3-4 Dividing Rational Numbers

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1 1. Find the multiplicative inverse of each number Sonia is making a quilted wall hanging that is 38 inches wide. If each quilt square is inches wide, how many squares will she need to complete one row of the wall hanging? 8 squares esolutions Manual - Powered by Cognero Page 1

2 Find the multiplicative inverse of each number or 26. esolutions Manual - Powered by Cognero Page 2

3 Hannah is making chocolate chip cookies. The dry ingredients are show below. How many batches of cookies can she make if she has sugar? cups of brown batches 35. How many play costumes can be made with yards of fabric if each costume requires yards? 12 costumes esolutions Manual - Powered by Cognero Page 3

4 np m 46. Ms. Augello is making tie dye shirts with her 40. Barbara babysat for hours and earned $ What was her hourly rate? $6/hour 41. A train traveled 405 miles in hours. How fast was the train traveling on average? (Hint: Distance equals the rate multiplied by the time.) 90 mph 42. Sydney reduced her favorite photograph to put in a scrapbook. How many times as wide is the actual photo than the reduced photo? students. Each gallon of hot water needs tie dye. If Ms. Augello has cup of cups of tie dye, how many batches of solution will she be able to make? 7 batches 47. Make a Conjecture The model below shows. How many s are in? There are s in. The model below shows. Evaluate each expression if m =, n =, How many s are in? and p = mn p There are 3 s in. Make a conjecture about what happens to the quotient as the value of the divisor increases. Test your conjecture. Sample answer: The quotient decreases; = 6. esolutions Manual - Powered by Cognero Page 4

5 48. Use Math Tools Choose two fractions and use an area model or number line to show that division of rational numbers is not commutative. Sample answer: 52. Building on the Essential Question Explain why, for a positive number n, > n. Sample answer: = 2n, so if n is positive 2n > n. 53. Heidi is having a party. She is planning that each of her 16 guests will have cup of snack mix. She has made 12 cups of snack mix. Which expression could Heidi use to determine if she has made enough snack mix for each of her guests? A 16 B C Persevere with Problems Give a counterexample to this statement. The quotient of two fractions between 0 and 1 is always a whole number. Sample answer: is, and is not a whole number. 50. Construct an Argument Which is greater or? Explain. ; 40 multiplied by a number less than 1 will be a number less than 40. However, 40 divided by a number less than 1 will be a number greater than Identify Structure Is a whole number divided by a proper fraction always, sometimes, or never greater than the whole number? always D (12) C 54. A bag of potting soil contains pounds of soil. Each flower that Mr. Henderson plants will need pound of soil. How many flowers will he be able to plant? F 16 G 28 H 32 J 34 J esolutions Manual - Powered by Cognero Page 5

6 55. A recipe for one batch of soft pretzels calls for cup of salt and cup of sugar. If Mrs. Valdez uses cup of salt and cups of sugar, how many batches of pretzels is she making? A B 3 C D 2 A 56. SHORT RESPONSE Popcorn is sold in a variety of sizes. Use the table to find how many times as large the regular bag of popcorn is than the snack bag or Find each product. Write in simplest form The White House covers an area of square mile. What fraction of a square mile is this? mi The Wildcat football team was penalized the same amount four times during the third quarter. The total of the four penalties was 60 yards. If 60 represents a loss of 60 yards, write a division sentence to represent this situation. Then express the number of yards of each penalty as an integer = y; 15 Find each product ( 6) 72 esolutions Manual - Powered by Cognero Page 6

7 66. 12( 11) ( 2)( 6) 48 Find each sum or difference ( 13) Divide the sum of 10 and 15 by Subtract the sum of 3 and 5 from (3 + 5) ( 26) ( 80) n + 2n 3n 72. 4x ( 3x) 1x or x 73. 5n 10n 5n Translate each of the following to a mathematical expression. 74. Add 7 and 5, and then multiply the result by 3. 3(7 + 5) 75. Subtract the quotient of 6 and 3 from 12. esolutions Manual - Powered by Cognero Page 7

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