Division with Remainders Worksheet with Complete Answers (PDF Format)

Complete worksheet with answers in PDF format: 15 comprehensive practice problems on division with remainders for 4th graders including step-by-step solutions and verification.

Worksheet: Division with Remainders (With Answers)
Download Full PDF Version with All Solutions

Instructions:

Solve each problem below. Show your work using long division method. Write your answer as "quotient R remainder". Verify your answer using: Dividend = (Divisor × Quotient) + Remainder

1 Basic Division
1
Calculate: 45 ÷ 6
Solution:

Step 1: 6 × 7 = 42

Step 2: 45 - 42 = 3

Step 3: Since 3 < 6, remainder = 3

Therefore: 45 ÷ 6 = 7 R 3

Verification:

(6 × 7) + 3 = 42 + 3 = 45 ✓

2 Basic Division
2
Calculate: 67 ÷ 8
Solution:

Step 1: 8 × 8 = 64

Step 2: 67 - 64 = 3

Step 3: Since 3 < 8, remainder = 3

Therefore: 67 ÷ 8 = 8 R 3

Verification:

(8 × 8) + 3 = 64 + 3 = 67 ✓

3 Long Division
3
Calculate: 94 ÷ 7
______
7 ) 94
- 7
--
24
- 21
---
3
Solution:

Step 1: 7 goes into 9 once (7 × 1 = 7)

Step 2: 9 - 7 = 2, bring down 4 to make 24

Step 3: 7 goes into 24 three times (7 × 3 = 21)

Step 4: 24 - 21 = 3

Therefore: 94 ÷ 7 = 13 R 3

Verification:

(7 × 13) + 3 = 91 + 3 = 94 ✓

4 Long Division
4
Calculate: 138 ÷ 9
______
9 ) 138
- 9
--
48
- 45
---
3
Solution:

Step 1: 9 goes into 13 once (9 × 1 = 9)

Step 2: 13 - 9 = 4, bring down 8 to make 48

Step 3: 9 goes into 48 five times (9 × 5 = 45)

Step 4: 48 - 45 = 3

Therefore: 138 ÷ 9 = 15 R 3

Verification:

(9 × 15) + 3 = 135 + 3 = 138 ✓

Worksheet Problems (Continued)
5 Multi-Digit Division
5
Calculate: 217 ÷ 12
______
12 ) 217
- 12
--
97
- 84
---
13
Solution:

Step 1: 12 goes into 21 once (12 × 1 = 12)

Step 2: 21 - 12 = 9, bring down 7 to make 97

Step 3: 12 goes into 97 eight times (12 × 8 = 96)

Step 4: 97 - 96 = 1

Therefore: 217 ÷ 12 = 18 R 1

Verification:

(12 × 18) + 1 = 216 + 1 = 217 ✓

6 Multi-Digit Division
6
Calculate: 342 ÷ 15
______
15 ) 342
- 30
--
42
- 30
---
12
Solution:

Step 1: 15 goes into 34 twice (15 × 2 = 30)

Step 2: 34 - 30 = 4, bring down 2 to make 42

Step 3: 15 goes into 42 twice (15 × 2 = 30)

Step 4: 42 - 30 = 12

Therefore: 342 ÷ 15 = 22 R 12

Verification:

(15 × 22) + 12 = 330 + 12 = 342 ✓

7 Word Problem
7
A school has 238 students going on a field trip. Buses can carry 14 students each. How many buses are needed? How many students will be on the last bus?
Solution:

Step 1: 238 ÷ 14 = ?

Step 2: 14 × 17 = 238

Step 3: 238 - 238 = 0

Therefore: 238 ÷ 14 = 17 R 0

So 17 buses are needed, with 0 students left over

Verification:

(14 × 17) + 0 = 238 + 0 = 238 ✓

Worksheet Problems (Continued) + Complete Answer Key
8 Word Problem
8
A teacher has 167 books to place on shelves. Each shelf holds 9 books. How many full shelves can be filled? How many books will be left over?
Solution:

Step 1: 167 ÷ 9 = ?

Step 2: 9 × 18 = 162

Step 3: 167 - 162 = 5

Therefore: 167 ÷ 9 = 18 R 5

So 18 full shelves can be filled with 5 books left over

Verification:

(9 × 18) + 5 = 162 + 5 = 167 ✓

9 Word Problem
9
A factory produces 483 toy cars and packs them in boxes that hold 16 cars each. How many full boxes can be made? How many cars will be left unpacked?
Solution:

Step 1: 483 ÷ 16 = ?

Step 2: 16 × 30 = 480

Step 3: 483 - 480 = 3

Therefore: 483 ÷ 16 = 30 R 3

So 30 full boxes can be made with 3 cars left unpacked

Verification:

(16 × 30) + 3 = 480 + 3 = 483 ✓

10 Word Problem
10
A store has 319 pencils to package in sets of 13. How many complete sets can be made? How many pencils will be left over?
Solution:

Step 1: 319 ÷ 13 = ?

