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Solving Proportions: Ratios and Cross Products

Learn how to solve proportions using ratios and cross products. Identify equivalent ratios and determine if ratios are proportional. Solve proportions when one of the four numbers is unknown. Apply proportions in physical science.

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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.

  4. Vocabulary cross product

  5. Cross Products

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

  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. 48 42 20 15 16 14 3 4 ? ? = = Lesson Quiz Tell whether each pair of ratios is proportional. yes 1. 2. no

  11. 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.

  12. 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.

  13. 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. 6p = 60 p = 10

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

  15. n 12 6 9 45 18 n 24 = = Lesson Quiz Solve each proportion. 3. n = 30 4. n = 16

  16. pounds length pounds length = 220 5 55 5 5x 5 x 4 = = Example: Physical Science Application 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? 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.

  17. pounds length pounds length = 450 6 90 6 6x 6 x 5 = = Try This 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? Set up the proportion. Let x represent Sharon’s weight. 90 • 5 = 6x Find the cross products. 450 = 6x Multiply. Solve. Divide both sides by 5. 75 = x Sharon weighs 75 lb.

  18. Lesson Quiz 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

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