Multi-Digit Division

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Multi-Digit Division · Grade 5 · Worksheet 1

1. The school librarian needs to organize 1,248 new books equally onto 8 empty bookshelves. How many books will be placed on each shelf? Answer: 156 Solution: We are told there are 1,248 books to be placed equally on 8 shelves. This means we need to divide 1,248 by 8. Write the division problem.
   Full step-by-step solution

   We are told there are 1,248 books to be placed equally on 8 shelves. This means we need to divide 1,248 by 8. Step 1: Write the division problem. 1248 ÷ 8 Step 2: Divide step-by-step. First, 8 does not go into 1, so we consider the first two digits: 12. 12 ÷ 8 = 1 remainder 4. Write 1 above the 2 in 1248. Step 3: Bring down the next digit (4) next to the remainder 4, making 44. 44 ÷ 8 = 5 remainder 4. Write 5 above the 4 in 1248. Step 4: Bring down the last digit (8) next to the remainder 4, making 48. 48 ÷ 8 = 6 remainder 0. Write 6 above the 8 in 1248. Step 5: The quotient is 156. So, 1248 ÷ 8 = 156. Step 6: Interpret the result. Each shelf will have 156 books. Final answer: 156

2. A rectangular garden is divided into 12 equal square plots arranged in 3 rows and 4 columns. If the total area of the garden is 600 square feet, what is the area of each square plot? Answer: 50 Solution: Let’s go step by step. The garden is a rectangle divided into 12 equal square plots arranged in 3 rows and 4 columns. Total area of the garden is given as 600 square feet.
   Full step-by-step solution

   Let’s go step by step. Step 1: Understand the problem. The garden is a rectangle divided into 12 equal square plots arranged in 3 rows and 4 columns. So there are 3 × 4 = 12 square plots in total. Step 2: Total area of the garden is given as 600 square feet. Since the 12 plots are equal in area, we can find the area of one plot by dividing the total area by the number of plots. Step 3: Calculation. Area of one plot = Total area ÷ Number of plots Area of one plot = 600 ÷ 12 Step 4: Perform the division. 600 ÷ 12 = 50 Step 5: Conclusion. Each square plot has an area of 50 square feet. Final answer: 50

3. 1,275 ÷ 15 = ? Answer: 85 Solution: Set up the division: 15 into 1,275 15 goes into 127 how many times? 15 × 8 = 120, so 8 times Subtract: 127 - 120 = 7 Bring down the 5 to make 75 15 goes into 75 how many times?
   Full step-by-step solution

   Step 1: Set up the division: 15 into 1,275 Step 2: 15 goes into 127 how many times? 15 × 8 = 120, so 8 times Step 3: Subtract: 127 - 120 = 7 Step 4: Bring down the 5 to make 75 Step 5: 15 goes into 75 how many times? 15 × 5 = 75, so 5 times Step 6: Subtract: 75 - 75 = 0 Step 7: The quotient is 85 Step 8: Check: 85 × 15 = 1,275 The answer is 85.

4. A factory produces 1,248 identical toy cars and needs to pack them equally into boxes that hold 24 cars each. How many boxes will be completely filled? Answer: 52 Solution: We are told that the factory produces 1,248 identical toy cars and each box holds 24 cars. We need to find how many boxes will be completely filled.
   Full step-by-step solution

   We are told that the factory produces 1,248 identical toy cars and each box holds 24 cars. We need to find how many boxes will be completely filled. Step 1: Understand the problem. We need to divide the total number of cars by the number of cars per box to find the number of full boxes. Step 2: Write the division. Total cars = 1,248 Cars per box = 24 Number of boxes = 1248 ÷ 24 Step 3: Perform the division. First, check how many times 24 goes into 1248. We can break it down: 24 × 50 = 1200 Subtract: 1248 − 1200 = 48 Now, 24 × 2 = 48 So, 24 × 50 + 24 × 2 = 24 × 52 = 1248. Step 4: Interpret the result. Since 1248 ÷ 24 = 52 exactly, there is no remainder. This means all 1,248 cars fit perfectly into 52 boxes, with no leftover cars. Step 5: Conclusion. The number of boxes completely filled is 52. ANSWER: 52

5. 1,575 ÷ 25 = ? Answer: 63 Solution: Set up the division problem: 25 into 1,575. 25 does not go into 1. 25 goes into 15 zero times, so consider the first two digits: 15.
   Full step-by-step solution

