1. Cross Products and Proportions
Proportion: two ratios that are equal.
Cross Products: checks to see if ratio’s are proportional. Multiply opposite numerator and denominators together. If they equal , the ratio’s are proportional.
Proportions
Cross Product 3 2 3 2 = = 6 4 6 4
3 ∙ 4 = 6 ∙ 2
12 = 12

2. Are the following ratios Proportional?5 1 8 10 = = 15 3 5 6
5 ∙ 3 = 15 ∙ 1
8 ∙ 6 = 5 ∙ 10
15 = 15
48 = 50
Yes No 6 9 6 4 = = 8 12 9 6
8 ∙ 9 = 6 ∙ 12
6 ∙ 6 = 9 ∙ 4
72 = 72
36 = 36
Yes
Yes

3. Proportions with a variable
To solve a proportion that contains a variable, you find the value that makes the equation true.
Cross Product to solve 3 x 3 x = = 6 4 6 4
3 ∙ 4 = 6x
12 = 6x
12 ÷ 6 = 6x ÷ 6
2 = x

4. Solve each proportion 3 2 10 x = = x 6 12 6
3 ∙ 6 = 2x
10 ∙ 6 = 12x
18 = 2x
60 = 12x
18 ÷ 2 = 2x ÷ 2
60 ÷ 12 = 12x÷12
9 = x
5 = x