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Long Division with a Remainder
(KS2, Year 5)

homesitemaparithmeticlong division with a remainder
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.

long division with 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. 140 divided by 6

Step-by-Step:

1

Identify the number being divided (called the dividend) and the number you are dividing by (called the divisor). 140 divided by 6 long division step 1

2

Write the dividend inside the long division bracket and the divisor outside to its left: 140 divided by 6 long division step 2

3

Divide the first digit of the dividend (1) by the divisor (6). Do not count remainders. 140 divided by 6 long division step 3
1 ÷ 6 = 0
6 goes into 1 0 times.

4

Write the answer (0) above the long division bracket. 140 divided by 6 long division step 4

5

Multiply the answer from Step 3 (0) with the divisor (6).
0 × 6 = 0
Write the answer underneath the digit divided into: 140 divided by 6 long division step 5

6

Subtract the bottom number (0) from the top number (1). 140 divided by 6 long division step 6
1 − 0 = 1

7

Bring down the next digit of the dividend (4). 140 divided by 6 long division step 7

8

Divide this number (14) by the divisor (6). Do not count remainders. 140 divided by 6 long division step 8
14 ÷ 6 = 2  r 2 
6 goes into 14 2 times.

9

Write the answer (2) above the long division bracket. 140 divided by 6 long division step 9

10

Multiply the answer from Step 8 (2) with the divisor (6).
2 × 6 = 12
Write the answer underneath the number divided into: 140 divided by 6 long division step 10

11

Subtract the bottom number (12) from the top number (14). 140 divided by 6 long division step 11
14 − 12 = 2

12

Bring down the next digit of the dividend (0). 140 divided by 6 long division step 12

13

Divide this number (20) by the divisor (6). Do not count remainders. 140 divided by 6 long division step 13
20 ÷ 6 = 3  r 2 
6 goes into 20 3 times.

14

Write the answer (3) above the long division bracket. 140 divided by 6 long division step 14

15

Multiply the answer from Step 13 (3) with the divisor (6).
3 × 6 = 18
Write the answer underneath the number divided into: 140 divided by 6 long division step 15

16

Subtract the bottom number (18) from the top number (20). 140 divided by 6 long division step 16
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. 140 divided by 6 long division step 17

18

Write the answer as 23 (the quotient), r (for remainder) 2 (the remainder). 140 divided by 6 long division step 18

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.

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: 7_apples 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: 7_apples_3r1 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

division explained
  • 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. long_division_remainder_short_cut 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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This page was written by Stephen Clarke.

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