1. Find two ratios that are equivalent to each given ratio. 3535 1. 45 30 3. 90 60 3232, 10 12 2. 20 24 5656, 8989 4. 24 27 16 18, 9 15 6 10, Possible answers: Warm Up

2. Pre-Algebra 7.4 Solving Proportions

3. Learn to solve proportions.

4. cross product Vocabulary

5. Cross Products

6. The cross product represents the numerator of the fraction when a common denominator is found by multiplying the denominators. Helpful Hint

7. Tell whether the ratios are proportional. 4 10 6 15 A. Since the cross products are equal, the ratios are proportional. 60 = ? 60 = 60 Find cross products. 60 4 10 6 15 Example: Using Cross Products to Identify Proportions

8. A mixture of fuel for a certain small engine should be 4 parts gasoline to 1 part oil. If you combine 5 quarts of oil with 15 quarts of gasoline, will the mixture be correct? 4 parts gasoline 1 part oil = ? 15 quarts gasoline 5 quarts oil 4 5 = 201 15 = 15 20 ≠ 15 The ratios are not equal. The mixture will not be correct. Set up ratios. Find the cross products. Example: Using Cross Products to Identify Proportions

9. Tell whether the ratios are proportional. Since the cross products are equal, the ratios are proportional. 20 20 = 20 Find cross products. 20 2424 5 10 2424 5 10 A. = ? Try This

10. Tell whether each pair of ratios is proportional. 48 42 = ? 16 14 1. 20 15 = ? 3434 2. yes no Lesson Quiz

11. A mixture for a certain brand of tea should be 3 parts tea to 1 part sugar. If you combine 4 tablespoons of sugar with 12 tablespoons of tea, will the mixture be correct? 3 parts tea 1 part sugar = ? 12 tablespoons tea 4 tablespoons sugar 3 4 = 121 12 = 12 12 = 12 The ratios are equal. The mixture will be correct. Set up ratios. Find the cross products. Try This

12. When you do not know one of the four numbers in a proportion, set the cross products equal to each other and solve. Solving with Cross-Products

13. Solve the proportion. 6p = 12 5 p = 10 6p = 60 Find the cross products. Solve. 5656 p 12 = ; the proportion checks. 5656 10 12 = Example: Solving Proportions

14. Solve the proportion. 14 3 = 2g 21 = g 42 = 2g Find the cross products. Solve. 2323 14 g = ; the proportion checks. 2323 14 21 = Try This

15. Solve each proportion. 3.4.n = 30 n = 16 45 18 n 12 = n 24 6969 = Lesson Quiz

16. Allyson weighs 55 lbs and sits on a seesaw 5 ft away from its center. If Marco sits 4 ft away from the center and the seesaw is balanced, how much does Marco weigh? 5x55x5 220 5 = 44 = x Set up the proportion. Let x represent Marco’s weight. Find the cross products. Multiply. Solve. Divide both sides by 5. Marco weighs 44 lb. 220 = 5x 55 4 = 5x x4x4 55 5 = pounds length = pounds length Example: Physical Science Application

17. Robert weighs 90 lbs and sits on a seesaw 6 ft away from its center. If Sharon sits 5 ft away from the center and the seesaw is balanced, how much does Sharon weigh? 6x66x6 450 6 = 75 = x Set up the proportion. Let x represent Sharon’s weight. Find the cross products. Multiply. Solve. Divide both sides by 5. Sharon weighs 75 lb. 450 = 6x 90 5 = 6x x5x5 90 6 = pounds length = pounds length Try This

18. 5. Two weights are balanced on a fulcrum. If a 6lb weight is positioned 1.5 ft from the fulcrum, at what distance from the fulcrum must an 18 lb weight be placed to keep the weights balanced? 0.5 ft Lesson Quiz