3-4 Dividing Rational Numbers

Transcription

1 1. Find the multiplicative inverse of each number. 5. of is multiplicative inverses. To find the multiplicative inverse of a mixed number, first write the mixed number as an improper fraction. = So, the multiplicative inverse of is of 63 is. Find each quotient. Write in simplest form esolutions Manual - Powered by Cognero Page 1

2 ALGEBRA Find each quotient. Write in simplest form. 10. MULTIPLE CHOICE 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? A 12. B 8 C D 190 To find the number of squares Sonia will need, divide the width of the wall hanging, 38 inches, by the width 13. of each quilt square, inches. 14. Find the multiplicative inverse of each number. Sonia will need 8 squares. So, Choice B is the correct answer. of is. esolutions Manual - Powered by Cognero Page 2

3 Find each quotient. Write in simplest form. of is or. 16. multiplicative inverses. To find the multiplicative inverse of a mixed number, first write the mixed number as an improper fraction. 21. = So, the multiplicative inverse of is multiplicative inverses. To find the multiplicative inverse of a mixed number, first write the mixed number as an improper fraction. = So, the multiplicative inverse of is of 19 is of 54 is. esolutions Manual - Powered by Cognero Page 3

4 COOKING Hannah is making chocolate chip cookies. How many batches of cookies can she make if she has recipe card. cups of brown sugar? Use the 26. To find the number of batches Hannah can make, divide the amount of brown sugar she has, cups, by the amount of brown sugar needed for one batch, cups. Hannah can make 5 batches of cookies. esolutions Manual - Powered by Cognero Page 4

5 29. DRAMA CLUB How many play costumes can be made with yards of fabric if each costume requires yards? 32. To find the number of costumes that can be made, divide the total amount of fabric, yards, by the amount of fabric needed for each costume, yards So, 12 costumes can be made. ALGEBRA Find each quotient. Write in simplest form. 34. BABYSITTING Barbara babysat for hours and earned $ What was her hourly rate? To find Barbara s hourly rate, divide the amount she earned, $19.50, by the number of hours she babysat, hours. First write as a mixed number = Then, divide. 31. So, Barbara earned $6 per hour. esolutions Manual - Powered by Cognero Page 5

6 35. TRAINS A train traveled 405 miles in hours. How fast was the train traveling on average? (Hint: distance equals the rate multiplied by the time.) To find how fast the train was traveling on average, divide the total distance, 405 miles, by the time, ALGEBRA Evaluate each expression if m =, n =, and p = mn p hours. So, the train was traveling 90 miles per hour on average. 36. PHOTOS Sydney reduced her favorite photograph to put in a scrapbook. How many times as wide is the actual photo than the reduced photo? 38. To find how many times as wide the actual photo is than the reduced photo, divide the width of the actual photo by the width of the reduced photo. 4 3 = So, the actual photo is photo. as wide as the reduced esolutions Manual - Powered by Cognero Page 6

7 39. np m 41. The model below shows. How many s are in? There s in. 40. TIE DYE Ms. Augello is making tie dye shirts with The model below shows. her students. Each gallon of hot water needs cup How many s are in? of tie dye. If Ms. Augello has cups of tie dye, how many batches of solution will she be able to make? To find the number of batches Ms. Augello will be able to make, divide the total amount of dye, batch, cups, by the amount of dye needed for one cup. 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: As the value of the divisor increases, the quotient decreases. = 6 So, Ms. Augello will be able to make 7 batches. = 3 = esolutions Manual - Powered by Cognero Page 7

8 42. OPEN ENDED Choose two fractions and use an area model or number line to show that division of rational numbers is not commutative. 44. WRITING IN MATH 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 40. So, division of rational numbers is not commutative. 43. CHALLENGE Give a counterexample to this statement. The quotient of two fractions between 0 and 1 is always a whole number. The quotient of two fractions between 0 and 1 is not always a whole number. The quotient of. The fraction is not a whole number. is 45. REASONING Is a whole number divided by a proper fraction always, sometimes, or never greater than the whole number? A whole number divided by a fraction is always greater than the whole number. For example,. 46. WRITING IN MATH Explain why, for a positive number n, > n. When a number is divided by a fraction, it is multiplied by the fraction s multiplicative inverse. So, if n is positive 2n > n. esolutions Manual - Powered by Cognero Page 8

9 47. 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 12 D (12) To find whether Heidi has made enough snack mix for her guests, divide the total amount of snack mix, 12 cups, by the amount she thinks each guest will 49. A recipe for one batch of soft pretzels calls for cup of salt and cup of sugar. If Mrs. Valdez used cup of salt and cups of sugar, how many batches of pretzels has she made? A B 3 C D 2 To find the number of batches Mrs. Valdez made, either divide the total amount of salt she used, cup, by the amount of salt needed for each batch, eat, cup. So, Choice C is the correct answer. cup, or, divide the total amount of sugar she used, 48. 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 To find how many plants Mr. Henderson will be able to plant, divide the total amount of potting soil, cups, by the amount of sugar needed for each batch, cup. Mrs. Valdez made batches of pretzels. So, Choice A is the correct answer. pounds, by the amount needed for each plant, pound. Mr. Henderson will be able to plant 34 flowers. So, Choice J is the correct answer. esolutions Manual - Powered by Cognero Page 9

10 50. 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. 53. To find how many times as large the regular bag of popcorn is than the snack bag, divide the amount in the regular bag by the amount in the snack bag So, the regular bag of popcorn is as the snack bag. times as large 51. Find each product. Write in simplest form esolutions Manual - Powered by Cognero Page 10

11 57. WHITE HOUSE The White House covers an area of square mile. What fraction of a square mile is this? The number is 28 thousandths = or So, the White House covers of a square mile. 58. SPORTS 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. To find the number of yards the football team was penalized each time, divide the total number of yards penalized by 4. This can be written as 60 4 = y, where y represents the number of yards penalized each time. So, the number of yards of each penalty is 15. Find each product ( 6) The product of two integers with different signs is negative. So, 12 ( 6) = 72. Find each sum or difference ( 13) ( 26) 42 + ( 26) = ( 80) 65. n + 2n n + 2n = 3n 66. 4x ( 3x) 67. 5n 10n ( 11) The product of two integers with the same sign is positive. So, 12( 11) = ( 2)( 6) esolutions Manual - Powered by Cognero Page 11