Multi-Digit Division

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Multi-Digit Division · Grade 5 · Worksheet 3

1. Liam is organizing a large donation of 95065 books to the school library. Each bookshelf can hold exactly 71 books. How many complete bookshelves can Liam fill? Answer: 1338 Solution: We have 95065 books total. Each shelf holds 71 books. Divide to find the number of shelves: 95065 ÷ 71 = 1338 shelves (ignore any remainder for complete shelves).
   Full step-by-step solution

   Step 1: We have 95065 books total. Step 2: Each shelf holds 71 books. Step 3: Divide to find the number of shelves: 95065 ÷ 71 = 1338 shelves (ignore any remainder for complete shelves). The answer is 1338.

2. The school library is organizing its collection of 1,248 books equally onto 8 new bookshelves. If each bookshelf holds the same number of books, how many books will be placed on each shelf? Answer: 156 Solution: We are told that there are 1,248 books in total and they must be divided equally among 8 bookshelves. This means we need to perform the division: total books ÷ number of shelves. Write the division problem.
   Full step-by-step solution

   We are told that there are 1,248 books in total and they must be divided equally among 8 bookshelves. This means we need to perform the division: total books ÷ number of shelves. Step 1: Write the division problem. Total books = 1248 Number of shelves = 8 So we compute: 1248 ÷ 8 Step 2: Break down the division. First, check how many times 8 goes into the first digit (1). 8 does not go into 1, so we consider the first two digits: 12. Step 3: Divide 12 by 8. 8 × 1 = 8, which is less than 12. 8 × 2 = 16, which is too big. So we use 1. Write 1 above the 2 (in the hundreds/tens place in long division). Step 4: Multiply and subtract. 1 × 8 = 8 12 − 8 = 4 Step 5: Bring down the next digit (4). Now we have 44. Step 6: Divide 44 by 8. 8 × 5 = 40, which fits. Write 5 above the 4 (in the tens place). Subtract: 44 − 40 = 4 Step 7: Bring down the last digit (8). Now we have 48. Step 8: Divide 48 by 8. 8 × 6 = 48 exactly. Write 6 above the 8 (in the ones place). Subtract: 48 − 48 = 0 Step 9: Combine the result. The numbers we wrote above were: 1 (hundreds), 5 (tens), 6 (ones) → 156. So, 1248 ÷ 8 = 156. Step 10: Interpret the result. Each bookshelf will hold 156 books. Final answer: 156

3. Aroha is designing a rectangular mosaic on a coordinate plane. The mosaic has corners at (1, 1), (46, 1), (46, 26), and (1, 26). She wants to cover the entire mosaic with identical square tiles, using the largest possible squares without cutting any tiles. What is the area of each square tile in square units? Answer: 25 Solution: Find the dimensions of the rectangle. The length goes from x=1 to x=46, so the length is 46 - 1 = 45 units. The width goes from y=1 to y=26, so the width is 26 - 1 = 25 units.
   Full step-by-step solution

   Step 1: Find the dimensions of the rectangle. The length goes from x=1 to x=46, so the length is 46 - 1 = 45 units. The width goes from y=1 to y=26, so the width is 26 - 1 = 25 units. Step 2: To use the largest possible identical square tiles with no leftover space, the side length of the square must be the greatest common divisor (GCD) of 45 and 25. Step 3: List the factors of 45: 1, 3, 5, 9, 15, 45. Step 4: List the factors of 25: 1, 5, 25. Step 5: The greatest common factor is 5. So each square tile has a side length of 5 units. Step 6: The area of each square tile is side × side = 5 × 5 = 25 square units. Step 7: Check: Number of tiles along the length = 45 ÷ 5 = 9. Number of tiles along the width = 25 ÷ 5 = 5. Total tiles = 9 × 5 = 45. Total area of mosaic = 45 × 25 = 1125 square units. Area of 45 tiles = 45 × 25 = 1125 square units. This matches. The answer is 25.

4. The city park department is planting trees along a new walking trail. They have 1,575 tree saplings that need to be distributed equally among 15 different sections of the trail. How many trees will be planted in each section? Answer: 105 Solution: Step 1: Identify the total number of trees: 1,575 Step 2: Identify the number of sections: 15 Step 3: Divide the total trees by the number of sections: 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…
   Full step-by-step solution

   Step 1: Identify the total number of trees: 1,575 Step 2: Identify the number of sections: 15 Step 3: Divide the total trees by the number of sections: 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 trees per section.

