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Understanding Cross Products in Proportions: Lesson 6.4

In Lesson 6.4, we explore the concept of cross products and their role in determining the equivalence of ratios. When two ratios form a proportion, their cross products will be equal. We demonstrate how to find cross products by multiplying the numerator of one ratio with the denominator of the other and vice versa. Through examples, we illustrate how to check if ratios form a proportion and how to solve for unknowns using cross products. This lesson provides essential skills for handling proportions in mathematics.

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Understanding Cross Products in Proportions: Lesson 6.4

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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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