Division with Remainders Practice Worksheet for 4th Grade Students

Complete worksheet with 10 practice problems on division with remainders: basic division, long division, word problems, and verification exercises.

Worksheet: Division with Remainders

Instructions:

Solve each problem below. Remember to write your answer as "quotient R remainder". Show your work for full credit.

Check your answers using: Dividend = (Divisor × Quotient) + Remainder

1 Basic Division
1
15 ÷ 4 =
Show your work:

4 × 3 = 12

15 - 12 = 3

So 15 ÷ 4 = 3 R 3

Verification:

(4 × 3) + 3 = 12 + 3 = 15 ✓

2 Basic Division
2
22 ÷ 5 =
Show your work:

5 × 4 = 20

22 - 20 = 2

So 22 ÷ 5 = 4 R 2

Verification:

(5 × 4) + 2 = 20 + 2 = 22 ✓

3 Long Division
3
37 ÷ 6 =
Show your work:

6 × 6 = 36

37 - 36 = 1

So 37 ÷ 6 = 6 R 1

Verification:

(6 × 6) + 1 = 36 + 1 = 37 ✓

4 Long Division
4
51 ÷ 7 =
Show your work:

7 × 7 = 49

51 - 49 = 2

So 51 ÷ 7 = 7 R 2

Verification:

(7 × 7) + 2 = 49 + 2 = 51 ✓

5 Long Division
5
68 ÷ 9 =
Show your work:

9 × 7 = 63

68 - 63 = 5

So 68 ÷ 9 = 7 R 5

Verification:

(9 × 7) + 5 = 63 + 5 = 68 ✓

Worksheet Problems (Continued)
6 Word Problem
6
Sarah has 43 stickers to share equally among 5 friends. How many stickers does each friend get and how many are left over?
Show your work:

43 ÷ 5 = ?

5 × 8 = 40

43 - 40 = 3

So each friend gets 8 stickers and 3 are left over

Verification:

(5 × 8) + 3 = 40 + 3 = 43 ✓

7 Word Problem
7
There are 58 students in a class. If each table seats 7 students, how many tables are needed and how many students will sit at the last table?
Show your work:

58 ÷ 7 = ?

7 × 8 = 56

58 - 56 = 2

So 8 tables are needed, with 2 students at the last table

Verification:

(7 × 8) + 2 = 56 + 2 = 58 ✓

8 Word Problem
8
Tom has 39 apples to pack into boxes that hold 6 apples each. How many full boxes can he make and how many apples will be left over?
Show your work:

39 ÷ 6 = ?

6 × 6 = 36

39 - 36 = 3

So Tom can make 6 full boxes with 3 apples left over

Verification:

(6 × 6) + 3 = 36 + 3 = 39 ✓

Worksheet Problems (Continued) + Answer Key
9 Word Problem
9
Emma has 74 candies to put in bags that hold 8 candies each. How many full bags can she make and how many candies will be left?
Show your work:

74 ÷ 8 = ?

8 × 9 = 72

74 - 72 = 2

So Emma can make 9 full bags with 2 candies left over

Verification:

(8 × 9) + 2 = 72 + 2 = 74 ✓

10 Challenge Problem
10
A baker has 89 cupcakes to arrange in trays that hold 10 cupcakes each. How many full trays can be filled and how many cupcakes will be on the last tray?
Show your work:

89 ÷ 10 = ?

10 × 8 = 80

89 - 80 = 9

So 8 full trays can be filled with 9 cupcakes on the last tray

Verification:

