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Page 1 of 4 The Distributive Property BEFORE Now You used order of operations to evaluate expressions. You’ll use the distributive So you can find the cost of a field property to evaluate expressions. trip, as in Ex. 6. WHY? In the Real World Word Watch distributive property, p. 159 Car Wash Your class held a two-day car wash to raise money. The class washed 40 cars on the first day and 30 cars on the second day. The class charged $5 for each car. How much money did the class raise? EXAMPLE 1 Evaluating Expressions Method 1 To answer the question above, first find the total number of cars washed. Then multiply to find the total amount raised. with Review Charge per car Total number of cars washed 5(40 30) 5(70) Remember that 5(70) is another way to write 5 70. 350 Method 2 To answer the question above, first find the amount raised each day. Then add to find the total amount raised. First day amount Second day amount 5 40 5 30 200 150 350 ANSWER Your class raised $350. The methods used in Example 1 show the distributive property . The Distributive Property Words You can multiply a number and a sum by multiplying the number by each part of the sum and then adding these products. The same property applies with subtraction. Numbers 3(4 6) 3(4) 3(6) 2(8 5) 2(8) 2(5) Algebra a(b c) ab ac a(b c) ab ac Lesson 4.2 The Distributive Property 159 Page 2 of 4 EXAMPLE 2 Using the Distributive Property a. 2(50 6) 2(50) 2(6) 100 12 86 24 112 62 Your turn now Use the distributive property to evaluate. 1. 2(17 10) EXAMPLE b. 10(8.6 2.4) 10(8.6) 10(2.4) 2. 7(20 3) 3 3. 100(6.8 4) 4. 0.5(24 18) Evaluating Using Mental Math a. To find 6(87), rewrite 87. b. To find 8(6.1), rewrite 6.1. 6(87) 6(90 3) 8(6.1) 8(6 0.1) 6(90) 6(3) 8(6) 8(0.1) 540 18 48 0.8 522 48.8 Science EXAMPLE 4 Using a Formula Astronomy The Hubble Telescope orbits Earth at a rate of about 4.78 miles per second. How far does the telescope travel in 3 seconds? Solution Use the formula Distance Rate Time. Distance (4.78)3 ■ Astronomy The Hubble Space Telescope is a satellite that takes photographs of outer space and sends them to Earth. The telescope was launched on April 24, 1990. Traveling at about 5 miles per second, how far does the telescope travel in 1 day? in 1 year? 160 Chapter 4 Use 4.78 for the rate and 3 for the time. (5 0.22)3 Rewrite 4.78 as 5 0.22. (5)3 (0.22)3 Use the distributive property. 15 0.66 Multiply. 14.34 Subtract. ANSWER The telescope travels about 14.34 miles in 3 seconds. Your turn now Use mental math to find the product. 5. 8(53) Decimal Multiplication and Division 6. 4(97) 7. 3(12.8) 8. 7(1.4) Page 3 of 4 INTERNET Exercises eWorkbook Plus CLASSZONE.COM More Practice, p. 711 Getting Ready to Practice 1. Vocabulary Rewrite the expression 2(3.1 7.4) using the distributive property. Copy and complete the statement using the distributive property. 2. 3(40 5) 3(_?_) _?_(5) 3. 7(50 2) 7(_?_) _?_(2) 4. 6(7 5.4) 6(_?_) _?_(5.4) 5. 8(3.2 9) 8(_?_) _?_(9) 6. Field Trip A class of 30 students is taking a field trip to a museum. The cost for each student is $9 for admission plus $5 more for the laser show. How much money is needed to pay for all the students to see the museum and the laser show? Practice and Problem Solving Use the distributive property to evaluate the expression. 7. 4(80 3) 8. 6(7 50) 9. 2(39 10) 11. 6(8.2 3) 12. 8(3.1 5.7) 13. 10(4.8 2.7) 14. 14(8.1 6) 15. 3(90 0.6) 16. 9(7 0.11) 17. 7(13 0.02) 19. Find the Error Describe and 10. 15(2 9) 18. 12(3 0.4) 2(32 6) 2(32) 6 correct the error in the solution. 64 6 70 with Example 1 2 3 4 Homework Exercises 7–18, 33 7–23 22–32 33, 37 Online Resources CLASSZONE.COM • More Examples • eTutorial Plus Copy and complete the statement. 20. 5(30 0.2) 5(30) _?_(0.2) 21. 7(40 8) _?_(40) _?_(8) 22. 4(7.9) 4(8 _?_) 23. 3(67) 3(_?_ 7) Use the distributive property and mental math to find the product. 24. 6(37) 25. 7(98) 26. 3(85) 27. 9(41) 28. 8(5.7) 29. 5(9.2) 30. 9(7.3) 31. 7(6.9) 32. Find the product 7(2.006) using the distributive property. 33. Lunch Costs For each day of school, you pay $2.50 for lunch and $.45 for milk. How much money do you spend in 5 days? Lesson 4.2 The Distributive Property 161 Page 4 of 4 U.S. Mint In Exercises 34–36, use the table. It shows what it cost to produce some U.S. coins in two different years. Currency 34. Evaluate the expression 50(2.0 1.6) to find how much more it cost to produce 50 dimes in 2000 than in 1995. 35. Evaluate the expression 50(0.8 0.7) to find how much more it cost to produce 50 pennies in 2000 than in 1995. Coin Penny Nickel Dime Quarter 1995 0.7¢ 2.74¢ 1.6¢ 3.65¢ 2000 0.8¢ 3.0¢ 2.0¢ 5.0¢ 36. Write an expression to find how much more it cost to produce 50 nickels in 2000 than in 1995. Then evaluate the expression. 37. Geometry Use the formula P 2(l w) to find the perimeter of a flower box with length 27 inches and width 6 inches. ■ Algebra Use the distributive property to rewrite the expression. For example, 2(x 4) 2x 8. U.S. Mint Coins are minted in Philadelphia and in Denver. Coins minted in Denver have a “D” on the front. Coins minted in Philadelphia have a “P” on the front. Do you think people in your class have coins from Denver or Philadelphia? Why? 38. 3(x 7) 39. 5(x 5.2) 40. 6(4 x) Challenge Rewrite the expression as a product using parentheses. 41. 4x 4y 42. 0.9m 0.9n 43. 5.5x 5.5y 5.5 Mixed Review Order the numbers from least to greatest. (Lesson 3.3) 44. 2.1, 2.9, 2.8, 2.6 45. 7.63, 7.06, 7.61, 7.6 46. 0.5, 0.55, 0.05, 0.005 Evaluate the expression when x 3.1 and y 5.62. (Lesson 3.6) 47. x 2.83 48. x y 49. y 3.092 Basic Skills Round to the place value of the red digit. 50. 63,498 51. 32,921 52. 204,238 Test-Taking Practice INTERNET State Test Practice CLASSZONE.COM 53. Multiple Choice Which expression is equal to 4(2 6)? A. 2(4 6) B. 4 2 6 C. 4 2 6 D. 4 2 4 6 54. Multiple Choice Which expression is equal to 2(4.9)? F. 2(4 9) 162 Chapter 4 Decimal Multiplication and Division G. 2(4 0.9) H. 2 4 9 I. 2(5 1)