Subtraction with borrowing – sometimes known as regrouping or exchanging – is a technique that lets us subtract any number from another. It works on a similar principle as addition with regrouping, which you might also hear referred to as carrying over.
We use subtraction with borrowing alongside column subtraction to use place value to help us “borrow” an amount from the next column along – the tens, hundreds, or even thousands.
Let’s see subtraction with borrowing in action:
The best way to understand subtraction with borrowing is to see it in action. So let’s work through an example together, looking at the simple question 42-17.
First, we line the numbers up as we would do with any column question:
42
17 –
——
But with our first step, we hit a problem. We can’t subtract 7 from 2 without going into tricky minus numbers, which wouldn’t help us in this situation. So instead, we can borrow ten from the next column along; this means that, instead of looking at 42 as 40+2, we can look at it as 30+12.
It helps us with the first stage of our problem since we can now calculate 12-7. Once we’re done with that, we’re also free to move one column to the left and finish the subtraction with 3-1.
4 3 12
1 7 –
———-
2 5
As you can see, we now have an overall answer of 25, which we have reached by using subtraction with borrowing.
When do I use subtraction with borrowing?
Subtraction with borrowing is used alongside the column method – where numbers are placed vertically, and you work through one place value column at a time.
We use this technique when the maximum number in a column is smaller than the bottom, as seen in the example above. In this case, the 2 in 42 was smaller than the 7 in 17, so we needed to borrow ten from the next column.
This method makes taking away much more straightforward, allowing children to complete subtraction questions involving two, three, or even four-digit numbers.
