Subtraction With Decomposition

Consider the following subtraction:

Subtraction 1

When subtracting one number from another, we start with the units in the right hand column and then move on to the tens in the left hand column. In each column we subtract the bottom number from the top number and write the result below. In this sum, we subtract 2 from 6 in the units column to get 4.

Subtraction - Units

Now we move along to the tens column and subtract 1 from 5 to get 4.

Subtraction - Tens

Thi is an easy sum because each number in the bottom row is smaller than the number in the top row. What happens if that’s not the case, as in the following example?

Subtraction 4

The problem is that we can’t take 9 from 4 in the units column. If you have only 4 apples, your mum can’t take 9 away from you. What we need here is something called decomposition. Decomposition happens when we borrow an amount from from the number on the left to give it to the number on the right. We only do this in the top row.

What this means here is that we can’t take 9 from 4 so we borrow a ten from the next column along (the 3). We will take 10 off the left hand number (3) and give it to the right hand number (4). The 3 is in the tens column, so it represents 30. Taking 10 off 30 leaves 20 (2) and adding 10 to 4 gives 14.

Decomposition In Subtraction

We can now subtract 9 from 14 in the units colun to get 5.

Subtraction With Decomposition - Units

Next, we subtract 1 from 2 in the tens column to get 1.

Subtraction With Decomposition - Tens

And that’s the answer. 34 – 19 = 15.

If you want to practise, here are some subtraction with no decomposition worksheets that you can download for free.