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Long Division
(KS2, Year 5)

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What Is Long Division? (Interactive Widget)

Use this interactive widget to see a step-by-step explanation of long division.

 

Here is a randomly generated long-division sum.

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What Is Long Division?

Long division is a method for dividing numbers.

long division Long division is used for dividing numbers that have many digits.

A Real Example of How to Do Long Division

Doing long division is easy.

Question

Divide the numbers below. 138 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). 138 divided by 6 long division step 1

2

Write the dividend inside the long division bracket and the divisor outside to its left: 138 divided by 6 long division step 2

3

Divide the first digit of the dividend (1) by the divisor (6). Do not count remainders. 138 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. 138 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: 138 divided by 6 long division step 5

6

Subtract the bottom number (0) from the top number (1). 138 divided by 6 long division step 6
1 − 0 = 1

7

Bring down the next digit of the dividend (3). 138 divided by 6 long division step 7

8

Divide this number (13) by the divisor (6). Do not count remainders. 138 divided by 6 long division step 8
13 ÷ 6 = 2  r 1 
6 goes into 13 2 times.

9

Write the answer (2) above the long division bracket. 138 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: 138 divided by 6 long division step 10

11

Subtract the bottom number (12) from the top number (13). 138 divided by 6 long division step 11
13 − 12 = 1

12

Bring down the next digit of the dividend (8). 138 divided by 6 long division step 12

13

Divide this number (18) by the divisor (6). Do not count remainders. 138 divided by 6 long division step 13
18 ÷ 6 = 3
6 goes into 18 3 times.

14

Write the answer (3) above the long division bracket. 138 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: 138 divided by 6 long division step 15

16

Subtract the bottom number (18) from the top number (18). 138 divided by 6 long division step 16
18 − 18 = 0
There are no more digits to bring down.

Answer:

The solution to 138 ÷ 6 is 23.

Lesson Slides

The slider below shows another real example of how to do long division.

Parts of a 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_short_cut Just remember that the answer must be written above the last digit. The 2 must be written above the 3 in 13, not the 1.
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This page was written by Stephen Clarke.

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