Long Division with a Remainder
(KS2, Year 5)

The Lesson

Long division is a method for dividing numbers. Long division is used for dividing numbers that have many digits. Sometimes a number will not divide exactly into another: there will be a remainder.

A Real Example of How to Do Long Division

Doing long division, when there will be a remainder, is easy.

Question

Divide the numbers below.

Step-by-Step:

1

Identify the number being divided (called the dividend) and the number you are dividing by (called the divisor).

2

Write the dividend inside the long division bracket and the divisor outside to its left:

3

Divide the first digit of the dividend (1) by the divisor (6). Do not count remainders.

1 ÷ 6 = 0
6 goes into 1 0 times.

4

Write the answer (0) above the long division bracket.

5

Multiply the answer from Step 3 (0) with the divisor (6).
0 × 6 = 0
Write the answer underneath the digit divided into:

6

Subtract the bottom number (0) from the top number (1).

1 − 0 = 1

7

Bring down the next digit of the dividend (4).

8

Divide this number (14) by the divisor (6). Do not count remainders.

14 ÷ 6 = 2  r 2 
6 goes into 14 2 times.

9

Write the answer (2) above the long division bracket.

10

Multiply the answer from Step 8 (2) with the divisor (6).
2 × 6 = 12
Write the answer underneath the number divided into:

11

Subtract the bottom number (12) from the top number (14).

14 − 12 = 2

12

Bring down the next digit of the dividend (0).

13

Divide this number (20) by the divisor (6). Do not count remainders.

20 ÷ 6 = 3  r 2 
6 goes into 20 3 times.

14

Write the answer (3) above the long division bracket.

15

Multiply the answer from Step 13 (3) with the divisor (6).
3 × 6 = 18
Write the answer underneath the number divided into:

16

Subtract the bottom number (18) from the top number (20).

20 − 18 = 2
There are no more digits to bring down.

17

The number above the long division bracket is the quotient. The number at the bottom is the remainder.

18

Write the answer as 23 (the quotient), r (for remainder) 2 (the remainder).

Answer:

The solution to 140 ÷ 6 is 23 r 2.

Lesson Slides

The slider below shows another real example of how to do long division with a remainder. Open the slider in a new tab

What Is a Remainder?

Division doesn't always work out perfectly. Numbers do not always divide into equal groups. For example, what is:
7 ÷ 2 = ?
Think about sharing 7 apples out into 2 equal groups:

Looking above, it can be seen that this is not possible to split the apples into 2 equal groups. 2 groups of 3 apples can be made, with 1 apple left over:

The answer to 7 ÷ 2 is 3 (as there are 3 apples in each group) remainder 1 (there is 1 apple left over). This can be written as:
7 ÷ 2 = 3 r 1
The r stands for remainder.

Parts of an Division

  • The number you divide into is the dividend.
  • The number you divide by is the divisor.
  • The result of the division is the quotient.

Short Cut for Long Division

When you gain enough confidence, you will notice that the first few steps in this lesson are not necessary. In Step 3 of the example, 1 is divided by 6, and so won't divide at least once. That is why 0 was written above. Instead, don't divide by the first digit of the dividend, but move along the digits, left to right, until you find the first number larger than the divisor.

Just remember that the answer must be written above the last digit. The 2 must be written above the 4 in 14, not the 1.
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See Also

Long division with decimals How to add on a number line Addition basics Long addition How to subtract on a number line Subtraction basics Long subtraction Multiplication basics Long multiplication Long multiplication with decimals A closer look at multiplication Division basics Long division What is place value? What is a number line?