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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