Multi-Digit Division

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Answer Key & Explanations

Multi-Digit Division · Grade 5 · Worksheet 2

1. The school librarian needs to organize 1,728 new books equally onto 12 empty bookshelves. How many books will be placed on each shelf? Answer: 144 Solution: We are told there are 1,728 books and 12 empty bookshelves. We need to place the books equally on the shelves, so we must divide the total number of books by the number of shelves. Write the division problem.
   Full step-by-step solution

   We are told there are 1,728 books and 12 empty bookshelves. We need to place the books equally on the shelves, so we must divide the total number of books by the number of shelves. Step 1: Write the division problem. Total books = 1,728 Number of shelves = 12 So, books per shelf = 1728 ÷ 12 Step 2: Break down the division. First, check how many times 12 goes into the first two digits (17). 12 × 1 = 12, which is less than 17. 17 − 12 = 5. Step 3: Bring down the next digit (2) from 1728, making 52. Now, 12 × 4 = 48, which is less than 52. 52 − 48 = 4. Step 4: Bring down the last digit (8) from 1728, making 48. Now, 12 × 4 = 48 exactly. 48 − 48 = 0. Step 5: The quotient is 144. So, 1728 ÷ 12 = 144. This means each shelf will have 144 books. Answer: 144

2. Emma is planning a road trip and will drive a total of 29796 miles over 26 days. If Emma drives the same number of miles each day, how many miles will Emma drive per day? Answer: 1146 Solution: Note the total distance: 29796 miles. Note the number of days: 26 days. Divide the total miles by the number of days: 29796 ÷ 26.
   Full step-by-step solution

   Step 1: Note the total distance: 29796 miles. Step 2: Note the number of days: 26 days. Step 3: Divide the total miles by the number of days: 29796 ÷ 26. Step 4: Calculate the quotient: 29796 ÷ 26 = 1146. The answer is 1146 miles per day.

3. Eva is saving money for a bicycle that costs $53909. If Eva saves $47 each week, how many weeks will it take to save enough money? Answer: 1147 Solution: Divide the total cost (53909) by the amount saved each week (47). Calculate 53909 ÷ 47. Perform the division: 47 goes into 53909 exactly 1147 times (since 1147 × 47 = 53909).
   Full step-by-step solution

   Step 1: Divide the total cost (53909) by the amount saved each week (47). Step 2: Calculate 53909 ÷ 47. Step 3: Perform the division: 47 goes into 53909 exactly 1147 times (since 1147 × 47 = 53909). Step 4: It will take 1147 weeks to save enough money. The answer is 1147.

4. The city recreation department is organizing a community sports day. They have 1,680 bottles of water that need to be distributed equally among 24 different activity stations. How many bottles of water will each station receive? Answer: 70 Solution: Identify the total number of water bottles: 1,680 Identify the number of stations: 24 Set up the division problem: 1,680 ÷ 24 Divide 1,680 by 24 24 × 70 = 1,680 Therefore, 1,680 ÷ 24 = 70 The answer is 70.
   Full step-by-step solution

   Step 1: Identify the total number of water bottles: 1,680 Step 2: Identify the number of stations: 24 Step 3: Set up the division problem: 1,680 ÷ 24 Step 4: Divide 1,680 by 24 24 × 70 = 1,680 Step 5: Therefore, 1,680 ÷ 24 = 70 The answer is 70.

5. Aroha is creating a rectangular tile pattern on a coordinate grid. The pattern has corners at (0, 0), (84, 0), (84, 48), and (0, 48). She wants to divide the entire rectangle into identical square tiles by drawing vertical and horizontal lines, using the largest possible squares with whole-number side lengths, with no leftover space. What is the area of each square tile in square units? Answer: 144 Solution: Identify the dimensions from the coordinates. The length is 84 units (from x=0 to x=84) and the width is 48 units (from y=0 to y=48).
   Full step-by-step solution

   Step 1: Identify the dimensions from the coordinates. The length is 84 units (from x=0 to x=84) and the width is 48 units (from y=0 to y=48). Step 2: To divide the rectangle into identical squares with no leftover space, the side length of each square must be a common divisor of 84 and 48. Step 3: Find the greatest common divisor (GCD) of 84 and 48. List the factors: 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The largest common factor is 12. Step 4: So each square tile has a side length of 12 units. Step 5: Calculate the area of each square tile: side × side = 12 × 12 = 144 square units. Step 6: Check: Number of squares along length = 84 ÷ 12 = 7, along width = 48 ÷ 12 = 4, total squares = 7 × 4 = 28, total area = 28 × 144 = 4032 square units, which matches the rectangle's area (84 × 48 = 4032). The answer is 144.

