Copyright 2013 Edmentum - All rights reserved.

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1 Division with Fractions 1. Solve the following. Copyright 2013 Edmentum - All rights reserved. Volume 2. A stick of butter has a length of 8 inches, a width of 2 inches, and a height of 2 inches. What is the volume of the stick of butter? 32 cubic inches 64 cubic inches 72 cubic inches 36 cubic inches Division with Fractions 3. Solve the following. Volume 4. Which measurement shows how much space is inside a rectangular prism? volume 1/31

2 6/14/13 volume Printable Worksheet area faces perimeter Division with Fractions 5. Solve the following. Multiplication with Fractions 6. Which of the following equations is modeled by the figure above? Multiplication with Fractions 7. Multiplication with Fractions 8. Solve. 2/31

3 8. Solve. Representing & Interpreting Data 9. A cellular phone company collected data about how much time customers spend on the phone. The line plot displays the fraction of an hour customers spent on the phone on one day. If the total number of hours were equally divided among the customers, what fraction of an hour would each customer have talked on the phone? Time Customers Spent on the Phone Multiplication with Fractions 10. Which of the following fractions makes the number sentence true? Units of Measure 11. Convert to cups: 5 pints 2.5 cups 3/31

4 1.25 cups 50 cups 10 cups Division with Fractions 12. Solve the following. Units of Measure 13. Convert to centimeters: 400 millimeters 40 centimeters 4 centimeters 4,000 centimeters 0.4 centimeter Units of Measure 14. Given that 1 pound = 16 ounces, convert 48 ounces to pounds. 5 pounds 19 pounds 2 pounds 3 pounds Units of Measure 15. Convert to tons: 14,000 pounds 7 tons 70 tons 0.35 tons 0.7 tons Units of Measure 16. Convert to meters: 43 km 43,000 m 4,300 m 430 m 4/31

5 430 m 430,000 m Units of Measure 17. Convert to yards. 18 feet 72 yards 6 yards 216 yards 1.8 yards Problem Solving with Fractions 18. Crystal bought a 5-foot roll of ribbon. How many -foot pieces are in the 5-foot roll? Volume 19. If each cube in the rectangular prism measures 1 cubic inch, what is the volume of the prism? 60 cubic in 23 cubic in 55 cubic in 47 cubic in Problem Solving with Fractions 20. Susanna found a roll of fabric she wanted to use to make a pillow. The roll had of a yard of fabric left. Susanna needed of the remaining fabric. Which fraction represents how much fabric Susanna needed? of a yard of a yard yards yards Division with Fractions 21. Solve the following. 5/31

6 Units of Measure 22. Convert to inches: 4 feet 16 inches 12 inches 40 inches 48 inches Problem Solving with Fractions 23. While cleaning the attic, Yuyan found some money. She decided to divide of the money equally among her 4 favorite charities. How much of the money Yuyan found did each charity receive? Units of Measure 24. Elijah needed to dig a row along a fence that was 5 feet long. He was able to dig all but 47 inches of the row before dark. How many inches was he able to dig before dark? (Hint: 1 foot = 12 inches) Division with Fractions 25. Which expression is equivalent to? 6/31

7 Problem Solving with Fractions 26. Multiplication with Fractions 27. Which of the following is not equivalent to the expression below? Division with Fractions 28. Which expression is equivalent to? Division with Fractions 29. Solve the following. 7/31

8 Problem Solving with Fractions 30. Bowie used cup of raspberries and cup of blueberries to make a berry smoothie. How much fruit did he use in total? of a cup of a cup of a cup of a cup Problem Solving with Fractions 31. What is the area of the figure above? Multiplication with Fractions 32. The product of and is shown on the grid below. 8/31

9 Based on the grid, what is the product of and? Representing & Interpreting Data 33. For her science project, Sylvia collected flowers and measured their length. The line plot displays the lengths of the flowers. If the flowers were laid end to end, what is the total length of all the flowers? Length of Flowers Volume 34. A moving company wants to buy a new type of truck and needs to know the volume of the storage compartment before they can decide if they should purchase the truck. What is the volume of the storage compartment? 1,224 ft3 1,244 ft3 1,238 ft3 1,248 ft3 9/31

