MathIsimple

Three-Digit by One-Digit Division (With Remainder)

Master the art of dividing three-digit numbers when there are leftovers! Learn to handle remainders and verify your answers with confidence.

Learning Scenario

Class Group Formation Challenge! The school has 258 students who need to be divided into 4 equal groups for a special activity. How many students will be in each group? Will there be any students left over? Let's solve this step by step!

What is a Remainder?

Definition

A remainder is what's left over when we can't divide a number evenly. It's the amount that doesn't fit into complete groups.

Think of it like this: If you have 10 cookies and want to share them equally among 3 friends, each friend gets 3 cookies, but there's 1 cookie left over - that's the remainder!

Important Rules About Remainders

  • •Remainder must be less than the divisor: If dividing by 4, remainder can only be 0, 1, 2, or 3
  • •Remainder can be zero: When numbers divide evenly, remainder is 0
  • •Check your work: Use the formula: Quotient × Divisor + Remainder = Dividend

Step-by-Step Process: 258 ÷ 4

Step 1: Set Up the Problem

258 ÷ 4

We write this as: 4 ⟌ 258

258 is the dividend (what we're dividing)

4 is the divisor (what we're dividing by)

Step 2: Divide Hundreds Place

6
4 ⟌ 258
-24
--
18

Question: How many 4s are in 25? Answer: 6 (write 6 above the 5)

Multiply: 6 × 4 = 24 (write 24 below the 25)

Subtract: 25 - 24 = 1 (write 1 below)

Step 3: Bring Down and Divide Tens

64
4 ⟌ 258
-24
--
18
-16
--
2

Bring down: Bring down the 8 to make 18

Question: How many 4s are in 18? Answer: 4 (write 4 above the 8)

Multiply: 4 × 4 = 16 (write 16 below the 18)

Subtract: 18 - 16 = 2 (write 2 below)

Step 4: Check for Remainder

64 R2
4 ⟌ 258
-24
--
18
-16
--
2

Remainder: We have 2 left over (can't divide 2 by 4)

Answer: 64 remainder 2, written as 64 R2

Meaning: 4 groups of 64, with 2 students left over

Final Answer

258 ÷ 4 = 64 R2
Each group will have 64 students, with 2 students left over!

How to Verify Your Answer

The Verification Formula

Quotient × Divisor + Remainder = Dividend
64 × 4 + 2 = 258

64 × 4 = 256

256 + 2 = 258 ✓

Why This Works

Quotient × Divisor gives us the number of items that were divided evenly.

+ Remainder adds back the items that were left over.

= Dividend should equal our original number.

Example: 64 groups × 4 students per group + 2 leftover students = 258 total students

Example Problems

Example 1: 347 ÷ 5

Step-by-Step Solution:

69 R2
5 ⟌ 347
-30
--
47
-45
--
2

Answer: 347 ÷ 5 = 69 R2

Verification: 69 × 5 + 2 = 345 + 2 = 347 ✓

Example 2: 892 ÷ 7

Step-by-Step Solution:

127 R3
7 ⟌ 892
-7
--
19
-14
--
52
-49
--
3

Answer: 892 ÷ 7 = 127 R3

Verification: 127 × 7 + 3 = 889 + 3 = 892 ✓

Interactive Activities

Activity 1: Practice Division with Remainders

Solve 456 ÷ 8 step by step:

? R?
8 ⟌ 456
-?
--
?

Activity 2: Real-World Problem

A school has 375 pencils and wants to distribute them equally among 6 classes. How many pencils will each class get? How many will be left over?

⟌

Common Mistakes to Avoid

❌ Forgetting to write the remainder

Always check if there's a remainder and write it as "R" followed by the number.

❌ Making the remainder too large

Remember: remainder must always be less than the divisor.

❌ Not verifying your answer

Always use the verification formula to check your work.

Practice Problems

Problem 1

A bakery has 523 cupcakes and wants to pack them equally into 9 boxes. How many cupcakes will be in each box? How many will be left over?

⟌

Problem 2

Solve: 789 ÷ 6

6 ⟌ 789

Key Takeaways

What You Learned

  • ✓Remainders are what's left over when division isn't even
  • ✓Remainder must always be less than the divisor
  • ✓Use verification formula to check your work
  • ✓Practice helps build confidence with remainders

Next Steps

  • →Practice with more division problems with remainders
  • →Learn estimation and real-world applications
  • →Apply these skills to solve complex problems