5. 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 meters, what is the area of each square plot? Answer: 50 Solution: We have a rectangular garden divided into 12 equal square plots. The arrangement is 3 rows and 4 columns, so total plots = 3 × 4 = 12. Total area of the garden = 600 square meters.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Understand the problem** We have a rectangular garden divided into 12 equal square plots. The arrangement is 3 rows and 4 columns, so total plots = 3 × 4 = 12. Total area of the garden = 600 square meters. --- **Step 2: Relate total area to each plot's area** Since all 12 plots are equal squares, Total area = 12 × (area of one square plot). Let the area of one square plot = A. Then: 12 × A = 600 --- **Step 3: Solve for A** Divide both sides by 12: A = 600 / 12 --- **Step 4: Perform the division** 600 ÷ 12 = 50 --- **Step 5: Conclusion** The area of each square plot is 50 square meters. --- **Final answer:** 50

6. The city recreation department is organizing a summer reading program. They have 1,575 books that need to be distributed equally among 15 different community centers. How many books will each community center receive? Answer: 105 Solution: Identify the total number of books: 1,575 Identify the number of community centers: 15 Set up the division problem: 1,575 ÷ 15 Divide 1,575 by 15 15 × 100 = 1,500 1,575 - 1,500 = 75 15 × 5 = 75 75 - 75 = 0 Add the partial quotients: 100 + 5 = 105 Each community center will receive 105 books.
   Full step-by-step solution

   Step 1: Identify the total number of books: 1,575 Step 2: Identify the number of community centers: 15 Step 3: Set up the division problem: 1,575 ÷ 15 Step 4: Divide 1,575 by 15 15 × 100 = 1,500 1,575 - 1,500 = 75 15 × 5 = 75 75 - 75 = 0 Step 5: Add the partial quotients: 100 + 5 = 105 Step 6: Each community center will receive 105 books.

7. A rectangular garden is divided into 8 equal sections arranged in 4 rows and 2 columns. If the total area of the garden is 1,200 square feet, what is the area of each section? Answer: 150 Solution: The garden is divided into 8 equal sections. The total area is 1,200 square feet. Since the sections are equal, the area of each section is the total area divided by the number of sections.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. The total area is 1,200 square feet. Step 2: Since the sections are equal, the area of each section is the total area divided by the number of sections. Step 3: Write the division: Area of each section = Total area / Number of sections Area of each section = 1,200 / 8 Step 4: Perform the division. 1,200 divided by 8 equals 150. Step 5: State the answer. Each section has an area of 150 square feet.

8. The school library is organizing 1,365 books equally onto 15 empty shelves. How many books will be placed on each shelf? Answer: 91 Solution: We are told that there are 1,365 books to be placed equally on 15 shelves. This means we need to divide the total number of books by the number of shelves. Write the division problem.
   Full step-by-step solution

   We are told that there are 1,365 books to be placed equally on 15 shelves. This means we need to divide the total number of books by the number of shelves. Step 1: Write the division problem. Total books = 1365 Number of shelves = 15 So, books per shelf = 1365 ÷ 15. Step 2: Perform the division step-by-step. First, check how many times 15 goes into the first two digits of 1365 (which is 13). 15 does not go into 13, so we consider the first three digits: 136. Step 3: Divide 136 by 15. 15 × 9 = 135, which is less than 136. Remainder = 136 − 135 = 1. So, the first digit of the quotient is 9 (for the hundreds and tens place). Step 4: Bring down the next digit, which is 5, making the number 15. Now divide 15 by 15. 15 × 1 = 15, remainder 0. So, the next digit of the quotient is 1. Step 5: Combine the quotient digits: 9 and 1, giving 91. Step 6: Check: 15 × 91 = 15 × 90 + 15 × 1 = 1350 + 15 = 1365, which matches the total books. Thus, each shelf will have 91 books.

9. Charlotte is organizing 69917 photographs into an album. Each page can hold exactly 90 photographs. How many full pages can Charlotte fill? Answer: 776 Solution: Start with 69917 photographs. Divide by 90 photographs per page: 69917 ÷ 90 = 776 with a remainder. The number of full pages is the whole number part: 776.
   Full step-by-step solution

   Step 1: Start with 69917 photographs. Step 2: Divide by 90 photographs per page: 69917 ÷ 90 = 776 with a remainder. Step 3: The number of full pages is the whole number part: 776. The answer is 776.