10 1,248 ft3 Representing & Interpreting Data 35. Jenny's math class is learning about fractions. The teacher has placed several partially filled water bottles on her desk. The number of bottles and amount of water each one is filled with is shown below. How much water will be in each bottle if the total amount of water is equally divided among the bottles? Volume 36. Before Emilia purchases a new bookshelf, she wants to make sure it will hold her books. If the bookshelf is 5 inches deep, what is the volume of the bookshelf? 1,200 in3 224 in3 640 in3 1,120 in3 Problem Solving with Fractions 37. While painting her room, Paige noticed she needed of a can of paint to paint one wall. The second wall needed of a can of paint. How much paint was used to cover both walls? of a can of paint of a can of paint of a can of paint 10/31

11 of a can of paint Units of Measure 38. Convert to meters: 6,000 centimeters 0.6 meter 600 meters 60 meters 6 meters Division with Fractions 39. Solve the following. Units of Measure 40. A roll of fabric was 144 inches long. A customer bought 3 feet of the fabric. How many feet of fabric were remaining? (Hint: 1 foot = 12 inches) Volume 41. If each cube in the rectangular prism measures 1 cubic centimeter, what is the volume of the prism? 8 cubic cm 12 cubic cm 24 cubic cm 6 cubic cm 11/31

12 6 cubic cm Division with Fractions 42. Solve the following. Representing & Interpreting Data 43. In the cafeteria, a principal asked students what fraction of their plates contained vegetables. The following table shows the data. Fraction of a Plate Number of Students If each dot represents 1 student, which dot plot matches the table? W. X. Y. Z. W Z Y X Representing & Interpreting Data 44. A cellular phone company collected data about how much time customers spend on the phone. The following 12/31

13 44. A cellular phone company collected data about how much time customers spend on the phone. The following table shows the data. Fraction of an Hour Number of Customers If each dot represents 1 customer, which dot plot matches the table? W. X. Y. Z. Z Y X W Multiplication with Fractions 45. Solve. 13/31

14 Representing & Interpreting Data 46. A banking Web site asks customers what fraction of their money they spend on housing. The line plot displays the customers' responses. What fraction of customers spend of their money on housing? Money Spent on Housing Multiplication with Fractions 47. Multiplication with Fractions 48. The product of and is shown on the grid below. Based on the grid, what is the product of and? 14/31

15 Problem Solving with Fractions 49. Stephen budgets of his money to spend on movies and music. Last month, he spent of the budgeted amount. How much of his total budget did he spend on movies and music last month? Problem Solving with Fractions 50. Tyrone, James, and Michael are training for a 10-kilometer race. After 30 minutes of a training run, Michael lead the group, and James had run of Michael's distance. Tyrone had run the distance James ran. Which fraction of Michael's distance did Tyrone run? Representing & Interpreting Data 51. A mall manager asks the store owners what fraction of their products are on sale. The store owners' responses are displayed on the line plot. What fraction of the stores have or less of their products on sale? Mall Stores Sale Items Representing & Interpreting Data 52. A restaurant is considering reducing its meal sizes, because it noticed many of its customers cannot finish their meals. The manager decided to weigh the left-over portion of the meals before putting them in to-go containers. The line plot displays the weights of the left-over portions of the meals. If the left-over portions are divided 15/31

16 The line plot displays the weights of the left-over portions of the meals. If the left-over portions are divided equally among the customers, how much food would each customer take home? Weight of Left-over Meals Volume 53. If each cube in the rectangular prism measures 1 cubic inch, what is the volume of the prism? 40 cubic in 168 cubic in 84 cubic in 144 cubic in Volume 54. If each cube in the rectangular prism measures 1 cubic foot, what is the volume of the prism? 8 cubic ft 7 cubic ft 6 cubic ft 11 cubic ft Volume /31

17 A swimming pool has a length of 26 feet, a width of 18 feet, and a depth of 7 feet. How much water can the swimming pool hold? 1,552 cubic feet 3,276 cubic feet 6,552 cubic feet 776 cubic feet Multiplication with Fractions 56. If five is multiplied by a fraction greater than one, which of the following is true about the product? The product is less than five. The product is equal to five. The product is greater than five. Representing & Interpreting Data 57. A baseball stadium reported the fraction of fans who bought hot dogs at each game throughout the season. The line plot displays hot dog sales data for each game. At what fraction of the games did more than of fans buy hot dogs? Hot Dog Sales at Baseball Games Volume 58. If each cube in the rectangular prism measures 1 cubic centimeter, what is the volume of the prism? 12 cubic cm 11 cubic cm 10 cubic cm 17 cubic cm 17/31

