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. … A Proportion is an equation that shows 2 ratios are equivalent …

4. cross product Vocabulary

5. Cross Products

6. The cross product represents the product of the extremes is equal to the product of the means. Helpful Hint means 2:6 = 3:9 extremes

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. 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

11. 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

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

13. Solve the proportion. 14 3 = 2g 21 = g 42 = 2g Find the cross products. Solve by dividing both sides by 2. 2323 14 g = ; the proportion checks. 2323 14 21 = Try This

14. Voyager I travels through space at about 38,600 mph. At that rate, about how far would Voyager I travel in a half hour? Set up the proportion. Let x represent the unknown distance. Find the cross products. Multiply. Voyager I travels 19,300 miles in a half hour. 19,300 = x 38600.5 = 1x x.5 38600 1 = miles 1 hours 1 = miles 2 hours 2 Example: distance = rate x time

15. If apples sell at 3 for $.75, how many apples can be bought with $4.25?.75x.75 12.75.75 = 17 = x Set up the proportion. Let x represent the unknown amount of apples Find the cross products. Multiply. Solve by dividing both sides by.75 $4.25 will buy 17 apples. 12.75 =.75x 4.25 3 =.75x x 4.25 3.75 = apples cost = Try This apples cost

16. Tell whether each pair of ratios is proportional. 48 42 = ? 16 14 1. 20 15 = ? 3434 2. Solve each proportion. 3.4. 5. A cake recipe calls for 1.5 cups of milk and 3 cups of flour. Mrs. Perona made a mistake and used 5 cups of flour. How many cups of milk should she use to keep the proportions correct? yes no n = 30 n = 16 2.5 cups of milk 45 18 n 12 = n 24 6969 = Lesson Quiz

17. Writing Proportions When you write a proportion, be sure that 2 equivalent ratios compare similar things…

18. Write 2 equal rates of miles to gallons. Try This Mrs. Perona gets 30 miles to a gallon of gas. At that given rate, how many gallons would Mrs. Perona use on a 3600 mile trip? Use cross product to solve…

19. Solve the proportion. 30x = 3600 1 x = 120 30x = 3600 Find the cross products. Solve by dividing both sides by 30. 3600 mi x gal 30 mi 1 gal Writing & Solving Proportions = Check Cross Product to make sure equal.

20. Writing Proportions Bob delivers 4 newspapers in 5 minutes. At this rate, how many newspapers can he deliver in 1 hour. x 60 4545 = Newpapers minutes x = 48 Newspapers

21. More Practice… Go to Workbook and Practice some more! 11-4 Proportions 11-5 Solve Proportions 11-6 Write Proportions