Master Proportions Easily in Pre-Algebra

1. Learn to solve proportions. 7-4 Solving Proportions Pre-Algebra

2. 6 8 9 12 6 8 9 12 72 96 72 96 7-4 Solving Proportions = = = Pre-Algebra One way to find whether ratios are equal is to find a common denominator. The ratios are equal if their numerators are equal after the fractions have been rewritten with a common denominator.

3. 7-4 Solving Proportions Pre-Algebra

4. Helpful Hint 7-4 Solving Proportions The cross product represents the numerator of the fraction when a common denominator is found by multiplying the denominators. Pre-Algebra

5. 6 15 6 15 ? 4 10 4 10 7-4 Solving Proportions = Pre-Algebra Example 1A: Using Cross Products to Identify Proportions Tell whether the ratios are proportional. A. 60 Find cross products. 60 60 = 60 Since the cross products are equal, the ratios are proportional.

6. 4 parts gasoline 1 part oil ? 15 quarts gasoline 5 quarts oil 7-4 Solving Proportions = Pre-Algebra Example 1B: Using Cross Products to Identify Proportions 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? Set up ratios. Find the cross products. 4 • 5 = 20 1 • 15 = 15 20 ≠ 15 The ratios are not equal. The mixture will not be correct.

7. 7-4 Solving Proportions Pre-Algebra When you do not know one of the four numbers in a proportion, set the cross products equal to each other and solve.

8. 10 12 5 6 p 12 5 6 7-4 Solving Proportions = ; the proportion checks. = Pre-Algebra Example 2: Solving Proportions Solve the proportion. 6p = 12 • 5 Find the cross products. Solve. 6p = 60 p = 10

9. 6 8 9 12 6 8 9 12 72 96 72 96 7-4 Solving Proportions = = = Pre-Algebra One way to find whether ratios are equal is to find a common denominator. The ratios are equal if their numerators are equal after the fractions have been rewritten with a common denominator.

10. 7-4 Solving Proportions Pre-Algebra

11. 5 10 5 10 ? 2 4 2 4 7-4 Solving Proportions = Pre-Algebra Try This: Example 1A Tell whether the ratios are proportional. A. 20 Find cross products. 20 20 = 20 Since the cross products are equal, the ratios are proportional.

12. 7-4 Solving Proportions Pre-Algebra When you do not know one of the four numbers in a proportion, set the cross products equal to each other and solve.

13. 14 21 2 3 14 g 2 3 7-4 Solving Proportions = ; the proportion checks. = Pre-Algebra Try This: Example 2 Solve the proportion. 14 • 3 = 2g Find the cross products. Solve. 42 = 2g 21 = g

14. mass 1 length 2 mass 2 length 1 Mass 2 7-4 Solving Proportions = Mass 1 Length 1 Length 2 Fulcrum Pre-Algebra Unequal masses will not balance on a fulcrum if they are an equal distance from it; one side will go up and the other side will go down. Unequal masses will balance when the following proportions is true:

15. 220 5 55 5 mass 2 length 1 5x 5 x 4 mass 1 length 2 7-4 Solving Proportions = = = Pre-Algebra Example 3: Physical Science Application Allyson weighs 55 lbs and sits on a seesaw 4 ft away from its center. If Marco sits 5 ft away from the center and the seesaw is balanced, how much does Marco weigh? Set up the proportion. Let x represent Marco’s weight. 55 • 4 = 5x Find the cross products. 220 = 5x Multiply. Solve. Divide both sides by 5. 44 = x Marco weighs 44 lb.

16. 7-4 Solving Proportions Pre-Algebra

17. 6 15 6 15 ? 4 10 4 10 7-4 Solving Proportions = Pre-Algebra Example 1A: Using Cross Products to Identify Proportions Tell whether the ratios are proportional. A. 60 Find cross products. 60 60 = 60 Since the cross products are equal, the ratios are proportional.

18. 7-4 Solving Proportions Pre-Algebra When you do not know one of the four numbers in a proportion, set the cross products equal to each other and solve.

19. 10 12 5 6 p 12 5 6 7-4 Solving Proportions = ; the proportion checks. = Pre-Algebra Example 2: Solving Proportions Solve the proportion. 6p = 12 • 5 Find the cross products. Solve. 6p = 60 p = 10