Short Division
Set it out in full first, with every subtraction written down. Once you can see where the leftovers come from, the short form is just the same working with the middle hidden.
What division is asking
756 divided by 3 asks how much each one gets when 756 is shared into three equal parts.
It also asks how many threes fit into 756, and those are two different questions with the same answer, which is a genuinely confusing thing to meet at nine years old. Sharing and grouping feel like different activities, and it is worth telling a child plainly that division covers both rather than letting them decide they have misunderstood something.
The full working
Set it out exactly as you would on paper. The divisor outside, the number being divided inside, the answer building along the top, and every subtraction written down underneath.
Follow the drawing, one line at a time.
- Threes into 7 go twice. Write 2 above the 7, write 6 underneath it, rule off, and subtract: 7 - 6 = 1.
- Bring the 5 down beside that 1 to make 15. Threes into 15 go five times. Write 5 on top, 15 underneath, subtract: 15 - 15 = 0.
- Bring the 6 down beside the 0 to make 6. Threes into 6 go twice. Write 2 on top, 6 underneath, subtract: 6 - 6 = 0.
- No digits left and nothing remaining, so the division is finished.
252
The same four moves, every time
Divide to get the digit on top. Multiply it by the divisor and write that underneath. Subtract. Bring down the next digit and start again.
That is the whole method, whether the divisor is 3 or 23.
The short form
Once you can do the full working without thinking, the middle of it can be left out. What was 7 - 6 = 1 becomes a small 1 tucked in front of the next digit, and the subtractions never get written at all. That is what short division is: the same method with the workings kept in your head.
The small carried digit is the whole shorthand, and it is worth knowing what it is really worth. When 7 is divided by 3 there is 1 left over, and that 1 is not one. It is one hundred, because the 7 sat in the hundreds column. Moved across in front of the 5 it becomes ten tens, which with the 5 tens already there makes 15 tens.
Use the full form until the short one is obvious
There are no marks for writing less. A child who is still unsure should set out every subtraction, because a wrong answer in the full form can be found and fixed, and a wrong answer in the short form usually cannot.
Zeros and remainders
Sometimes a digit is too small to divide at all. In 4,736 divided by 8, the first digit is 4 and there are no eights in 4, so the answer digit there is zero and the whole 4 carries across. A child who skips writing that zero ends up with an answer one digit too short, and then everything is ten times too small.
When the last column will not divide exactly, whatever is left is the remainder. 25 divided by 4 is 6 remainder 1, and that leftover 1 is real: it is the piece that could not be shared.
Common mistakes
1. Forgetting to carry the remainder across
Dividing 756 by 3, writing 2 above the 7, and then dividing the 5 on its own. The leftover from the previous column has to join the next digit, because it has not been used yet. Saying the "remainder one, carry the one" sentence out loud is what fixes this.
2. Skipping the zero at the front
In 4,736 divided by 8, going straight to 47 without writing anything above the 4. The answer is 592, and skipping that step is how children end up writing it in the wrong columns. Write the zero, then cross it out at the end if it is a leading zero.
3. Dividing in the wrong direction
Reading 756 divided by 3 and working out 3 divided by 756, or starting from the right. Division is the one written method that runs left to right, and unlike multiplication it does not give the same answer both ways round.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
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What to learn next
Long division is the same method with the working written out in full, which becomes necessary once the divisor is too big to hold the multiples in your head.
For parents
Check the answer by multiplying it back. If 756 divided by 3 gives 252, then 252 times 3 should give 756. It takes twenty seconds, it uses a skill they already have, and it means your child finds their own errors instead of waiting for a red mark to tell them.
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