6. Anna is organizing 66161 photographs into an album. Each page can hold exactly 96 photographs. How many full pages can Anna fill? Answer: 689 Solution: Start with 66161 photographs. Divide by 96 photographs per page: 66161 ÷ 96 = 689 with a remainder. The number of full pages is the whole number part: 689.
   Full step-by-step solution

   Step 1: Start with 66161 photographs. Step 2: Divide by 96 photographs per page: 66161 ÷ 96 = 689 with a remainder. Step 3: The number of full pages is the whole number part: 689. The answer is 689.

7. 1,215 ÷ 27 = ? Answer: 45 Solution: Set up the division: 1,215 ÷ 27. 27 does not go into 1 or 12, so consider 121. 27 × 4 = 108, which fits into 121.
   Full step-by-step solution

   Step 1: Set up the division: 1,215 ÷ 27. Step 2: 27 does not go into 1 or 12, so consider 121. 27 × 4 = 108, which fits into 121. Write 4 above the line. Step 3: Subtract 108 from 121: 121 - 108 = 13. Step 4: Bring down the next digit (5), making the new number 135. Step 5: 27 × 5 = 135, which fits perfectly. Write 5 above the line. Step 6: Subtract 135 from 135: 135 - 135 = 0. The final answer is 45.

8. 756 ÷ 12 = ? Answer: 63 Solution: Set up the division problem. We want to divide 756 by 12. Think of it as: how many times does 12 go into 756?
   Full step-by-step solution

   Let's solve 756 ÷ 12 step by step. Step 1: Set up the division problem. We want to divide 756 by 12. Think of it as: how many times does 12 go into 756? Step 2: Start with the first digit(s). The first digit is 7, but 12 is bigger than 7, so we take the first two digits: 75. Step 3: Divide 75 by 12. 12 × 6 = 72, which is less than 75. 12 × 7 = 84, which is too big. So, 12 goes into 75 six times. Write 6 above the 5 (tens place of the quotient). Step 4: Multiply and subtract. 6 × 12 = 72. 75 − 72 = 3. Step 5: Bring down the next digit. Bring down the 6 from 756, making the new number 36. Step 6: Divide 36 by 12. 12 × 3 = 36 exactly. So, write 3 above the 6 (units place of the quotient). Step 7: Multiply and subtract again. 3 × 12 = 36. 36 − 36 = 0. There is no remainder. Step 8: Conclusion. The quotient is 63. So, 756 ÷ 12 = 63.

9. The school library is organizing its book collection and needs to distribute 1,248 books equally among 8 classrooms. How many books will each classroom receive? Answer: 156 Solution: We need to divide 1,248 books equally among 8 classrooms. This means we perform the division: 1,248 ÷ 8. Set up the division.
   Full step-by-step solution

   We need to divide 1,248 books equally among 8 classrooms. This means we perform the division: 1,248 ÷ 8. Step 1: Set up the division. We can use long division: 8 into 1,248. Step 2: Divide 8 into the first digit (1). 1 is less than 8, so we take the first two digits: 12. 12 ÷ 8 = 1, since 8 × 1 = 8. Write 1 above the 2 in 12. Step 3: Subtract 8 from 12: 12 − 8 = 4. Step 4: Bring down the next digit (4) next to the 4, making 44. Now divide 8 into 44: 44 ÷ 8 = 5, because 8 × 5 = 40. Write 5 above the 4 in 1,248. Step 5: Subtract 40 from 44: 44 − 40 = 4. Step 6: Bring down the last digit (8) next to the 4, making 48. Now divide 8 into 48: 48 ÷ 8 = 6, because 8 × 6 = 48. Write 6 above the 8 in 1,248. Step 7: Subtract 48 − 48 = 0. There is no remainder. So, 1,248 ÷ 8 = 156. Each classroom will receive 156 books.