Multi-Digit Division

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Answer Key & Explanations

Multi-Digit Division · Grade 5 · Worksheet 2

1. 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.

2. 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.

3. The school library is organizing its collection of 1,248 books equally onto 8 bookshelves. How many books will be placed on each shelf? Answer: 156 Solution: We are told there are 1,248 books total and they are to be divided equally among 8 bookshelves. To find how many books go on each shelf, we need to divide the total number of books by the number of shelves.
   Full step-by-step solution

   We are told there are 1,248 books total and they are to be divided equally among 8 bookshelves. To find how many books go on each shelf, we need to divide the total number of books by the number of shelves. Step 1: Write the division problem. Total books = 1248 Number of shelves = 8 So, books per shelf = 1248 ÷ 8 Step 2: Perform the division step-by-step. 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. 8 goes into 12 one time. 1 × 8 = 8 Subtract: 12 − 8 = 4 Step 3: Bring down the next digit (4) from 1248, so now we have 44. 8 goes into 44 five times because 8 × 5 = 40. Subtract: 44 − 40 = 4 Step 4: Bring down the last digit (8) from 1248, so now we have 48. 8 goes into 48 six times because 8 × 6 = 48. Subtract: 48 − 48 = 0 Step 5: The quotient is 156, with remainder 0. So, 1248 ÷ 8 = 156. Step 6: Interpret the result. This means each shelf will have 156 books. Final answer: 156

4. 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.

5. 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

6. A factory produces 1,728 toy cars and needs to pack them equally into boxes that hold 24 cars each. How many boxes will be completely filled? Answer: 72 Solution: We are told that the factory produces 1,728 toy cars and each box holds 24 cars. We want to find how many boxes will be completely filled.
   Full step-by-step solution

   We are told that the factory produces 1,728 toy cars and each box holds 24 cars. We want 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: Total cars ÷ Cars per box = Number of boxes completely filled. Step 2: Write the division Number of boxes = 1,728 ÷ 24. Step 3: Break down the division We can simplify 1,728 ÷ 24 step by step. First, note that 24 = 8 × 3. So 1,728 ÷ 24 = 1,728 ÷ (8 × 3) = (1,728 ÷ 8) ÷ 3. Step 4: Divide 1,728 by 8 1,728 ÷ 8: 8 × 200 = 1,600, subtract: 1,728 − 1,600 = 128. 8 × 16 = 128, subtract: 128 − 128 = 0. So 200 + 16 = 216. Thus 1,728 ÷ 8 = 216. Step 5: Divide 216 by 3 216 ÷ 3: 3 × 70 = 210, subtract: 216 − 210 = 6. 3 × 2 = 6, subtract: 6 − 6 = 0. So 70 + 2 = 72. Thus 216 ÷ 3 = 72. Step 6: Conclusion Therefore, 1,728 ÷ 24 = 72. So 72 boxes will be completely filled. Final answer: 72

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. 1,248 ÷ 26 = ? Answer: 48 Solution: We are dividing 1,248 by 26 using long division. Check how many times 26 goes into the first two digits of 1,248. The first two digits are 12.
   Full step-by-step solution

   Let's solve 1,248 ÷ 26 step by step. We are dividing 1,248 by 26 using long division. Step 1: Check how many times 26 goes into the first two digits of 1,248. The first two digits are 12. 26 is bigger than 12, so we take the first three digits: 124. Step 2: How many times does 26 go into 124? Estimate: 26 × 4 = 104 (less than 124) 26 × 5 = 130 (too big, more than 124) So we use 4. Write 4 above the third digit of 1,248 (above the 4 in 1248). Step 3: Multiply 26 × 4 = 104. Subtract 104 from 124: 124 − 104 = 20. Step 4: Bring down the next digit (8) from 1,248. Now we have 208. Step 5: How many times does 26 go into 208? Estimate: 26 × 8 = 208 exactly. So we use 8. Write 8 above the last digit of 1,248 (above the 8 in 1248). Step 6: Multiply 26 × 8 = 208. Subtract: 208 − 208 = 0. No remainder. So the quotient is 48. Final check: 26 × 48 = 26 × 50 − 26 × 2 = 1,300 − 52 = 1,248. Correct. ANSWER: 48

9. The school district is organizing a math competition and needs to distribute 1,575 pencils equally among 35 participating classrooms. How many pencils will each classroom receive? Answer: 45 Solution: Step 1: Identify the total number of pencils: 1,575 Step 2: Identify the number of classrooms: 35 Step 3: Set up the division problem: 1,575 ÷ 35 Step 4: Divide 1,575 by 35 35 × 45 = 1,575 Step 5: Verify: 35 × 45 = 1,575 Step 6: Each classroom will receive 45 pencils The answer is 45.
   Full step-by-step solution

   Step 1: Identify the total number of pencils: 1,575 Step 2: Identify the number of classrooms: 35 Step 3: Set up the division problem: 1,575 ÷ 35 Step 4: Divide 1,575 by 35 35 × 45 = 1,575 Step 5: Verify: 35 × 45 = 1,575 Step 6: Each classroom will receive 45 pencils The answer is 45.