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Subtracting larger numbers

To subtract longer numbers, write one number under another so that they line up on the right-hand side, similar to addition. Subtraction is different from addition. 8 + 6 is the same as 6 + 8 but 8 - 6 is not the same as 6 - 8. So make sure that you write them in the right order!

Each column is subtracted separately, like addition. It is quite easy if each answer ends up zero or more.

Subtracting with borrow (method 1)

There are three different ways of subtracting if a column ends up less than zero. All of them work, but children can get confused if they are shown different methods by different people! So I have listed them all.

In this example, the problem is subtracting 6 from 4. The first method takes 1 from the top number of column on the left, by subtracting 1 from the digit. This is called borrowing. You cross out the existing digit to stop getting confused! In this example 9 becomes 8. When you move this 1 to the column where you need it, it becomes 10. You put a 1 before the digit. In this example 4 becomes 14. All this is marked in red, so you can see what's happening.

There is a problem if the left-hand column contains 0. You can't put -1 there! So you have to 'borrow' another 1 from the column further to the left. If you have a string of zeroes, then you may have to do this several times, which can get messy!

Subtracting with carry (method 2)

Here is the same calculation using the second method.

When you need an extra 10, instead of subtracting 1 from the top number, on the next column to the left, you add 1 to the bottom number in that column. This is a carry. You still add 10 where you need it.

There are two problems here. One is that you have two 1s but the right-hand one means add ten and the left-hand one means add one. I've added a little plus to the left-hand one to try to distinguish them. The other problem is explaining to children why you add ten in one place, and add one in another place, and that ends up as zero. The reason is that the one is in the next column (which makes it the same value as the ten), and that you are adding it to a number which is going to be subtracted, which is the same as taking it away. A little confusing, perhaps!

Subtracting with carry (method 3)

Here is a third method which I think is elegant! When you need an extra 10, you mark it like the other methods. Then you put -1 under the answer line, in the same place that you would put a carry for addition. In this example, the calculation for the hundreds then becomes 9 - 2 - 1. This means that the whole calculation look neater. It also is closer to the addition carry, which might make it easier to understand.