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# Ch. 7 Learning Goal: Ratios & Proportions

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1. Ch. 7 Learning Goal: Ratios & Proportions • Learn to find equivalent ratios to create proportions (7-1) • Learn to work with rates and ratios (7-2) • Learn to use one or more conversion factors to solve rate problems (7-3) • Learn to solve proportions (7-4) • Learn to identify and create dilations of plane figures (7-5) • Learn to determine whether figures are similar, to use scale factors, and to find missing dimensions similar figures (7-6) • Learn to make comparisons between and find dimensions of scale drawings and actual objects (7-7) • Learn to make comparisons between and find dimensions of scale models and actual objects (7-8) • Learn to make scale models of solid figures (7-9)

3. Pre-Algebra Homework Page 358 #15-28 Mid-Chapter 7 Chop Chop Quiz Tomorrow!

4. 7-4 Solving Proportions Warm Up Problem of the Day Lesson Presentation Pre-Algebra

5. 7-4 Solving Proportions 6 10 , 9 15 5 6 , 16 18 , 3 2 , Pre-Algebra 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.

6. Possible answer: 23 •• 23 56 •• • 14 7 = = 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.

7. Today’s Learning Goal Assignment Learn to solve proportions.

8. Vocabulary cross product

9. mass 1 length 2 mass 2 length 1 = Mass 2 Mass 1 Length 1 Length 2 Fulcrum 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:

10. 6 8 9 12 72 96 72 96 = = 6 8 9 12 = One way to find whether ratios, such as those above, 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.

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

12. 6 15 6 15 4 10 4 10 ? = Additional 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.

13. 4 parts gasoline 1 part oil ? 15 quarts gasoline 5 quarts oil = Additional 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.

14. 5 10 5 10 2 4 2 4 ? = 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.

15. 3 parts tea 1 part sugar ? 12 tablespoons tea 4 tablespoons sugar = Try This: Example 1B 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.

16. When you do not know one of the four numbers in a proportion, set the cross products equal to each other and solve.

17. 5 6 p 12 = 10 12 5 6 = ; the proportion checks. Additional Example 2: Solving Proportions Solve the proportion. 6p = 12 • 5 Find the cross products. Solve. 6p = 60 p = 10

18. 2 3 14 g = 14 21 2 3 = ; the proportion checks. Try This: Example 2 Solve the proportion. 14 • 3 = 2g Find the cross products. Solve. 42 = 2g 21 = g

19. mass 2 length 1 mass 1 length 2 = 220 5 55 5 5x 5 x 4 = = Additional 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.

20. mass 2 length 1 mass 1 length 2 = 450 6 90 6 6x 6 x 5 = = Try This: Example 3 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? 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.

21. 48 42 20 15 16 14 3 4 ? ? = = n 12 6 9 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. 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