Maths 5 min Ages 9+

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

  1. 01 What dividend, divisor, and quotient mean
  2. 02 The 4-step loop you run for every digit
  3. 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?"

D Divide
M Multiply
S Subtract
B Bring down
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

D

How many 3s fit in 8? → 2
3×2=6 ✓ — 3×3=9 is too big

M

Write 2 above the bar. Multiply: 3 × 2 = 6. Write it below the 8.

S

8 − 6 = 2. Write the remainder below.

B

Bring the 4 down beside the 2. You now have 24.

       2
     ────
  3 ) 8 4
      6 ↓
      ───
      2 4

Round 2 — the number 24

D

How many 3s fit in 24? → 8
3×8=24 — exact!

M

Write 8 above. Multiply: 3 × 8 = 24. Write it below.

S

24 − 24 = 0. No remainder.

B

No more digits. Done.

       2 8
     ────
  3 ) 8 4
      6
      ───
      2 4
      2 4
      ───
        0
Answer: 84 ÷ 3 = 28 remainder 0 — each friend gets exactly 28 cookies.

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.

Your turn

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

  1. Dividend ÷ Divisor = Quotient
  2. D — Divide: how many times does it fit?
  3. M — Multiply: divisor × that number
  4. S — Subtract: find what's left over
  5. B — Bring down: pull the next digit
  6. ↺ Repeat D → M → S → B until no digits remain
  7. Remainder = what's left (always smaller than the divisor)

Screenshot to keep — your take-away card

Long Division smallguides.uk

"Does McDonald's Sell Burgers?" → D · M · S · B

D
DivideHow many times does it fit?
M
MultiplyDivisor × that number
S
SubtractFind what's left over
B
Bring downPull the next digit

Review schedule

  • Recite DMSB from memory Tonight
  • 96 ÷ 4 Tomorrow · = 24
  • 117 ÷ 5 In 3 days · = 23 r 2
  • 256 ÷ 8 In 1 week · = 32

Keep going

Long division is a skill, not a fact — it takes a few rounds to stick. You've got the foundation. Next levels:

  • Divide by a 2-digit number (e.g. 144 ÷ 12)
  • Divide with decimals (e.g. 8.4 ÷ 3)
  • Explain it to someone else in under 60 seconds

Teaching it is the fastest way to make it permanent.