Olivia

2 minute read

To long divide you need to turn a long hard problem into many smaller problems.

The key here is to think about numbers digit by digit.

Let’s divide 936 by 4. Sometimes this is written as a slash, /, to represent a fraction. Fractions are division.

We need to turn this into a smaller problem. So we’ll break it into smaller steps by trying to divide each digit by 4, one digit at a time.

You know how in multiplication and addition you work right to left? Well, divison is backwards.

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We divide by left to right. Super weird, huh?

We try to divide by the biggest number first.

Write the number you are dividing on the left hand side, like so:

4 | 936| — | — |

Now we try to divide 9 by 4, digit by digit.

   
4 936

So

How many 4’s does it take to make 9? So 2 fours is 8, and that’s almost 9. If we add another 4 we get 12, which is too much. So we stay at 8 and say the result is:

  2
4 936

This step is kinda pointless, but I’ll include it here.

We multiply the number we have from:

by the number we’re dividing by, 4.

So we have

Now we write the “8” below the 9 and make it negative.

  2
4 936
  -8

And this is simple maths

This is just a way to find the remainder.

We need to write down this remainder, make it important because it’s useful to us.

Now you might think that the next step is:

and it is.. Sort of. We have that remainder still. If the remainder exists (which it does here) we need to add the next digit to the remainder. Here’s the funny part:

  2
4 936
  -8
  13

Since the remainder is from the left handside, it’s worth more than 1. It’s actually 10.

Remember this from school?

How you have different units in every number? That counts here. Our remainder came one from the left, so it’s actually worth 10.

It’s like our remainder is teaming up with the next digit over.

So now our remainder was 1, but now it’s 13 so 4 can divide into it.

How many 4’s does it take to make 13?

We just count.

Uh oh! Too large. So our smallest number is 3. So that’s the next digit we have.

  23
4 936
  -8
  13

Now we have a remainder of 1 again so we do

  23
4 936
  -8
  13
  12

We get the 12 from 3*4.

Now we subtract 13 from 12 which is 1.

  23
4 936
  -8
  13
  12
  1

Now we bring down the number 6 to the remainder:

  23
4 936
  -8
  13
  12
  16

That makes 16!

How many 4’s go into 16?

Well that’s 4 * 4, which gives us 4 back!

So our answer is:

  234
4 936
  -8
  13
  12
  16
  16

Now we subtract 16 from 16, but that results in 0 so we have no remainder left. Nothing to do now!!

Extra resources

https://www.youtube.com/watch?v=LGqBQrUYua4

https://www.youtube.com/watch?v=HdU_rf7eMTI

https://www.khanacademy.org/math/arithmetic-home/multiply-divide/mult-digit-div-2/v/division-2