How to do long division


A beginner’s guide to long division

The “long” in long division just means that the number you’re dividing by (the “divisor”) is longer than one digit. So 369 ÷ 33 (369 divided by 33) is long division, but 369 ÷ 3 is not.

So, how do you actually do long division without a calculator? Let’s try dividing 3708 by 36. The starting point would look like this:

From here on, you need to work in chunks from left to right, i.e. from the 3 to the 8.

Start with the 3 on its own – does the 36 divide into that? Obviously not. You therefore need to bring the 7 onboard and ask yourself whether 36 divides into 37. Yes, it does: once. You therefore write a “1” above the line, directly above the 7.

You also have a remainder of 1. Carry the remainder and write it next to the 0, as a superscript. You therefore end up with this:

The superscripted 1 (the remainder you got when you divided 36 into 37) now needs to be looked at alongside the next number in your 3708, i.e. the 0. This gives the number 10. Ask yourself whether 36 divides into 10. Answer: no, it doesn’t. It goes zero times in other words, which is why you need to write a zero immediately above the line:

But you’ve still got that 10 – what do you do with it? Answer: it becomes another remainder, which you tack onto the front of the 8, as follows:

So what you now need to ask yourself is “how many times does 36 go into 108? You may need to use a bit of trial and error for this. Try multiplying 36 by 2, then by 3 etc. As luck would have it, 36 goes into 108 exactly 3 times. So you end up with:

So in other words, 3708 ÷ 36 = 103

To check whether this (or any) division is correct, work backwards and multiply 103 by 36! (Long multiplication article to be added shortly – watch this space.)

What happens with a divisor that doesn’t go exactly?

With 3708 ÷ 36, we were lucky – 36 goes into 3708 exactly 103 times. Supposing you’re doing a sum like 3709 ÷ 36?

The initial stages are exactly the same as for 3708 ÷ 36:

But then you come to the remainder, which is 1. You can either just quote your answer as having a remainder (“103 remainder 1”), or you can add a decimal point. Let’s say we’re going to give the answer to one decimal place. This means that we have to work out the answer to two decimal places, and round up if necessary.

Add a decimal point after the 9, then put in a couple of zeros. Remember that you need to put a decimal point in your answer, exactly above the decimal point in the after the 9 of 3709. If you carry on as before, you find you end up with this:

Rounding off to one decimal place therefore gives you an answer of 103.0

Doing your working underneath instead

Going back to 3708 ÷ 36, some people prefer to do their working out underneath, instead of writing the remainders as subscripts next to the original figures. So the first stage of 3708 ÷ 36 would look like this:

You write the 36 underneath the 37, take one away from the other, and then bring down the 0 and the 8 to give 108. I personally prefer the other method but your mileage might vary, as they say!

© Empress Felicity April 2012