Long division

Long division is on the syllabus for both 11+ and 13+ exams, so it’s important to know when and how to do it.

The basic idea is that it’s tricky to do short division when the number you’re dividing by (the ‘divisor’) is outside your times tables, ie more than 12. Using long division makes it easier by including a way of calculating the remainder using a proper subtraction sum. It also makes it neater because you don’t have to try and squeeze two-digit remainders in between the digits underneath the answer line (the ‘dividend’).

So how does it work? Well, the only difference involves the remainder. In normal short division, you work it out in your head and put it above and to the left of the next digit in the dividend. In long division, you work out the multiple of the divisor, write it down under the dividend and subtract one from the other to get the remainder. You then pull down the next digit of the dividend and put it on the end of the remainder, repeating as necessary.

To take the example at the top of the page, what is 522 divided by 18?

  1. How many 18s in 5?
  2. It doesn’t go
  3. How many 18s in 52?
  4. Two (write 2 on the answer line, and write 36 under the dividend with a line beneath it)
  5. What’s 52 – 36?
  6. 16 (write it on the next line)
  7. Pull down the next digit from the dividend (write it after the 16)
  8. How many 18s in 162?
  9. Nine (write it on the answer line, giving 29 as the answer, or ‘quotient’)

That’s the basic method, but here are a couple of tips to help you out.

The first is that you can make life easier for yourself by guessing round numbers. Working with numbers outside your times tables is tricky, so you can use ‘trial and error’ to come up with the right multiple of the divisor by trying ‘easy’ ones like 5 or 10. If it’s too big or too small, you can simply try again with a smaller or bigger number.

The second is that you can often divide the divisor by two to force it back into your times tables. Why divide by 18 when you can simply divide by nine and halve the result? You just have to be careful that you only deal in even multiples, eg 52 ÷ 18 is tricky, but the nearest even multiple of 9 is 4 (as 5 is an odd number and 6 x 9 = 54, which is too much), so the answer must be 4.

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