18 17 cubic cm Problem Solving with Fractions 59. Caterers made 266 cups of punch for a party. They will distribute the punch equally into 6 bowls. How many cups of punch will each bowl have? Representing & Interpreting Data 60. A popular online music store allowed shoppers to listen to an entire album before buying it. Of the people who listened to the whole album, the store tracked what fraction of the album each person actually bought. The line plot displays the fraction of the album each shopper bought. What fraction of the shoppers bought less than the album? Portion of an Album Purchased of Answers 1. B 2. A 3. C 4. A 5. A 6. A 7. A 8. C 9. A 10. B 11. D 12. C 13. A 14. D 15. A 16. A 17. B 18/31

19 17. B 18. B 19. A 20. B 21. D 22. D 23. A 24. C 25. D 26. D 27. D 28. D 29. C 30. A 31. A 32. A 33. D 34. D 35. C 36. D 37. C 38. C 39. A 40. A 41. A 42. A 43. C 44. B 45. B 46. A 47. A 48. D 49. C 50. C 51. A 52. D 53. D 54. C 55. B 56. C 57. A 58. C 59. C 60. C Explanations 1. When dividing a fraction by a whole number, start off by converting the whole number to a fraction,. Now the problem is. To divide a fraction by a fraction, flip the second fraction and multiply. 2. The volume of a rectangular prism is given by the formula: V = L W H. V = L W H = 8 in 2 in 2 in = 32 cubic in The volume of the stick of butter is 32 cubic inches. 19/31

20 The volume of the stick of butter is 32 cubic inches. 3. When dividing a fraction by a whole number, start off by converting the whole number to a fraction,. Now the problem is. To divide a fraction by a fraction, flip the second fraction and multiply. 4. Volume is the space taken up by a 3-dimensional object, such as a box. 5. When dividing a whole number by a fraction, start off by converting the whole number to a fraction,. Now the problem is. To divide a fraction by a fraction, flip the second fraction and multiply. 6. Each section of the figure has of it shaded. Since there are 5 sections, the figure shows. When all of the shaded pieces are combined, there are 10 shaded pieces that each represent. So, the solution is. Therefore, the following equation is modeled by the figure. 7. To multiply fractions, multiply the numerators together and the denominators together. Then, if possible, simplify the result. 8. First, write 5 as a fraction:. Next, multiply the numerators, and then the denominators: 9. Multiply the number of dots in each column by the value of each column. 20/31

21 Add the values together. Finally, divide 10 by the total number of customers, 24. If the total hours talked were equally divided among the customers, each customer would have talked hour. of an 10. When a number is multiplied by a fraction, the solution is equal to the given number if the fraction is equal to one, less than the given number if the fraction is less than one, and greater than the given number if the fraction is greater than one. Since the solution should be greater than the given number, the fraction multiplied should be greater than one. The only fraction greater than one is. 11. Since there are 2 cups in 1 pint, multiply 5 pints by 2 to convert to cups. 5 pints 2 cups/pint = 10 cups 12. When dividing a fraction by a whole number, start off by converting the whole number to a fraction,. Now the problem is. To divide a fraction by a fraction, flip the second fraction and multiply. 13. Since there are 10 millimeters in 1 centimeter, divide 400 millimeters by 10 to convert to centimeters. 400 millimeters 10 millimeters/centimeter = 40 centimeters 14. Since there are 16 ounces in 1 pound, divide 48 ounces by 16 to convert to pounds. 48 ounces 16 ounces/pound = 3 pounds 15. Since there are 2,000 pounds in 1 ton, divide 14,000 pounds by 2,000 to convert to tons. 14,000 lb 2,000 lb/ton = 7 tons 16. Since there are 1,000 meters in 1 kilometer, multiply 43 kilometers by 1,000 to convert to meters. 43 km 1,000 m/km = 43,000 m 21/31

22 43 km 1,000 m/km = 43,000 m 17. Since there are 3 feet in 1 yard, divide 18 feet by 3 to convert to yards. 18 feet 3 feet/yard = 6 yards 18. To find how many -foot pieces are in the 5-foot roll, divide 5 by. So, there are 20 -foot pieces in the 5-foot roll? 19. To find the volume of the figure, multiply the length, width, and height. First, multiply the length and width to find the number of cubes of one layer. This value is also the area of the base. Now, multiply this product by the height, or number of layers. Multiply 5 by 4 to determine the number of cubes in one layer. Then, multiply by 3 layers. V = l w h V = V = 60 cubes Each cube has a volume of 1 cubic inch. So, the volume of the figure is 60 cubic in. 20. The roll has of a yard left, and Susanna needs of it. To find out how much fabric she needs, multiply by. Susanna needs of a yard. 21. When dividing a whole number by a fraction, start off by converting the whole number to a fraction,. Now the problem is. To divide a fraction by a fraction, flip the second fraction and multiply. 22. Since there are 12 inches in 1 foot, multiply 4 feet by 12 to convert to inches. 22/31

