Formal Long Division (3)

In this worksheet we will divide numbers with up to 4 digits by 2-digit numbers using long division.

There will be remainders which should be written as fractions.

 

Let's look at   1986 ÷ 15

 

We start by setting out the calculation as usual, like this, and then start dividing.

 

 

First we divide 19 ÷ 15 = 1 rem 4.

(Remember that 1 × 15 = 15 and so the remainder is 19 - 15 = 4.)

 

 

Bring the 8 down next to the 4.

Then we divide 48 ÷ 15 = 3 rem 3.

(Remember that 3 × 15 = 45 and so the remainder is 48 - 45 = 3.)

 

 

Bring the 6 down next to the 3.

Now we divide 36 ÷ 15 = 2 rem 6.

(Remember that 2 × 15 = 30 and so the remainder is 39 - 30 = 9.)

 

The final remainder is 6, but we want to write this as a fraction.

 

We are dividing by 15, so a remainder of 6 is actually the fraction 6/15.

 

6

15

 

To reduce this fraction to its lowest terms, we look for the highest number that goes into 6 and 15.

This will be 3, because 2 × 3 = 6 and 5 × 3 = 15.

So we divide the top and the bottom numbers by the magic number 3, to get 2 and 5.

 

6	=	2
15		5

 

We have shown that 1986 ÷ 15 =

132	2
	5

 

In this worksheet, this will be written as 132 2/5  with a space between the 132 and the 2/5.