3.6 Solve Proportions Using Cross Products Cross product: The product of the numerator of one ratio and the denominator of the other ratio. 3

4 = 6

x Cross Multiply 3

4 = 6

x Example: 4(6) = 3(x) Cross product.

24 = 3x Simplify.

3 3 Divide each side by 3.

8 = x Check your answer by substituting 8 for x in the original proportion. 3

4 = 6

8 3

4 = 6

8 Original Proportion Cross

Multiply 4(6) = 8(3) 24 = 24 Simplify Example: 5m

6 10

12 = 6(10) = 12(5m) Original proportion Cross product 60 = 60m

60 = 60 Simplify Divide each side by 60 1 = m 4

x 8

x-3 Example: = 4

x 8

x-3 = Cross Multiply 4(x-3) = 8(x) 4x-12 = 8x

-4x -4x Distributive Property Simplify Subtract 4x from both sides -12 = 4x

4x 4x Simplify -3 = x Divide 4x from both sides a) b) c) Practice Problems: x-3

25 x-5

35 = 18

24 3

x = 3m

9 12

18 = a) 18

24 3

x = = 18(x) = 24(3) 18x = 72

18 18 x = 4 b) x-3

25 x+5

35 = = 35(x-3) = 25(x+5) 35x-105 = 25x+125

-25x -25x

10x-105 = 125

+105 +105

10x = 230

10 10 x = 23 3m

9 12

18 c) = = 18(3m) = 12(9) 54m = 108

54 54 m = 2 Story Problem: A recipe that makes 12 biscuits calls for 2 cups of flour. How much flour does it take to make 30 biscuits? Answer: 5 cups of flour

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# Solve Proportions Using Cross Products

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