Cross Products
Part of the Decimals, Percents & Ratios section of Coddy's Pre-Algebra journey. Lesson 48 of 56.
In a proportion a/b = c/d, multiply across the equals sign: the top left by the bottom right, and the bottom left by the top right. These cross products are always equal: a × d = b × c. In 3/4 = 9/12, the cross products are 3 · 12 and 4 · 9, and both are 36.
Why does it work? Give both fractions the same bottom, 4 · 12 = 48. Then 3/4 is 36 over 48 and 9/12 is also 36 over 48. The new tops are exactly the cross products, 3 · 12 and 9 · 4. Equal fractions with the same bottom must have the same top, so the cross products match.
That makes cross products a quick test of whether two ratios are equal, with no simplifying. Are 4/6 and 10/15 equal? 4 · 15 is 60 and 6 · 10 is 60, so yes. Are 3/4 and 5/7? 3 · 7 is 21 but 4 · 5 is 20, so no.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Decimals, Percents & Ratios
4Dividing Decimals
Dividing by a DecimalDividing by 10 and 100Dividing by a Whole NumberUnit PriceRecap: Dividing7Percent Problems
Finding the WholeDiscountsTax and TipsPercent IncreasePercent DecreaseRecap: Percent Problems10Proportions
Solving a ProportionCross ProductsScale DrawingsPercent as a ProportionRecap: Proportions