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Using Cross Products

This lesson explores the concept of cross products in proportional relationships. When two ratios are equivalent, their cross products are equal. For example, the ratios 4:3 and 12:9 form a proportion since their cross products (12 x 3 and 9 x 4) yield the same result (36). Conversely, ratios such as 5:2 and 8:3 do not form a proportion due to differing cross products (16 and 15). Students will learn how to solve proportions by setting up equations using cross products and applying inverse operations to isolate variables.

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Using Cross Products

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  1. Using Cross Products Lesson 6-4

  2. Cross Products • When you have a proportion (two equal ratios), then you have equivalent cross products. • Find the cross product by multiplying the denominator of each ratio by the numerator of the other ratio.

  3. Example: Do the ratios form a proportion? Check using cross products. 4 3 , 12 9 These two ratios DO form a proportion because their cross products are the same. 12 x 3 = 36 9 x 4 = 36

  4. Example 2 5 2 , 8 3 No, these two ratios DO NOT form a proportion, because their cross products are different. 8 x 2 = 16 3 x 5 = 15

  5. Solving a Proportion Using Cross Products • Use the cross products to create an equation. • Solve the equation for the variable using the inverse operation.

  6. Example: Solve the Proportion Start with the variable. 20 k = 17 68 Simplify. Now we have an equation. To get the k by itself, divide both sides by 68. 68k 17(20) = 68k = 340 68 68 k 5 =

  7. Homework Time

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