Step 2: 13 × 24 = 312

Step 3: 319 - 312 = 7

Therefore: 319 ÷ 13 = 24 R 7

So 24 complete sets can be made with 7 pencils left over

Verification:

(13 × 24) + 7 = 312 + 7 = 319 ✓

Complete Answer Key:
  • 1. 45 ÷ 6 = 7 R 3
  • 2. 67 ÷ 8 = 8 R 3
  • 3. 94 ÷ 7 = 13 R 3
  • 4. 138 ÷ 9 = 15 R 3
  • 5. 217 ÷ 12 = 18 R 1
  • 6. 342 ÷ 15 = 22 R 12
  • 7. 238 ÷ 14 = 17 R 0 (17 buses needed, 0 on last bus)
  • 8. 167 ÷ 9 = 18 R 5 (18 full shelves, 5 left over)
  • 9. 483 ÷ 16 = 30 R 3 (30 full boxes, 3 left over)
  • 10. 319 ÷ 13 = 24 R 7 (24 complete sets, 7 left over)
  • 11. 567 ÷ 18 = 31 R 9
  • 12. 724 ÷ 23 = 31 R 11
  • 13. 847 ÷ 25 = 33 R 22
  • 14. 956 ÷ 32 = 29 R 28
  • 15. 1023 ÷ 41 = 24 R 39
    • Division with Remainders - Complete Summary
    Dividend = (Divisor × Quotient) + Remainder
    Division Algorithm
    Grade 4 Division with Remainders - Complete Guide
    Core Definitions
  • Dividend: The number being divided (the larger number)
  • Divisor: The number we divide by (the smaller number)
  • Quotient: The result of division (how many times it divides)
  • Remainder: What's left over after division
  • Division Algorithm: The fundamental relationship between all four values
    • Long Division Steps
  • Step 1 (Divide): How many times does divisor go into current number?
  • Step 2 (Multiply): Multiply divisor by the quotient digit
  • Step 3 (Subtract): Subtract the product from current number
  • Step 4 (Bring Down): Bring down the next digit
  • Step 5 (Repeat): Continue until no digits remain
    • Remainder Rules
  • Rule 1: Remainder is always less than the divisor
  • Rule 2: If remainder is 0, division is exact
  • Rule 3: Remainder cannot equal or exceed the divisor
  • Rule 4: Always verify: (Divisor × Quotient) + Remainder = Dividend
    • Examples (Progressive Difficulty)
  • Basic: 24 ÷ 4 = 6 R 0 (exact division)
  • Simple: 25 ÷ 4 = 6 R 1 (remainder = 1)
  • Medium: 83 ÷ 7 = 11 R 6 (larger numbers)
  • Advanced: 317 ÷ 15 = 21 R 2 (multi-digit division)
  • Complex: 1023 ÷ 41 = 24 R 39 (large numbers with large remainders)
    • Problem-Solving Strategy
  • Step 1: Read the problem carefully and identify what is being asked
  • Step 2: Determine what numbers represent dividend and divisor
  • Step 3: Perform the division using long division method
  • Step 4: Interpret the quotient and remainder in context
  • Step 5: Verify your answer and check if it makes sense
    • Tips for Success
  • Tip 1: Always write out your long division steps clearly
  • Tip 2: Check that remainder < divisor
  • Tip 3: Use multiplication facts to help with division
  • Tip 4: Always verify your answer using the division algorithm
  • Tip 5: For word problems, answer the specific question asked
    • Common Mistakes to Avoid
  • Mistake 1: Having remainder ≥ divisor
  • Mistake 2: Forgetting to bring down the next digit
  • Mistake 3: Not verifying the answer
  • Mistake 4: Misreading word problems
  • Mistake 5: Arithmetic errors in multiplication or subtraction
    • Real-World Applications
  • Sharing items among people
  • Organizing objects into equal groups
  • Calculating transportation needs
  • Packaging products efficiently
  • Planning events and seating arrangements
  • Resource allocation and distribution
    • 137 items
    ÷
    11 per group
    →
    12 groups
    5 left over
    137 ÷ 11 = 12 R 5
    Verification:

    (11 × 12) + 5 = 132 + 5 = 137 ✓

    Questions & Answers

    Question: I'm having trouble with long division. How do I know when to stop bringing down numbers?

    Answer: Great question! You stop bringing down numbers when:

    • You've brought down all the digits from the dividend
    • The number you're working with is smaller than the divisor
    • There are no more digits to bring down

    Once you reach this point, whatever number is left becomes your remainder. Remember the acronym: DMSB (Divide, Multiply, Subtract, Bring down).

    Question: How can I help my child practice division with remainders effectively?

    Answer: Here are effective strategies:

    • Start with concrete examples: Use physical objects like blocks or counters
    • Practice basic facts: Strengthen multiplication facts to support division
    • Use graph paper: Helps keep long division organized
    • Check answers together: Reinforce the verification process
    • Connect to real life: Use word problems that relate to daily activities

    Consistent practice with immediate feedback works best!

    Question: How do I know if my remainder is correct? Sometimes I get confused about whether it's too big.

    Answer: There's a simple rule to check:

    • The remainder must always be smaller than the divisor
    • If your remainder is equal to or bigger than the divisor, you made a mistake
    • Always check: (Divisor × Quotient) + Remainder = Original Dividend

    Example: In 23 ÷ 5 = 4 R 3, check that 3 < 5 ✓

    Then verify: (5 × 4) + 3 = 20 + 3 = 23 ✓