{"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. 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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: