Pre-Algebra Chapter 6 - Ramsey School District

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Cross products can be used to determine whether two ratios form a proportion. • Words The cross products of a proportion are equal. • Symbols If b a d c , then ad bc. If ad bc, then b a d c . Property of Proportions Example 1 Identify Proportions Determine whether each pair of ratios forms a proportion. a. 1 3 , 3 9 b. 1 . 2 , 2 4. 0 5 1 3 3 9 Write a proportion. 1 . 2 2 4. 0 5 Write a proportion. 1 9 3 3 Cross products 1.2 5 4.0 2 Cross products 9 9 Simplify. 6 8 Simplify. So, 1 3 3 9 . So, 1 . 2 2 4. 0 5 . Study Tip Cross Products When you find cross products, you are cross multiplying. Example 2 Solve Proportions Solve each proportion. a 52 a. b. 1 2.5 15 7 2 5 1 00 m . 5 a 52 1 2.5 15 7 2 5 1 00 m . 5 a 100 25 · 52 Cross products 12.5 7.5 m 15 Cross products 100a 1300 Multiply. 93.75 15m Multiply. 1 00 10 a 0 30 1 0 0 0 . 75 1 1 5m 5 15 Divide. a 13 6.25 m The solution is 13. The solution is 6.25. USE PROPORTIONS TO SOLVE REAL-WORLD PROBLEMS When you solve a problem using a proportion, be sure to compare the quantities in the same order. Example 3 Use a Proportion to Solve a Problem FOOD Refer to the recipe at the beginning of the lesson. How much soda should be used if 16 ounces of each type of juice are used? Explore You know how much soda to use for 12 ounces of each type of juice. You need to find how much soda to use for 16 ounces of each type of juice. Plan www.pre-alg.com/extra_examples Write and solve a proportion using ratios that compare juice to soda. Let s represent the amount of soda to use in the new recipe. (continued on the next page) Lesson 6-2 Using Proportions 271
TEACHING TIP Solve juice in original recipe soda in original recipe 53 1 3 juice in new recipe soda in new recipe 1 2 1 6 40 s Write a proportion. 12 s 40 16 Cross products 12s 640 Multiply. 1 2s 12 40 1 2 Divide. s 53 1 3 ounces of soda should be used. Simplify. Explore Check the cross products. Since 12 53 1 640 and 40 16 640, 3 the answer is correct. Proportions can also be used in measurement problems. Attractions The world’s largest baseball bat is located in Louisville, Kentucky. It is 120 feet long, has a diameter from 3.5 to 9 feet, and weighs 68,000 pounds. Source: World’s Largest Roadside Attractions Example 4 Convert Measurements ATTRACTIONS Louisville, Kentucky, is home to the world’s largest baseball glove. The glove is 4 feet high, 10 feet long, 9 feet wide, and weighs 15 tons. Find the height of the glove in centimeters if 1 ft 30.48 cm. Let x represent the height in centimeters. customary measurement → 1 ft 4 ft ← customary measurement metric measurement → 30. 48 cm x cm ← metric measurement 1 x 30.48 4 Cross products x 121.92 Simplify. The height of the glove is 121.92 centimeters. Concept Check Guided Practice GUIDED PRACTICE KEY 1. Define proportion. 2. OPEN ENDED Find two counterexamples for the statement Two ratios always form a proportion. Determine whether each pair of ratios forms a proportion. 3. 1 4 , 4 4. 2 . 1 , 3 16 3. 5 7 ALGEBRA Solve each proportion. k 5. 3 3 5 7 6. 3 t 1 8 10 5 7. 24 8 . 4 m Application 8. PHOTOGRAPHY A3” 5” photo is enlarged so that the length of the new photo is 7 inches. Find the width of the new photo. 272 <strong>Chapter</strong> 6 Ratio, Proportion, and Percent
Page 1 and 2: Ratio, Proportion, and Percent •
Page 3 and 4: Ratios and Rates Vocabulary • rat
Page 5 and 6: Study Tip Look Back To review dimen
Page 7 and 8: Standardized Test Practice Extendin
Page 9: Using Proportions Vocabulary • pr
Page 13 and 14: 41. SNACKS The Skyway Snack Company
Page 15 and 16: Scale Drawings and Models Vocabular
Page 17 and 18: Interior Designer Interior designer
Page 19 and 20: 21. CRITICAL THINKING What does it
Page 21 and 22: To write a fraction as a percent, w
Page 23 and 24: Practice and Apply Homework Help Fo
Page 25 and 26: A Preview of Lesson 6-5 Using a Per
Page 27 and 28: Using the Percent Proportion • Us
Page 29 and 30: Example 4 Find the Part What number
Page 31 and 32: 25. LIFE SCIENCE Carbon constitutes
Page 33 and 34: Find the percent of each number men
Page 35 and 36: Practice and Apply Homework Help Fo
Page 37 and 38: Using Percent Equations Vocabulary
Page 39 and 40: Simple interest is the amount of mo
Page 41 and 42: 42. CRITICAL THINKING Determine whe
Page 43 and 44: Percent of Change Vocabulary • pe
Page 45 and 46: PERCENT OF DECREASE When the amount
Page 47 and 48: Standardized Test Practice 26. RESE
Page 49 and 50: Probability and Predictions Vocabul
Page 51 and 52: USE A SAMPLE TO MAKE PREDICTIONS No
Page 53 and 54: Standardized Test Practice 37. FOOD
Page 55 and 56: Vocabulary and Concept Check base (
Page 57 and 58: Chapter 6 Study Guide and Review 6-
Page 59 and 60: • Extra Practice, see pages 736-7
Page 61 and 62:
Part 1 Record your answers on the a
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Pre-Algebra Chapter 6 - Ramsey School District

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