Operations and calculations

5. Division

5.2. Long division

Long division is an expanded version of the short division method. It’s useful when the divisor is a larger number, with two digits or more.

Let’s look at an example.


3888 ÷ 12

We start off in the same way, setting out our digits with the dividend (3888) in a box and the divisor (12) to the left of the box.

The dividend (3888) is placed in a two sided box with the divisor (12) to the left.

Looking at the first digit of the dividend: 3 cannot be divided by 12, so we combine it with the digit on its right, to make 38.

How many times can 38 be divided by 12?

The nearest we can get, without going over, is 3 x 12 = 36, so we write 3 above the line and 36 below 38, ready to subtract it.

38 – 36 = 2

3 is placed above the line and 36 below 38. Subtracting 36 from 38 leaves 2.

Now we pull down the next digit in the dividend (8), placing it next to the remainder (2) to make 28. How many times can 28 be divided by 12?

The nearest we can get, without going over, is 2 x 12 = 24, so we write 2 above the line and 24 below 28, ready to subtract it.

28 – 24 = 4

8 is pulled down to make 28. 2 x 12 is 24, so this is written below, and subtracted from, 28, leaving 4.

Next, we pull down the final digit in the dividend (8), placing it next to the remainder (4) to make 48.

How many times can 48 be divided by 12?

4 x 12 = 48, with no remainder, so we write 4 above the line and we can write 48 below, just to confirm this.

The final digit is pulled down to make 8. 4 x 12 is 48, with no remainder.

3888 ÷ 12 = 324


Try it out

4037 ÷ 11

Solution as described below

4 cannot be divided by 11, so combine it with the next number to make 40.

3 x 11 = 33

Write 3 above the line and take 33 away from 40, to leave a remainder of 7.

Pull down the next digit (3) to make 73.

6 x 11 = 66

Write 6 above the line and take 66 away from 73, to leave 7.

Pull down the final digit (7) in the dividend, to make 77.

7 x 11 = 77

Write 7 above the line and 77 below 77, to confirm there is no remainder.

4037 ÷ 11 = 367