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Formal Long Division (3)

In this worksheet, students must divide numbers up to 4 digits by a two-digit number using the formal written method of long division. There may be remainders, which should be written as reduced fractions.

Worksheet Overview

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.

 

Long division

 

First we divide 19 ÷ 15 = 1 rem 4.

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

 

Long division

 

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.)

 

Long division

 

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.)

 

Long division with a fraction remainder

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.

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