Division with Remainders Comprehensive Worksheets Collection

Complete collection of division with remainders worksheets: 20 practice problems across multiple levels, detailed solutions, and comprehensive study guide for 4th grade students.

Worksheets Collection: Division with Remainders
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Instructions:

Complete all worksheets in order. Start with basic problems and progress to advanced word problems. Show your work using long division method. Verify all answers using: Dividend = (Divisor × Quotient) + Remainder

1 Basic Division (Beginner) Level 1
1
Calculate: 24 ÷ 5
Solution:

Step 1: 5 × 4 = 20

Step 2: 24 - 20 = 4

Step 3: Since 4 < 5, remainder = 4

Therefore: 24 ÷ 5 = 4 R 4

Verification:

(5 × 4) + 4 = 20 + 4 = 24 ✓

2 Basic Division (Beginner) Level 1
2
Calculate: 37 ÷ 6
Solution:

Step 1: 6 × 6 = 36

Step 2: 37 - 36 = 1

Step 3: Since 1 < 6, remainder = 1

Therefore: 37 ÷ 6 = 6 R 1

Verification:

(6 × 6) + 1 = 36 + 1 = 37 ✓

3 Intermediate Division Level 2
3
Calculate: 83 ÷ 7
______
7 ) 83
- 7
--
13
- 14
---
6
Solution:

Step 1: 7 goes into 8 once (7 × 1 = 7)

Step 2: 8 - 7 = 1, bring down 3 to make 13

Step 3: 7 goes into 13 once (7 × 1 = 7)

Step 4: 13 - 7 = 6

Therefore: 83 ÷ 7 = 11 R 6

Verification:

(7 × 11) + 6 = 77 + 6 = 83 ✓

4 Intermediate Division Level 2
4
Calculate: 142 ÷ 9
______
9 ) 142
- 9
--
52
- 45
---
7
Solution:

Step 1: 9 goes into 14 once (9 × 1 = 9)

Step 2: 14 - 9 = 5, bring down 2 to make 52

Step 3: 9 goes into 52 five times (9 × 5 = 45)

Step 4: 52 - 45 = 7

Therefore: 142 ÷ 9 = 15 R 7

Verification:

(9 × 15) + 7 = 135 + 7 = 142 ✓

Worksheets Collection (Continued)
5 Advanced Division Level 3
5
Calculate: 257 ÷ 12
______
12 ) 257
- 24
--
17
- 12
---
5
Solution:

Step 1: 12 goes into 25 twice (12 × 2 = 24)

Step 2: 25 - 24 = 1, bring down 7 to make 17

Step 3: 12 goes into 17 once (12 × 1 = 12)

Step 4: 17 - 12 = 5

Therefore: 257 ÷ 12 = 21 R 5

Verification:

(12 × 21) + 5 = 252 + 5 = 257 ✓

6 Advanced Division Level 3
6
Calculate: 384 ÷ 16
______
16 ) 384
- 32
--
64
- 64
---
0
Solution:

Step 1: 16 goes into 38 twice (16 × 2 = 32)

Step 2: 38 - 32 = 6, bring down 4 to make 64

Step 3: 16 goes into 64 four times (16 × 4 = 64)

Step 4: 64 - 64 = 0

Therefore: 384 ÷ 16 = 24 R 0

Verification:

(16 × 24) + 0 = 384 + 0 = 384 ✓

7 Word Problem (Beginner) Level 1
7
Sarah has 43 stickers to share equally among 5 friends. How many stickers does each friend get and how many are left over?
Solution:

Step 1: 43 ÷ 5 = ?

Step 2: 5 × 8 = 40

Step 3: 43 - 40 = 3

Therefore: 43 ÷ 5 = 8 R 3

So each friend gets 8 stickers and 3 are left over

Verification:

(5 × 8) + 3 = 40 + 3 = 43 ✓

Worksheets Collection (Continued) + Study Guide
8 Word Problem (Intermediate) Level 2
8
A school has 178 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: 178 ÷ 14 = ?

Step 2: 14 × 12 = 168

Step 3: 178 - 168 = 10

Therefore: 178 ÷ 14 = 12 R 10

So 12 buses are filled completely, and 1 bus has 10 students

Total buses needed: 13

Verification:

(14 × 12) + 10 = 168 + 10 = 178 ✓

9 Word Problem (Advanced) Level 3
9
A factory produces 567 toy cars and packs them in boxes that hold 18 cars each. How many full boxes can be made? How many cars will be left unpacked?
Solution:

Step 1: 567 ÷ 18 = ?

Step 2: 18 × 31 = 558

Step 3: 567 - 558 = 9

Therefore: 567 ÷ 18 = 31 R 9

So 31 full boxes can be made with 9 cars left unpacked

Verification:

(18 × 31) + 9 = 558 + 9 = 567 ✓

10 Word Problem (Advanced) Level 3
10
A store has 724 pencils to package in sets of 23. How many complete sets can be made? How many pencils will be left over?
Solution:

Step 1: 724 ÷ 23 = ?

Step 2: 23 × 31 = 713

Step 3: 724 - 713 = 11

Therefore: 724 ÷ 23 = 31 R 11

So 31 complete sets can be made with 11 pencils left over

Verification:

(23 × 31) + 11 = 713 + 11 = 724 ✓

Complete Worksheets Collection:
  • Worksheet 1: Basic Division (Problems 1-5) - Beginner Level
  • Worksheet 2: Intermediate Division (Problems 6-10) - Intermediate Level
  • Worksheet 3: Advanced Division (Problems 11-15) - Advanced Level
  • Worksheet 4: Word Problems (Problems 16-20) - Mixed Levels
  • Study Guide: Complete review of all concepts
  • Answer Key: All problems with detailed solutions
  • Practice Tests: 3 comprehensive tests included
    • Division with Remainders - Complete Study Guide
    Dividend = (Divisor × Quotient) + Remainder
    Division Algorithm
    Grade 4 Division with Remainders - Complete Study 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 ✓