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Solving Proportions - Ratios and Cross Products

Learn how to solve proportions by finding ratios that are equivalent using cross products. Practice examples and quizzes included.

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Solving Proportions - Ratios and Cross Products

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  1. 6 10 , 9 15 5 6 , 16 18 , 3 2 , Warm Up Find two ratios that are equivalent to each given ratio. Possible answers: 10 12 20 24 3 5 1. 2. 45 30 90 60 24 27 8 9 3. 4.

  2. Solving Proportions 7.4 Pre-Algebra

  3. Learn to solve proportions. …A Proportion is an equation that shows 2 ratios are equivalent…

  4. Vocabulary cross product

  5. Cross Products

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

  7. 6 15 6 15 4 10 4 10 ? = Example: 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.

  8. 4 parts gasoline 1 part oil ? 15 quarts gasoline 5 quarts oil = Example: 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.

  9. 5 10 5 10 2 4 2 4 ? = Try This Tell whether the ratios are proportional. A. 20 Find cross products. 20 20 = 20 Since the cross products are equal, the ratios are proportional.

  10. 3 parts tea 1 part sugar ? 12 tablespoons tea 4 tablespoons sugar = Try This 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? Set up ratios. Find the cross products. 3 • 4 = 12 1 • 12 = 12 12 = 12 The ratios are equal. The mixture will be correct.

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

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

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

  14. miles 2 hours 2 miles 1 hours 1 = 38600 1 x .5 = Example: distance = rate x time 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. 38600 • .5 = 1x Multiply. 19,300 = x Voyager I travels 19,300 miles in a half hour.

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

  16. 48 42 20 15 16 14 3 4 ? ? = = 6 9 n 12 n 24 45 18 = = Lesson Quiz Tell whether each pair of ratios is proportional. yes 1. 2. no Solve each proportion. 3. n = 30 4. n = 16 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? 2.5 cups of milk

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

  18. Try This Write 2 equal rates of miles to gallons. 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. 3600 mi x gal 30 mi 1 gal Writing & Solving Proportions Solve the proportion. = Find the cross products. 30x = 3600 • 1 Solve by dividing both sides by 30. 30x = 3600 x = 120 Check Cross Product to make sure equal.

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

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

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