Long Division Step by Step
Long division looks scary — but once you learn the “bus stop” method it becomes a simple repeating pattern. Let’s break it down so it actually makes sense.
The Bus Stop Method
Imagine a bus stop shelter — you draw a line over the number you’re dividing (the dividend) and the number you’re dividing by (the divisor) sits to the left. Then you work through each digit from left to right asking: “How many times does the divisor go in?”
The four steps repeat for every digit:
- Divide — how many times does it go in?
- Multiply — divisor × your answer.
- Subtract — take that away from the current number.
- Bring down — bring the next digit down and repeat.
Key Formulas
- Dividend ÷ Divisor = Quotient (answer)
- Quotient × Divisor + Remainder = Dividend (use this to check!)
Worked Examples
Example 1 — 96 ÷ 4
- 4 into 9 goes 2 times (2 × 4 = 8). Write 2 above the 9. Remainder 1.
- Bring down the 6 to make 16.
- 4 into 16 goes 4 times exactly. Write 4 above the 6.
Answer: 24
Check: 24 × 4 = 96 ✓
Example 2 — 672 ÷ 14
- 14 into 6? Doesn’t go (0 times). So look at first two digits: 14 into 67.
- 14 × 4 = 56. Write 4. Remainder 67 − 56 = 11.
- Bring down the 2 to make 112.
- 14 × 8 = 112. Write 8. Remainder 0.
Answer: 48
Check: 48 × 14 = 672 ✓
Example 3 — 5,437 ÷ 23
- 23 into 54 → 23 × 2 = 46. Write 2. Remainder 8.
- Bring down 3 → 83. 23 × 3 = 69. Write 3. Remainder 14.
- Bring down 7 → 147. 23 × 6 = 138. Write 6. Remainder 9.
Answer: 236 remainder 9
Check: 236 × 23 + 9 = 5,428 + 9 = 5,437 ✓
Dealing with Remainders
A remainder is the little bit left over that won’t divide evenly. You can write it in different ways depending on the question:
- r 9 — just write the remainder (Example 3 above).
- 236 and 9/23 — as a fraction.
- 236.39… — as a decimal (add a decimal point and zeros, keep dividing).
In SATs they’ll usually tell you which form they want — read the question carefully!
Checking Your Answer
Division and multiplication are opposites. To check your answer, multiply the quotient by the divisor and add any remainder. If you get back to the original number, you’re right! Always do this in the test — it only takes a few seconds and catches silly mistakes.
Common Mistakes
- Forgetting to write a 0 in the answer when the divisor doesn’t go in.
- Bringing down the wrong digit or skipping a digit.
- Subtracting incorrectly mid-way through (take your time).
- Not checking with multiplication at the end.
Practice Questions
- 845 ÷ 5
- 756 ÷ 12
- 1,368 ÷ 18
- 2,945 ÷ 31 (give remainder)
- 4,032 ÷ 16
Answers: 1) 169 2) 63 3) 76 4) 95 r 0 5) 252