Subtraction with borrowing

How to do subtraction with borrowing – a quick, easy guide with illustrations

We’ll start with a straghtforward example, namely 733 – 216.

If you lay it out on the page in the traditional way, with the smaller number under the larger number, you get this:

Like all subtraction problems, you start with the units column, on the right hand side. When you realise that it’s not possible to take 6 away from 3, you borrow a 1 from the number in the tens column, which in this case is another 3. Cross that 3 out and put a superscript 2 just to the left of it.

In the units column, you’re now taking 6 away from 13 to give 7, and in the tens column, you’re taking 1 away from 2 to give 1.

Your final answer is 517.

And now for something a little bit harder…

Like 914 – 486. Your “borrowing pattern” will end up like this:

First of all, you’ve borrowed from the 1 in the 914, giving 14 – 6 in the units column. The answer you put in the units column is therefore 8.

In the tens column, you’re then left with 0 – 8. This isn’t possible so you borrow a 1 from the 9 in the hundreds column, giving 10 – 8 in the units column, i.e. an answer of 2.

Finally, when you get to the hundreds column, you’re left with 8 – 4, which is of course 4.

The answer is therefore 428.

Borrowing from zeros

Suppose we want to work out 103 – 45. This will give you an answer of 58:

You can’t actually borrow from the zero, because that would give you -1. So what you need to do is look at the everything to the left of the “3” in the 103, and borrow from that. In other words, you’re borrowing a 1 from 10, leaving you with a 9.

The same principle also applies when you do 306 – 187:

Look at the diagram above and you’ll see that the 30 that’s to the left of the 6 in the number 306 becomes 29.

Borrowing from numbers with lots of zeros

What about something like 2000 – 123? This causes a major headache for a lot of people who are learning subtraction.

In this case, you borrow a 1 from the 200 (the number to the left of the zero in the units column), so that it becomes 199. Once you’ve done that, it all becomes more straightforward!

Another technique you can use is to subtract a 1 from each number in your calculation. So 2000 – 123 becomes 1999 – 122. Alternatively you can take 1 from the 2000 and add 1 to the answer you get at the end. Whichever method suits you best!

© Empress Felicity February 2012