Division with Remainders: Practice Problems

Comprehensive collection of division with remainders problems for grade 4 mathematics: word problems, practice exercises, and step-by-step solutions.

Problem Types
\(Dividend = Divisor × Quotient + Remainder\)
Division Algorithm
Types of Problems:
  • Basic Division: Simple division facts with remainders
  • Word Problems: Real-world scenarios requiring division
  • Multi-step Problems: Problems requiring multiple operations
  • Missing Number: Problems with missing dividends, divisors, or remainders
  • Comparison Problems: Comparing different division scenarios
Key Components:

Dividend: The number being divided (the total amount)

Divisor: The number by which we divide (the group size)

Quotient: The result of division (number of complete groups)

Remainder: What's left over after division (leftover items)

Division Algorithm: The fundamental relationship: Dividend = Divisor × Quotient + Remainder

Important Rules:

• Remainder must always be smaller than the divisor

• Use the division algorithm to verify your answer

• In word problems, interpret quotient and remainder in context

• Always check your work by multiplying and adding remainder

Easy Problems
Level 1: Basic Facts

These problems involve 2-digit dividends and 1-digit divisors:

Problem 1: Basic Division
Calculate: 13 ÷ 4
Solution: 13 ÷ 4 = 3 remainder 1
Check: 4 × 3 + 1 = 12 + 1 = 13 ✓
Problem 2: Basic Division
Calculate: 23 ÷ 5
Solution: 23 ÷ 5 = 4 remainder 3
Check: 5 × 4 + 3 = 20 + 3 = 23 ✓
Problem 3: Basic Division
Calculate: 37 ÷ 6
Solution: 37 ÷ 6 = 6 remainder 1
Check: 6 × 6 + 1 = 36 + 1 = 37 ✓
Problem 4: Basic Division
Calculate: 45 ÷ 7
Solution: 45 ÷ 7 = 6 remainder 3
Check: 7 × 6 + 3 = 42 + 3 = 45 ✓
Problem 5: Basic Division
Calculate: 58 ÷ 8
Solution: 58 ÷ 8 = 7 remainder 2
Check: 8 × 7 + 2 = 56 + 2 = 58 ✓
Word Problems
Problem 1: Packing Bags
Word Problem
Sarah has 37 apples. She wants to pack them in bags of 6 apples each. How many full bags can she make and how many apples will remain?
Step 1: Identify the division problem

Total apples ÷ Apples per bag = 37 ÷ 6

Step 2: Perform the division

37 ÷ 6 = 6 remainder 1

Step 3: Interpret the result

Sarah can make 6 full bags with 1 apple remaining

6 full bags, 1 apple remaining
Problem 2: Sharing Equally
Word Problem
A teacher has 45 candies to distribute equally among 7 students. How many candies does each student get and how many remain?
Step 1: Set up the division

Total candies ÷ Number of students = 45 ÷ 7

Step 2: Perform the division

45 ÷ 7 = 6 remainder 3

Step 3: Interpret the result

Each student gets 6 candies with 3 candies remaining

Each student gets 6 candies, 3 candies remain
Challenge Problems
Problem 1: Transportation
There are 89 students going on a field trip. Each bus can carry 12 students. How many buses are needed and how many seats will be empty in the last bus?
Solution: 89 ÷ 12 = 7 remainder 5
Since 5 students remain, we need 1 more bus.
Total buses needed: 7 + 1 = 8 buses
Empty seats in last bus: 12 - 5 = 7 seats
8 buses needed, 7 empty seats in last bus
Problem 2: Packing
A store has 157 items to pack in boxes that hold 8 items each. How many full boxes can be filled and how many items will remain?
Solution: 157 ÷ 8 = 19 remainder 5
19 full boxes can be filled with 5 items remaining
19 full boxes, 5 items remaining
Tip 1: Always read word problems carefully and identify what you need to find.
Tip 2: In transportation problems, round up if there's a remainder.
Tip 3: Check that your remainder is smaller than the divisor.
Tip 4: Always verify your answer using the division algorithm.

Questions & Answers

Question: How do I know when to round up in word problems?

Answer: You need to round up when the remainder represents additional items that still need accommodation:

  • Transportation problems: If you have 23 people and buses hold 10 people each, 23÷10=2 remainder 3. You need 3 buses, not 2, because the 3 remaining people still need transportation.
  • Container problems: If you have 47 items and boxes hold 6 items each, 47÷6=7 remainder 5. You need 8 boxes, not 7, because the 5 remaining items need their own box.
  • Grouping problems: If you have 31 students and groups must have 4 students each, 31÷4=7 remainder 3. You need 8 groups because the 3 remaining students form another group.

Always consider the real-world context of the problem!

Question: Why does the remainder have to be smaller than the divisor?

Answer: The remainder must be smaller than the divisor because of the definition of division:

  • If the remainder were equal to or larger than the divisor, it would mean we could still divide further
  • For example, if we said 17 ÷ 5 = 2 remainder 7, this would be wrong because 7 > 5
  • We could take another group of 5 from the remainder: 7 - 5 = 2
  • This means the real answer is 17 ÷ 5 = 3 remainder 2

Think of it this way: if you have 17 cookies and bags hold 5 cookies each, you can't say you have 2 full bags with 7 cookies left over. You'd make another full bag with 5 of those 7 cookies, leaving only 2 cookies remaining.

The remainder represents what truly cannot be grouped anymore.

Question: How can I check if my division answer is correct?

Answer: You can always verify your division using the division algorithm:

Formula: Dividend = Divisor × Quotient + Remainder

Example: For 23 ÷ 5 = 4 remainder 3

  • Multiply: 5 × 4 = 20
  • Add remainder: 20 + 3 = 23
  • Compare to original: 23 = 23 ✓

Also check that remainder < divisor (3 < 5 ✓).

This verification process catches most calculation errors!