1. Course 3 5-4 Solving Proportions 5-4 Solving Proportions Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Course 3 5-4 Solving Proportions Warm Up 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:

3. Course 3 5-4 Solving Proportions Problem of the Day Replace each with a digit from 1 to 7 to write a proportion. Use each digit once. The digits 2 and 3 are already shown. 2 3 = 147147 2 3 56 = Possible answer:

4. Course 3 5-4 Solving Proportions Learn to solve proportions.

5. Course 3 5-4 Solving Proportions Vocabulary cross product

6. Course 3 5-4 Solving Proportions 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 proportion is true: mass 2 length 1 mass 1 length 2 = Mass 1 Mass 2 Fulcrum Length 1Length 2

7. Course 3 5-4 Solving Proportions One way to find whether ratios, such as those on the previous slide, are equal is to find a common denominator. Since and,. 72 96 6868 = 72 96 9 12 = 9 12 6868 =

8. Course 3 5-4 Solving Proportions

9. Course 3 5-4 Solving Proportions The cross product represents the numerator of the fraction when a common denominator is found by multiplying the denominators. Helpful Hint

10. Course 3 5-4 Solving Proportions Tell whether the ratios are proportional. 4 10 6 15 Since the cross products are equal, the ratios are proportional. 60 = ? Additional Example 1A: Using Cross Products to Identify Proportions 60 = 60 Find cross products. 60 4 10 6 15

11. Course 3 5-4 Solving 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? 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 equal ratios. Find the cross products. Additional Example 1B: Using Cross Products to Identify Proportions

12. Course 3 5-4 Solving Proportions Tell whether the ratios are proportional. Check It Out: Example 1A Since the cross products are equal, the ratios are proportional. 20 20 = 20 Find cross products. 20 2424 5 10 2424 5 10 = ?

13. Course 3 5-4 Solving Proportions 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? Check It Out: Example 1B 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 equal ratios. Find the cross products.

14. Course 3 5-4 Solving Proportions Solve the proportion. x ÷ 15 = 16 Find the unit rates. The numerators are equal because the denominators are equal. Additional Example 2: Solving Proportions Using Unit Rates $48 3 items $x 15 items = $16 1 item $(x ÷ 15) 1 item = Multiply both sides by 15. 15(x ÷ 15) = 16(15) x = 240 Simplify.

15. Course 3 5-4 Solving Proportions Solve the proportion. x ÷ 18 = 15 Find the unit rates. The numerators are equal because the denominators are equal. Check It Out: Example 2 $60 4 items $x 18 items = $15 1 items $(x ÷ 18) 1 item = Multiply both sides by 18. 18(x ÷ 18) = 15(18) x = 270 Simplify.

16. Course 3 5-4 Solving Proportions Solve the proportion. 1y = 7 Multiply to write the fractions with the LCD. The numerators are equal because the denominators are equal. 1313 y 21 = Divide both sides by 1. 7171 1y11y1 = Additional Example 3: Using Equivalent Fractions = (y 1) (21 1) (1 7) (3 7) 1y 21 = 7 21 y = 7Simplify.

17. Course 3 5-4 Solving Proportions Solve the proportion. 1y = 12 Multiply to write the fractions with the LCD. The numerators are equal because the denominators are equal. 3434 y 16 = Divide both sides by 1. 12 1 1y11y1 = Check It Out: Example 3 = (y 1) (16 1) (3 4) (4 4) 1y 16 = 12 16 y = 12Simplify.

18. Course 3 5-4 Solving Proportions J & A Department Store is selling 3 pairs of children’s socks for $5. Mrs. Wagner wants to buy a dozen pairs of socks. How much will this cost? 12 pairs 3 pairs = 4 4 x $5 = $20 Set up the proportion. Divide to find the factor of change. A dozen pairs of socks will cost $20. Additional Example 4: Business Application 3 pairs $5.00 = 12 pairs $d 1 dozen pairs of socks = 12 pairs of socks Multiply by the factor of change to find cost.

19. Course 3 5-4 Solving Proportions The Hardware Store is selling 6 light bulbs for $7. Mr. Raynold wants to buy 3 dozen light bulbs. How much will this cost? 36 bulbs 6 bulbs = 6 6 x $7 = $42 Set up the proportion. Divide to find the factor of change. 3 dozen light bulbs will cost $42. Check It Out: Example 4 6 bulbs $7.00 = 36 bulbs $d 3 dozen light bulbs = 36 light bulbs Multiply by the factor of change to find cost.

20. Course 3 5-4 Solving Proportions 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? 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. Additional Example 5: Physical Science Application 220 = 5x 55 4 = 5x x4x4 55 5 = mass 1 length 2 = mass 2 length 1

21. Course 3 5-4 Solving Proportions Robert weighs 90 lbs and sits on a seesaw 5 ft away from its center. If Sharon sits 6 ft away from the center and the seesaw is balanced, how much does Sharon weigh? Check It Out: Example 5 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 6. Sharon weighs 75 lb. 450 = 6x 90 5 = 6x x5x5 90 6 = mass 1 length 2 = mass 2 length 1

22. Course 3 5-4 Solving Proportions Lesson Quiz Tell whether each pair of ratios is proportional. 48 42 = ? 16 14 1. 40 15 = ? 3434 2. Solve each proportion. 3.4. 5. Two weights are balanced on a fulcrum. If a 6 lb 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? yes no n = 30 n = 16 0.5 ft 45 18 n 12 = n 24 6969 =