Long
Division
You already know how to do this. Division is just repeated subtraction — and you do that every time you share pizza. In 5 minutes you'll be able to divide any number by a single digit and explain how you did it.
What you'll learn
- 01 What dividend, divisor, and quotient mean
- 02 The 4-step loop you run for every digit
- 03 How to find a quotient and a remainder
What is long division?
Long division is a method for splitting a big number into equal groups. Every problem has three parts:
DIVIDEND ÷ DIVISOR = QUOTIENT
"the total "number of "how many
to share" groups" each"
Think of 84 cookies shared between 3 friends. The dividend is 84, the divisor is 3, and the quotient — the answer you're after — is how many cookies each person gets.
The 4-step loop
Every digit in the dividend runs through the same four steps. Here's the mnemonic to remember them:
"Does McDonald's Sell Burgers?"
| Step | Name | Question to ask |
|---|---|---|
| D | Divide | How many times does the divisor fit into this number? |
| M | Multiply | Write divisor × that number below |
| S | Subtract | Find what's left over |
| B | Bring down | Pull the next digit down beside the remainder |
Step by step: 84 ÷ 3
We'll run DMSB twice — once for each digit in the dividend. Set up looks like this:
_ _
────
3 ) 8 4
Round 1 — the digit 8
How many 3s fit in 8? → 2
3×2=6 ✓ — 3×3=9 is too big
Write 2 above the bar. Multiply: 3 × 2 = 6. Write it below the 8.
8 − 6 = 2. Write the remainder below.
Bring the 4 down beside the 2. You now have 24.
2
────
3 ) 8 4
6 ↓
───
2 4
Round 2 — the number 24
How many 3s fit in 24? → 8
3×8=24 — exact!
Write 8 above. Multiply: 3 × 8 = 24. Write it below.
24 − 24 = 0. No remainder.
No more digits. Done.
2 8
────
3 ) 8 4
6
───
2 4
2 4
───
0
What about remainders?
Not every division comes out clean. Try 85 ÷ 3 — only the last digit changes:
2 8
────
3 ) 8 5
6
───
2 5
2 4
───
1 ← remainder!
Write it as 28 r 1.
Rule to remember
The remainder is always smaller than the divisor. If it's bigger, your D step was too small — go back and try the next number up.
Quick check
Say the mnemonic out loud before moving on:
"Does McDonald's Sell ?"
D · M · S · B — got it? Move on.
Solve: 69 ÷ 3
_ _
────
3 ) 6 9
Work through D → M → S → B twice, once for each digit.
Ask yourself: "how many 3s fit?" for each group of digits.
Show answer
69 ÷ 3 = 23
2 3
────
3 ) 6 9
6 ↓
───
9
9
─
0
Round 1: 3 fits into 6 → 2 times. 3×2=6. 6−6=0. Bring down 9.
Round 2: 3 fits into 9 → 3 times. 3×3=9. 9−9=0. Done.
If you got it — you've got long division.
The 7 things to remember
- Dividend ÷ Divisor = Quotient
- D — Divide: how many times does it fit?
- M — Multiply: divisor × that number
- S — Subtract: find what's left over
- B — Bring down: pull the next digit
- ↺ Repeat D → M → S → B until no digits remain
- Remainder = what's left (always smaller than the divisor)
Screenshot to keep — your take-away card
"Does McDonald's Sell Burgers?" → D · M · S · B
Review schedule
- Recite DMSB from memory
- 96 ÷ 4
- 117 ÷ 5
- 256 ÷ 8