Arabic Numbers --- Introduction --- Add --- Subtract --- Multiply --- Divide --- Practise sums --- Less than 1 --- Types of numbers
If you want to practise your mental arithmetic at subtraction, click here.
Subtract is sometimes also known as minus or take away.
Subtraction is the opposite of addition. If you want to subtract this number by that number, you can work it out by thinking "What number added to that number gives this number?"
Multiplication tables are well known. There are addition and subtraction tables as well. Here are the subtraction tables laid out for you to look at. Click on numbers at the top and the side.
Subtraction is not commutative. 3-2 is not the same thing as 2-3. Also it matters the order you subtract numbers. So subtraction is not associative either. For example: 9 - (6 - 4) = 9 - 2 = 7 but (9 - 6) - 4 = 3 - 4 = -1
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.
Click on Get sum for some practice in subtracting. When the sum appears, enter the answer in the boxes. There are boxes provided for carries using method 3, but you don't have to use them.
Throughout history, people have used an abacus to help them with addition and subtraction. Even earlier, people used their fingers. Now we tend to use a calculator.
However, it's best to make sure that you can do simple sums in your head. Click here to learn to do mental arithmetic quickly and accurately.
© Jo Edkins 2006 - Return to Numbers index