{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2018-02-13T02:22:14+00:00","modifiedTime":"2023-06-06T18:16:37+00:00","timestamp":"2023-06-06T21:01:02+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":"Pre-Algebra: Cross-Multiply to Solve Equations","strippedTitle":"pre-algebra: cross-multiply to solve equations","slug":"pre-algebra-practice-questions-cross-multiply-solve-equations","canonicalUrl":"","seo":{"metaDescription":"When an algebraic equation contains fractions, you can use cross-multiplication to solve the equation. The following practice questions contain two equal fracti","noIndex":0,"noFollow":0},"content":"When an algebraic equation contains fractions, you can use cross-multiplication to solve the equation. The following practice questions contain two equal fractions, where you need to cross-multiply to solve them.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n \t<li>Rearrange the equation<img class=\"alignnone size-full wp-image-249972\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3301.gif\" alt=\"PREALGEBRA_3301\" width=\"80\" height=\"45\" />\r\n\r\nto solve for <em>x</em>.</li>\r\n \t<li>Solve the equation<img class=\"alignnone size-full wp-image-249973\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3302.gif\" alt=\"PREALGEBRA_3302\" width=\"108\" height=\"45\" /></li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n \t<li><em>x</em> = –4Remove the fraction from the equation by cross-multiplying:\r\n\r\n<img class=\"alignnone size-full wp-image-249974\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3303.gif\" alt=\"PREALGEBRA_3303\" width=\"101\" height=\"79\" />\r\n\r\nMultiply to remove the parentheses from the left side of the equation:\r\n\r\n8<em>x</em> + 40 = –2<em>x</em>\r\n\r\nAt this point, you can solve for <em>x</em>:\r\n\r\n<img class=\"alignnone size-full wp-image-249975\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3304.gif\" alt=\"PREALGEBRA_3304\" width=\"108\" height=\"124\" /></li>\r\n \t<li><em>x</em> = 5Remove the fractions from the equation by cross-multiplying:\r\n\r\n<img class=\"alignnone size-full wp-image-249976\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3305.gif\" alt=\"PREALGEBRA_3305\" width=\"189\" height=\"79\" />\r\n\r\nRemove the parentheses from the left side of the equation by multiplying through by <em>x</em>; remove parentheses from the right side of the equation by FOILing:\r\n\r\n4<em>x</em><sup>2</sup> – 7<em>x</em> = 4<em>x</em><sup>2</sup> – 10<em>x</em> + 6<em>x</em> – 15\r\n\r\nRearrange the equation:\r\n\r\n4<em>x</em><sup>2</sup> – 7<em>x</em> – 4<em>x</em><sup>2</sup> + 10<em>x</em> – 6<em>x</em> = –15\r\n\r\nNotice that the two <em>x</em><sup>2</sup> terms cancel each other out:\r\n\r\n<img class=\"alignnone size-full wp-image-249977\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3306.gif\" alt=\"PREALGEBRA_3306\" width=\"147\" height=\"124\" /></li>\r\n</ol>","description":"When an algebraic equation contains fractions, you can use cross-multiplication to solve the equation. The following practice questions contain two equal fractions, where you need to cross-multiply to solve them.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n \t<li>Rearrange the equation<img class=\"alignnone size-full wp-image-249972\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3301.gif\" alt=\"PREALGEBRA_3301\" width=\"80\" height=\"45\" />\r\n\r\nto solve for <em>x</em>.</li>\r\n \t<li>Solve the equation<img class=\"alignnone size-full wp-image-249973\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3302.gif\" alt=\"PREALGEBRA_3302\" width=\"108\" height=\"45\" /></li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n \t<li><em>x</em> = –4Remove the fraction from the equation by cross-multiplying:\r\n\r\n<img class=\"alignnone size-full wp-image-249974\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3303.gif\" alt=\"PREALGEBRA_3303\" width=\"101\" height=\"79\" />\r\n\r\nMultiply to remove the parentheses from the left side of the equation:\r\n\r\n8<em>x</em> + 40 = –2<em>x</em>\r\n\r\nAt this point, you can solve for <em>x</em>:\r\n\r\n<img class=\"alignnone size-full wp-image-249975\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3304.gif\" alt=\"PREALGEBRA_3304\" width=\"108\" height=\"124\" /></li>\r\n \t<li><em>x</em> = 5Remove the fractions from the equation by cross-multiplying:\r\n\r\n<img class=\"alignnone size-full wp-image-249976\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3305.gif\" alt=\"PREALGEBRA_3305\" width=\"189\" height=\"79\" />\r\n\r\nRemove the parentheses from the left side of the equation by multiplying through by <em>x</em>; remove parentheses from the right side of the equation by FOILing:\r\n\r\n4<em>x</em><sup>2</sup> – 7<em>x</em> = 4<em>x</em><sup>2</sup> – 10<em>x</em> + 6<em>x</em> – 15\r\n\r\nRearrange the equation:\r\n\r\n4<em>x</em><sup>2</sup> – 7<em>x</em> – 4<em>x</em><sup>2</sup> + 10<em>x</em> – 6<em>x</em> = –15\r\n\r\nNotice that the two <em>x</em><sup>2</sup> terms cancel each other out:\r\n\r\n<img class=\"alignnone size-full wp-image-249977\" src=\"https://www.dummies.com/wp-content/uploads/PREALGEBRA_3306.gif\" alt=\"PREALGEBRA_3306\" width=\"147\" height=\"124\" /></li>\r\n</ol>","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> earned degrees in mathematics and English from Rutgers University. He is the founder of SimpleStep Learning, an online educational platform that teaches courses in basic concepts in ten minutes or less, keeping students engaged and learning in every moment. Mark is also author of several other successful <i>For Dummies</i> books.</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":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":"Practice questions","target":"#tab1"},{"label":"Answers and explanations","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using 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Pre-Algebra: Cross-Multiply to Solve Equations

By: Mark Zegarelli and

Updated: 06-06-2023

From The Book: Basic Math & Pre-Algebra Workbook For Dummies with Online Practice

Basic Math & Pre-Algebra Workbook For Dummies with Online Practice

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When an algebraic equation contains fractions, you can use cross-multiplication to solve the equation. The following practice questions contain two equal fractions, where you need to cross-multiply to solve them.

Practice questions

Rearrange the equation
to solve for x.
Solve the equation

Answers and explanations

x = –4Remove the fraction from the equation by cross-multiplying:
Multiply to remove the parentheses from the left side of the equation:
8x + 40 = –2x
At this point, you can solve for x:
x = 5Remove the fractions from the equation by cross-multiplying:
Remove the parentheses from the left side of the equation by multiplying through by x; remove parentheses from the right side of the equation by FOILing:
4x² – 7x = 4x² – 10x + 6x – 15
Rearrange the equation:
4x² – 7x – 4x² + 10x – 6x = –15
Notice that the two x² terms cancel each other out: