Homeschool Math

Division Guide

Long Division with Remainders

Step-by-Step Visual Guide

Remainders trip up most kids because they don't know what to do when the number doesn't divide evenly. This guide shows exactly what a remainder means — and how to find it every time without guessing.

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The Chant:

Divide → Multiply → Subtract → Bring Down → Repeat

When nothing is left to bring down and you can't divide again — that leftover number is your remainder.

How to Divide with Remainders

Let's use 85 ÷ 4 as our example

85 ÷ 4 = ?
Start with the problem
85 ÷ 4

We need to divide 85 by 4. The chant is: Divide → Multiply → Subtract → Bring down. Repeat.

Step 1: Divide
How many times does 4 go into 8?
8 ÷ 4 = 2

4 goes into 8 exactly 2 times. Write 2 above the 8 in the tens place.

Step 2: Multiply
2 × 4 = 8
2 × 4 = 8

Multiply your answer (2) by the divisor (4). Write 8 below the 8.

Step 3: Subtract
8 − 8 = 0
8 − 8 = 0 → bring down 5

Subtract. The result is 0. Bring down the next digit (5).

Step 4: Divide again
How many times does 4 go into 5?
5 ÷ 4 = 1 remainder 1

4 goes into 5 once (4 × 1 = 4). Write 1 above the 5. Multiply: 1 × 4 = 4.

Step 5: Find the remainder
5 − 4 = 1
85 ÷ 4 = 21 R1 ✓

Subtract: 5 − 4 = 1. Nothing left to bring down. The remainder is 1.

What Does a Remainder Actually Mean?

A remainder is what is left over when a number cannot be divided into perfectly equal groups. It is always smaller than the divisor — if it isn't, you haven't divided enough times.

85 ÷ 4 = ?
4 × 21 = 84 (closest without going over)
85 − 84 = 1 left over
= 21 remainder 1 → written as 21 R1 ✓

Real world example: 85 sweets shared equally between 4 children. Each child gets 21 sweets and 1 is left over.

Try These Examples

Same four steps every time — the remainder appears at the very end

47 ÷ 3
3 into 4 = 1 r1 → bring 7 → 3 into 17 = 5 r2
= 15 R2 ✓
63 ÷ 5
5 into 6 = 1 r1 → bring 3 → 5 into 13 = 2 r3
= 12 R3 ✓
91 ÷ 6
6 into 9 = 1 r3 → bring 1 → 6 into 31 = 5 r1
= 15 R1 ✓
78 ÷ 7
7 into 7 = 1 r0 → bring 8 → 7 into 8 = 1 r1
= 11 R1 ✓
100 ÷ 9
9 into 10 = 1 r1 → bring 0 → 9 into 10 = 1 r1
= 11 R1 ✓
58 ÷ 4
4 into 5 = 1 r1 → bring 8 → 4 into 18 = 4 r2
= 14 R2 ✓

Common Mistakes (And How to Fix Them)

❌ Forgetting the remainder at the end
✓ After the final subtraction, if there is a number left over that is smaller than the divisor — that is your remainder. Write it as "R" followed by the number.
❌ Writing a remainder larger than the divisor
✓ The remainder must always be smaller than the divisor. If it isn't, you haven't divided enough times — go back and increase your quotient by 1.
❌ Forgetting to bring down the next digit
✓ After every subtraction, ask: "Is there another digit to bring down?" If yes, bring it down before dividing again.

Build on the basics first with our long division steps guide, then come back here for remainders.

Multiplication & Division Foundations

GRADES 3–5

$57

Long division with remainders is the point where many kids hit a wall — not because it's too hard, but because the conceptual link between multiplication and division was never made solid. This course builds both operations together from equal groups through to long division, so the procedure makes sense rather than being a set of steps to memorise.

Get Multiplication & Division Foundations on Gumroad →

More Math Tricks & Guides

Long Division Steps for Kids
The basic method without remainders
Multiplying by 9 Trick
Fast multiplication method
Place Value Explained
Understanding digit positions
Division Worksheets
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