Short Division

Say 728 raffle tickets need splitting fairly between 4 school teams, or a £96 prize is shared among 3 friends — numbers too big to divide in one glance. Short division is the quick pen-and-paper method that handles exactly this, and it's how you'll divide by hand long after the calculator battery dies.

Once a number has more than one digit, you can't always do the division in your head at once. Short division — often called the "bus stop" method — breaks it into a tidy line of single-digit divisions you can do, working left to right, one digit at a time.

The dividend sits inside the "bus stop", the divisor sits outside on the left, and the answer (the quotient) is built on top:

728 \div 4 = 182

Why left to right? Because the leftmost digit is the biggest place value — the hundreds before the tens, the tens before the ones — so you share out the big chunks first and let whatever is left over trickle down to the smaller columns. Every step is just one small division fact, so if you know your times tables, you already have everything you need.

The shape gives it away: the line on top and the little wall on the left look just like a bus shelter a bus, with the digits of the dividend waiting underneath like passengers in a queue. You serve them one at a time, in order, from the front — never out of turn, never all at once. The answer grows on the roof above their heads.

The method, step by step

Take the digits of the dividend in order, from the left. For each digit:

  1. Divide the current digit by the divisor.
  2. Write how many times it goes on top — that's the next digit of the answer.
  3. Whatever is left over (the remainder) is carried to the next digit on the right, where it joins on as a tens part.

So a carried remainder of 3, dropped in front of a digit 2, makes the number 32 to divide next. When you reach the very last digit (the ones) and there is still something left over, that final leftover is the remainder of the whole answer — you write it after the quotient, like 47 \div 4 = 11 \text{ r } 3.

Three worked examples

1. No carries — 96 \div 3. Each digit divides exactly:

96 \div 3 = 32

2. A carry between the columns — 75 \div 5:

75 \div 5 = 15

3. A leftover at the end — 47 \div 4:

47 \div 4 = 11 \text{ r } 3 The two carrying traps that trip everyone up:

Short division is just fair sharing written neatly. To split 96 cookies a cookie a cookie a cookie among 3 friends, you don't hand them out one by one — you deal the 9 tens first (3 tens each), then the 6 ones (2 each). Everyone ends up with 32. The bus-stop columns are simply the tens pile and the ones pile, shared out biggest-first.

See it built

Watch each digit divided in turn. When a digit doesn't divide exactly, the remainder is carried to the next digit along (shown in a different colour), making a bigger number to divide there. Step through it.

Try a fresh one

Here is a random 2-digit ÷ 1-digit bus stop, worked one column at a time. Step through the tens, then the ones, watching any leftover get carried across. Press Refresh for a brand-new division — some come out exactly, some finish with a remainder.

See it explained

Sal Khan works through dividing a multi-digit number by a single digit, carrying as he goes.