(10 × 8) + 9 = 80 + 9 = 89 ✓

Dividend = (Divisor × Quotient) + Remainder
Verification Formula
Answer Key:
  • 1. 15 ÷ 4 = 3 R 3
  • 2. 22 ÷ 5 = 4 R 2
  • 3. 37 ÷ 6 = 6 R 1
  • 4. 51 ÷ 7 = 7 R 2
  • 5. 68 ÷ 9 = 7 R 5
  • 6. Each friend gets 8 stickers, 3 left over
  • 7. 8 tables needed, 2 students at last table
  • 8. 6 full boxes, 3 apples left over
  • 9. 9 full bags, 2 candies left over
  • 10. 8 full trays, 9 cupcakes on last tray
    • Division with Remainders - Complete Summary
    Complete Summary: Division with Remainders
    Core Definitions
  • Dividend: The number being divided (the top number)
  • Divisor: The number we divide by (the bottom number)
  • Quotient: The result of division (how many times it divides)
  • Remainder: What's left over after division
  • Division with remainder: When one number doesn't divide evenly into another
    • Core Rules and Laws
  • Remainder Rule: Remainder is always less than the divisor
  • Division Algorithm: Dividend = (Divisor × Quotient) + Remainder
  • Exact Division: When remainder is 0
  • Remainder Bounds: 0 ≤ Remainder < Divisor
  • Verification: Always check your answer using the division algorithm
    • Step-by-Step Methods
  • Step 1: Identify dividend and divisor
  • Step 2: Find how many times divisor fits in dividend
  • Step 3: Multiply divisor by quotient
  • Step 4: Subtract to find remainder
  • Step 5: Verify: (Divisor × Quotient) + Remainder = Dividend
    • Examples (Simple to Advanced)
  • Simple: 10 ÷ 3 = 3 R 1 (because 3×3=9, 10-9=1)
  • Medium: 25 ÷ 4 = 6 R 1 (because 4×6=24, 25-24=1)
  • Advanced: 87 ÷ 9 = 9 R 6 (because 9×9=81, 87-81=6)
  • Word Problem: 43 ÷ 7 = 6 R 1 (6 friends get 7 each, 1 left over)
    • Tips and Tricks
  • Tip 1: Always check that remainder < divisor
  • Tip 2: Use multiplication facts to help with division
  • Tip 3: Draw pictures for word problems
  • Tip 4: Always verify your answer using the division algorithm
  • Tip 5: Remember: remainder cannot equal or exceed the divisor
    • Common Mistakes to Avoid
  • Mistake 1: Having remainder ≥ divisor
  • Mistake 2: Not verifying the answer
  • Mistake 3: Incorrect subtraction in the division process
  • Mistake 4: Confusing quotient and remainder
  • Mistake 5: Forgetting to include remainder in the final answer
    • Key Takeaways for Memorization
  • Memory Aid: "Divide, Multiply, Subtract, Check"
  • Formula: Dividend = Divisor × Quotient + Remainder
  • Rule: Remainder < Divisor
  • Process: Always verify your answer
  • Concept: Remainder is what's left after equal sharing
    • Long Division Steps
  • Divide: How many times does divisor go into current number?
  • Multiply: Multiply divisor by the quotient digit
  • Subtract: Subtract the product from current number
  • Bring Down: Bring down the next digit
  • Repeat: Continue until no digits remain
    • Real-World Applications
  • Sharing items among people
  • Grouping objects into equal sets
  • Distributing resources fairly
  • Calculating leftover materials
    • 20 apples
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    🍎
    🍎
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    ÷
    6 baskets
    🧺
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    🧺
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    =
    3 per basket
    2 left over
    20 ÷ 6 = 3 R 2

    Questions & Answers

    Question: I don't understand why we sometimes have remainders in division. Why can't everything divide evenly?

    Answer: Great question! In real life, things don't always divide evenly. Think of it this way:

    • If you have 7 cookies and want to share them equally among 3 friends, each friend gets 2 cookies (3×2=6), and 1 cookie is left over
    • The remainder represents the "leftovers" that can't be shared equally
    • Mathematically, when the dividend isn't a multiple of the divisor, there will be a remainder

    Example: 7 ÷ 3 = 2 R 1 because 3 × 2 = 6, and 7 - 6 = 1 leftover

    Remainders help us deal with real-world situations where equal sharing isn't perfectly possible!

    Question: My child struggles with long division. How can I help them understand the steps better?

    Answer: Try these strategies to help your child with long division:

    • Use manipulatives: Physical objects like counters or base-ten blocks to model the division process
    • Remember the acronym: DMSB (Divide, Multiply, Subtract, Bring down)
    • Start simple: Begin with 2-digit dividends and single-digit divisors
    • Practice multiplication facts: Strong knowledge of multiplication helps with division

    Visual representation is key: Show how many groups of the divisor fit into the dividend step by step.

    Encourage your child to always check their work: (Divisor × Quotient) + Remainder should equal the original dividend.

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

    Answer: There's an easy rule to check if your remainder is correct:

    • 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 ✓

    If you got 23 ÷ 5 = 4 R 7, you'd know it's wrong because 7 > 5, so you could still divide more!