   Step 1: Set up the division problem: 25 into 1,575. Step 2: 25 does not go into 1. 25 goes into 15 zero times, so consider the first two digits: 15. Step 3: 25 does not go into 15, so consider the first three digits: 157. Step 4: 25 goes into 157 six times because 25 × 6 = 150. Step 5: Subtract 150 from 157: 157 - 150 = 7. Step 6: Bring down the next digit (5), making the new number 75. Step 7: 25 goes into 75 three times because 25 × 3 = 75. Step 8: Subtract 75 from 75: 75 - 75 = 0. Step 9: There are no more digits to bring down, so the quotient is 63. The answer is 63.

6. Ben is organizing 71485 photographs into an album. Each page can hold exactly 95 photographs. How many full pages can Ben fill? Answer: 752 Solution: Start with 71485 photographs. Divide by 95 photographs per page: 71485 ÷ 95 = 752 with a remainder. The number of full pages is the whole number part: 752.
   Full step-by-step solution

   Step 1: Start with 71485 photographs. Step 2: Divide by 95 photographs per page: 71485 ÷ 95 = 752 with a remainder. Step 3: The number of full pages is the whole number part: 752. The answer is 752.

7. A rectangular garden is divided into 12 equal square plots arranged in 3 rows and 4 columns. If the total area of the garden is 432 square meters, what is the area of each square plot? Answer: 36 Solution: 1. The garden is divided into 12 equal square plots arranged in 3 rows and 4 columns. This means there are 3 × 4 = 12 plots in total.
   Full step-by-step solution

   Let's go step-by-step. 1. The garden is divided into 12 equal square plots arranged in 3 rows and 4 columns. This means there are 3 × 4 = 12 plots in total. 2. The total area of the garden is given as 432 square meters. Since all 12 plots are equal in area, we can find the area of one plot by dividing the total area by the number of plots. 3. Calculation: Area of one plot = Total area ÷ Number of plots Area of one plot = 432 ÷ 12 4. Perform the division: 432 ÷ 12 = 36 5. So, each square plot has an area of 36 square meters. Final answer: 36

8. The school librarian is organizing 1,728 new books equally onto shelves. If each shelf can hold 24 books, how many shelves will be completely filled with books? Answer: 72 Solution: We are told there are 1,728 books in total and each shelf holds 24 books. We want to find how many shelves will be completely filled.
   Full step-by-step solution

   We are told there are 1,728 books in total and each shelf holds 24 books. We want to find how many shelves will be completely filled. Step 1: Understand the operation needed. To find the number of shelves completely filled, we divide the total number of books by the number of books per shelf. So: Total books ÷ Books per shelf = Number of shelves completely filled. Step 2: Write the division. 1728 ÷ 24 Step 3: Break down the division. First, check how many times 24 goes into 1728. We can do this step-by-step: 24 × 70 = 1680 Subtract: 1728 − 1680 = 48 Now, 24 × 2 = 48 So total: 70 + 2 = 72 Step 4: Interpret the result. 1728 ÷ 24 = 72 exactly, with no remainder. That means all 72 shelves are completely filled, with no extra books left over. Final answer: 72 shelves.

9. A community garden is planning their spring planting. They have 1,575 flower bulbs that need to be divided equally among 15 different garden beds. How many bulbs will be planted in each garden bed? Answer: 105 Solution: Step 1: Identify the total number of bulbs: 1,575 Step 2: Identify the number of garden beds: 15 Step 3: Divide the total bulbs by the number of beds: 1,575 ÷ 15 Step 4: Calculate 15 × 100 = 1,500 Step 5: Subtract: 1,575 - 1,500 = 75 Step 6: Calculate 15 × 5 = 75 Step 7: Add the partial results:…
   Full step-by-step solution

   Step 1: Identify the total number of bulbs: 1,575 Step 2: Identify the number of garden beds: 15 Step 3: Divide the total bulbs by the number of beds: 1,575 ÷ 15 Step 4: Calculate 15 × 100 = 1,500 Step 5: Subtract: 1,575 - 1,500 = 75 Step 6: Calculate 15 × 5 = 75 Step 7: Add the partial results: 100 + 5 = 105 Step 8: Verify: 15 × 105 = 1,575 The answer is 105.