23 22. Since there are 12 inches in 1 foot, multiply 4 feet by 12 to convert to inches. 4 feet 12 inches/foot = 48 inches 23. Yuyan divided of the money she found equally among 4 charities. So, Yuyan donated of the money to each charity. 24. Use the fact that 1 foot = 12 inches. Change 5 feet into inches by multiplying by 12 inches per foot. 5 feet 12 inches per foot = 60 inches Then, subtract 47 inches from 60 inches. 60 inches - 47 inches = 13 inches So, Elijah was able to dig 13 inches before dark. 25. A number expressed as a fraction is equivalent to the numerator divided by the denominator. Since 14 is the numerator and 29 is the denominator, the correct answer is To find which is not equivalent, simplify each of the expressions and find which one is different. So, the only expression that is not equivalent is below. 28. A number expressed as a fraction is equivalent to the numerator divided by the denominator. Since 9 is the numerator and 10 is the denominator, the correct answer is. 29. When dividing a whole number by a fraction, start off by converting the whole number to a fraction,. Now the problem is. 23/31

24 To divide a fraction by a fraction, flip the second fraction and multiply. 30. To find the total amount of fruit, add the two amounts using a common denominator. Bowie used of a cup of fruit for his smoothie. 31. From the key, find the area of 1 square. Since there are 12 squares in the figure, multiply this by 12 to find the area of the figure. Another way to find the area is just to multiply the length and the width. From the figure, the length is cm and the width is cm. Notice both methods give the same answer. 32. Start by examining the model. There are 6 columns and one is shaded. This represents. There are 3 rows and one has a pattern. This represents. Now, look at the space that is shaded by both and. This area represents the product of and. So, the product of and is, as shown by the model. 33. To find the total number of feet in each column, multiply the number of dots in each column by the value of each column. 24/31

25 Now, add the total number of feet in each column. The total length of the flowers is feet. 34. Divide the figure into rectangular prisms. Calculate the volume of the two rectangular prisms. 2 ft 18 ft 8 ft = 288 ft 3 8 ft 15 ft 8 ft = 960 ft 3 To find the volume of the storage compartment, add the two volumes. 288 ft ft 3 = 1,248 ft 3 The volume of the storage compartment is 1,248 ft Multiply the number of dots in each column by the value of each column. Add the values together. Finally, divide the sum, 3, by the total number of bottles, 6. If the water was equally divided among 6 bottles, each bottles would hold of a liter. 36. Divide the figure into rectangles. 25/31

26 Calculate the areas of the two rectangles. 20 in 8 in = 160 in 2 16 in 4 in = 64 in 2 Add the two areas together to find the area of the bookshelf. 160 in in 2 = 224 in 2 To find the volume of the bookshelf, multiply the area by 5 in, or the depth of the bookshelf. 224 in 2 5 in = 1,120 in 3 The volume of the bookshelf is 1,120 in To find the total amount of paint used, add the two amounts using a common denominator. Paige used of a can of paint. 38. Since there are 100 centimeters in 1 meter, divide 6,000 centimeters by 100 to convert to meters. 6,000 centimeters 100 centimeters/meter = 60 meters 39. When dividing a fraction by a whole number, start off by converting the whole number to a fraction,. Now the problem is. To divide a fraction by a fraction, flip the second fraction and multiply. 40. Use the fact that 1 foot = 12 inches. Change 144 inches into feet by dividing by 12 inches per foot. 144 inches 12 inches per foot = 12 feet Then, subtract 3 feet from 12 feet. 12 feet - 3 feet = 9 feet So, 9 feet of fabric remained. 41. To find the volume of the figure, multiply the length, width, and height. 26/31

