),a[2]++,this.set(f,a.join(\":\")),!c}return!0};\r\nthis.go=function(){if(this.check()){var a=document.createElement(\"script\");a.type=\"text/javascript\";a.src=g;document.body&&document.body.appendChild(a)}};\r\nthis.start=function(){var t=this;\"complete\"!==document.readyState?window.addEventListener?window.addEventListener(\"load\",function(){t.go()},!1):window.attachEvent&&window.attachEvent(\"onload\",function(){t.go()}):t.go()};};\r\ntry{(new g(100,\"r\",\"QSI_S_ZN_5o5yqpvMVjgDOuN\",\"https://zn5o5yqpvmvjgdoun-wiley.siteintercept.qualtrics.com/SIE/?Q_ZID=ZN_5o5yqpvMVjgDOuN\")).start()}catch(i){}})();\r\n</script><div id='ZN_5o5yqpvMVjgDOuN'></div>\r\n","enabled":false},{"pages":["all"],"location":"header","script":"\r\n<script>\r\n (function(h,o,t,j,a,r){\r\n h.hj=h.hj||function(){(h.hj.q=h.hj.q||[]).push(arguments)};\r\n h._hjSettings={hjid:257151,hjsv:6};\r\n a=o.getElementsByTagName('head')[0];\r\n r=o.createElement('script');r.async=1;\r\n r.src=t+h._hjSettings.hjid+j+h._hjSettings.hjsv;\r\n a.appendChild(r);\r\n })(window,document,'https://static.hotjar.com/c/hotjar-','.js?sv=');\r\n</script>","enabled":false},{"pages":["article"],"location":"header","script":" <script src=\"//get.s-onetag.com/bffe21a1-6bb8-4928-9449-7beadb468dae/tag.min.js\" async defer></script>","enabled":true},{"pages":["homepage"],"location":"header","script":"<meta name=\"facebook-domain-verification\" content=\"irk8y0irxf718trg3uwwuexg6xpva0\" />","enabled":true},{"pages":["homepage","article","category","search"],"location":"footer","script":"\r\n<noscript>\r\n<img height=\"1\" width=\"1\" src=\"https://www.facebook.com/tr?id=256338321977984&ev=PageView&noscript=1\"/>\r\n</noscript>\r\n","enabled":true}]}},"pageScriptsLoadedStatus":"success"},"navigationState":{"navigationCollections":[{"collectionId":287568,"title":"BYOB (Be Your Own Boss)","hasSubCategories":false,"url":"/collection/for-the-entry-level-entrepreneur-287568"},{"collectionId":293237,"title":"Be a Rad Dad","hasSubCategories":false,"url":"/collection/be-the-best-dad-293237"},{"collectionId":295890,"title":"Career Shifting","hasSubCategories":false,"url":"/collection/career-shifting-295890"},{"collectionId":294090,"title":"Contemplating the Cosmos","hasSubCategories":false,"url":"/collection/theres-something-about-space-294090"},{"collectionId":287563,"title":"For Those Seeking Peace of Mind","hasSubCategories":false,"url":"/collection/for-those-seeking-peace-of-mind-287563"},{"collectionId":287570,"title":"For the Aspiring Aficionado","hasSubCategories":false,"url":"/collection/for-the-bougielicious-287570"},{"collectionId":291903,"title":"For the Budding Cannabis Enthusiast","hasSubCategories":false,"url":"/collection/for-the-budding-cannabis-enthusiast-291903"},{"collectionId":299891,"title":"For the College Bound","hasSubCategories":false,"url":"/collection/for-the-college-bound-299891"},{"collectionId":291934,"title":"For the Exam-Season Crammer","hasSubCategories":false,"url":"/collection/for-the-exam-season-crammer-291934"},{"collectionId":301547,"title":"For the Game Day Prepper","hasSubCategories":false,"url":"/collection/big-game-day-prep-made-easy-301547"}],"navigationCollectionsLoadedStatus":"success","navigationCategories":{"books":{"0":{"data":[{"categoryId":33512,"title":"Technology","hasSubCategories":true,"url":"/category/books/technology-33512"},{"categoryId":33662,"title":"Academics & The Arts","hasSubCategories":true,"url":"/category/books/academics-the-arts-33662"},{"categoryId":33809,"title":"Home, Auto, & Hobbies","hasSubCategories":true,"url":"/category/books/home-auto-hobbies-33809"},{"categoryId":34038,"title":"Body, Mind, & Spirit","hasSubCategories":true,"url":"/category/books/body-mind-spirit-34038"},{"categoryId":34224,"title":"Business, Careers, & Money","hasSubCategories":true,"url":"/category/books/business-careers-money-34224"}],"breadcrumbs":[],"categoryTitle":"Level 0 Category","mainCategoryUrl":"/category/books/level-0-category-0"}},"articles":{"0":{"data":[{"categoryId":33512,"title":"Technology","hasSubCategories":true,"url":"/category/articles/technology-33512"},{"categoryId":33662,"title":"Academics & The Arts","hasSubCategories":true,"url":"/category/articles/academics-the-arts-33662"},{"categoryId":33809,"title":"Home, Auto, & Hobbies","hasSubCategories":true,"url":"/category/articles/home-auto-hobbies-33809"},{"categoryId":34038,"title":"Body, Mind, & Spirit","hasSubCategories":true,"url":"/category/articles/body-mind-spirit-34038"},{"categoryId":34224,"title":"Business, Careers, & Money","hasSubCategories":true,"url":"/category/articles/business-careers-money-34224"}],"breadcrumbs":[],"categoryTitle":"Level 0 Category","mainCategoryUrl":"/category/articles/level-0-category-0"}}},"navigationCategoriesLoadedStatus":"success"},"searchState":{"searchList":[],"searchStatus":"initial","relatedArticlesList":[],"relatedArticlesStatus":"initial"},"routeState":{"name":"Article3","path":"/article/academics-the-arts/math/basic-math/applying-order-of-operations-to-expressions-with-only-multiplication-and-division-150507/","hash":"","query":{},"params":{"category1":"academics-the-arts","category2":"math","category3":"basic-math","article":"applying-order-of-operations-to-expressions-with-only-multiplication-and-division-150507"},"fullPath":"/article/academics-the-arts/math/basic-math/applying-order-of-operations-to-expressions-with-only-multiplication-and-division-150507/","meta":{"routeType":"article","breadcrumbInfo":{"suffix":"Articles","baseRoute":"/category/articles"},"prerenderWithAsyncData":true},"from":{"name":null,"path":"/","hash":"","query":{},"params":{},"fullPath":"/","meta":{}}},"dropsState":{"submitEmailResponse":false,"status":"initial"},"profileState":{"auth":{},"userOptions":{},"status":"success"}}

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

$Book image$

Explore Book Buy On Amazon

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.

This article can be found in the category:

Basic Math ,