Grade 3 Long Division: Division With Remainders

Learn what to do when numbers don't divide evenly

What You'll Learn

Understand what a remainder means
Write answers with remainders correctly
Know when to stop dividing

📖What is a Remainder?

A remainder is what's left over when a number doesn't divide evenly. For example, 47 ÷ 5 = 9 R2, because 5 × 9 = 45, and 47 - 45 = 2.

⚠️

The remainder must always be smaller than the divisor. If it's not, you need to increase your quotient!

💡

To check: (quotient × divisor) + remainder = dividend. So for 47 ÷ 5 = 9 R2: (9 × 5) + 2 = 45 + 2 = 47 ✓

💡Where this fits

Common Core teaches dividing with remainders in grade 4 (4.NBT.B.6), so this lesson is a stretch for this grade. Singapore-style programs start it in grade 3. Make sure division facts within 100 are quick first.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
65 ÷ 8 = ?
1. Use the partial quotients method.
2. How many 8s can you subtract from 65?
3. 8 × 5 = 40
4. 8 × 2 = 16
5. 8 × 1 = 8
6. Add the quotients: 5 + 2 + 1 = 8
7. Remainder: 1
8. 65 ÷ 8 = 8 R1
Answer: 8 R1
Example 2
59 ÷ 4 = ?
1. Use the partial quotients method.
2. How many 4s can you subtract from 59?
3. 4 × 10 = 40
4. 4 × 2 = 8
5. 4 × 2 = 8
6. Add the quotients: 10 + 2 + 2 = 14
7. Remainder: 3
8. 59 ÷ 4 = 14 R3
Answer: 14 R3
Example 3
98 ÷ 3 = ?
1. Use the partial quotients method.
2. How many 3s can you subtract from 98?
3. 3 × 20 = 60
4. 3 × 10 = 30
5. 3 × 2 = 6
6. Add the quotients: 20 + 10 + 2 = 32
7. Remainder: 2
8. 98 ÷ 3 = 32 R2
Answer: 32 R2