27 41. To find the volume of the figure, multiply the length, width, and height. First, multiply the length and width to find the number of cubes of one layer. This value is also the area of the base. Now, multiply this product by the height, or number of layers. Multiply 2 by 2 to determine the number of cubes in one layer. Then, multiply by 2 layers. V = l w h V = V = 8 cubes Each cube has a volume of 1 cubic centimeter. So, the volume of the figure is 8 cubic cm. 42. When dividing a whole number by a fraction, start off by converting the whole number to a fraction,. Now the problem is. To divide a fraction by a fraction, flip the second fraction and multiply. 43. There were 5 students with of a plate of vegetables. There were 9 students with There were 6 students with of a plate of vegetables. of a plate of vegetables. The only dot plot that matches up with the information in the table is Y. 44. There were 5 customers who spend of an hour on the phone. There were 5 customers who spend of an hour on the phone. There were 5 customers who spend of an hour on the phone. There were 2 customers who spend of an hour on the phone. There were 2 customers who spend of an hour on the phone. 27/31

28 There were 3 customers who spend There were 2 customers who spend of an hour on the phone. of an hour on the phone. The only dot plot that matches up with the information in the table is Y. 45. First, write 18 as a fraction:. Next, multiply the numerators, and then the denominators: 46. Count the dots in the column. Of the 20 customers, 6 spend of their money on housing. Express these customers as a fraction of all customers. Of all the customers, spend of their money on housing. 47. To multiply fractions, multiply the numerators together and the denominators together. Then, if possible, simplify the result. 48. Start by examining the model. There are 4 columns and three are shaded. This represents. There are 2 rows and one has a pattern. This represents. Now, look at the space that is shaded by both and. This area represents the product of and. So, the product of and is, as shown by the model. 49. Stephen can spend of his money on movies and music each month. Last month, he did not spend all of the amount. He only spent. To find how much of all his money he spent, multiply the two fractions together. 28/31

29 Last month, Stephen spent of his money on movies and music. 50. Tyrone ran of James' distance, and James ran of Michael's distance. To find how much of Michael's distance Tyrone ran, multiply the two distances together. Tyrone ran of Michael's distance. 51. Count the dots to the left of, and including, the column. Of the 26 stores, 13 had or less of their products on sale. Express these 13 stores as a fraction of the whole group. At the mall, of the stores had or less of their products on sale. 52. Multiply the number of dots in each column by the value of each column. Now, add the total weight in each column. The restaurant measured a total of 8 pounds of food. Finally, divide 8 by the total number of customers, 16. If the amount of food were equally divided among all 16 customers, they would each take home food. of a pound of 53. To find the volume of the figure, multiply the length, width, and height. First, multiply the length and width to find the number of cubes of one layer. This value is also the area of the base. Now, multiply this product by the height, or number of layers. Multiply 6 by 6 to determine the number of cubes in one layer. Then, multiply by 4 layers. V = l w h V = V = 144 cubes 29/31

30 Each cube has a volume of 1 cubic inch. So, the volume of the figure is 144 cubic in. 54. To find the volume of the figure, multiply the length, width, and height. First, multiply the length and width to find the number of cubes of one layer. This value is also the area of the base. Now, multiply this product by the height, or number of layers. Multiply 3 by 1 to determine the number of cubes in one layer. Then, multiply by 2 layers. V = l w h V = V = 6 cubes Each cube has a volume of 1 cubic foot. So, the volume of the figure is 6 cubic ft. 55. The volume of a rectangular prism is given by the formula: V = L W H. V = L W H = 26 ft 18 ft 7 ft = 3,276 cubic ft The swimming pool can hold 3,276 cubic feet of water. 56. When a number is multiplied by a fraction, it is multiplied by the numerator and divided by the denominator. If a fraction is greater than one, then the numerator is larger than the denominator. This means that the given number is multiplied by a number larger than the number it is being divided by. So, the product will be greater than the given number. In this case, that means if five is multiplied by a fraction greater than one, the product is greater than five. 57. Count the dots greater than, but not including,. At 9 of the 16 games, more than of fans bought hot dogs. So, more than of fans bought hot dogs at of games. 58. To find the volume of the figure, multiply the length, width, and height. First, multiply the length and width to find the number of cubes of one layer. This value is also the area of the base. Now, multiply this product by the height, or number of layers. 30/31

31 Multiply 5 by 2 to determine the number of cubes in one layer. Then, multiply by 1 layer. V = l w h V = V = 10 cubes Each cube has a volume of 1 cubic centimeter. So, the volume of the figure is 10 cubic cm. 59. To find how much punch will be in each bowl, divide 266 by 6. Therefore, each bowl will have cups of punch. 60. Count the dots less than, but not including,. Of the 18 shoppers, 8 bought less than of the album. Express as a fraction and reduce. So, of the shoppers bought less than of the album. 31/31