Concept 5 of 10
The Mind-Ninja: Short Division
Today's big idea
Carry each remainder in your head so the whole division fits on one line.
7,295 divided by 5: each leftover rides in front of the next digit, giving 1,459.
How it works
👀 What's going on?
Long division fills half a page with subtractions and crossings out. Short division reaches the same answer in one line, by keeping the leftovers in your head instead of writing them down.
💡 Here's the trick
Look at 7,295 divided by 5 above. 5 goes into 7 once with 2 left over, and that 2 rides in front of the next digit to make 22. 5 goes into 22 four times with 2 left, which rides on to make 29. Keep going and the answer 1,459 appears digit by digit along the top.
🪄 How to do it
- 1.Start at the leftmost digit of the number in the picture above.
- 2.Divide, write the answer digit on top, and hold the remainder in your head.
- 3.Put that remainder in front of the next digit and repeat.
✍️ Try it
Work out 8,232 divided by 6. Three of the steps leave something to carry.
6 into 8 is 1 with 2 left, making 22. 6 into 22 is 3 with 4 left, making 43. 6 into 43 is 7 with 1 left, making 12. 6 into 12 is 2 exactly. Reading the top row gives 1,372.
⚠️ Watch out
You might be thinking that when the divisor will not go, you can simply move along. Try 4,505 divided by 5. At the third digit, 5 into 0 goes zero times, and that 0 still has to be written down. Leave it out and you get 91 instead of 901.
🌟 Why this matters
Splitting a bill between friends is a division. So is working out how many days a packet of food will last, or what each person owes.
Exam tip: Short division is the fastest reliable way to divide by a single digit when the clock is running.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“6,132 ÷ 4 using short division.”
- 1
4 into 6
Goes 1 time, remainder 2. Carry the 2 to the next digit.
- 2
4 into 21 (the carried 2 + next digit)
Goes 5 times, remainder 1. Carry.
- 3
4 into 13, then 4 into 12
4 into 13 = 3 rem 1. 4 into 12 = 3 rem 0. ✓
- 4
Quotient ✓
6,132 ÷ 4 = 1,533
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Short division, left to right. For each digit: how many times does 5 fit? The leftover REMAINDER rides along to the next digit.
7,295 ÷ 5
Step 1 of 4: 5 into 7 goes how many times?
Quick check
✅ VERIFICATION
Work out 6,045 divided by 5 using short division.
⚡ Finish the activity above first to answer.
Keep going!
Up next: Long Division
Write the subtraction down and the head-work disappears.