Explanation of Long Division
To understand how long division works, it is good to look at all the steps of an example.
Example: Divide 124 by 5 using Long Division
Steps:
-
The number that is divided is placed between slashes.
-
The number used to divide is placed to the left.
-
The number 5 does not fit into 1.
-
The number 5 does fit into 12.
The number of times 5 fits into 12 (2 times) is placed on the right.
-
The number 10 (= 5×2) is placed under 12 and subtracted.
-
The 4 is "added".
-
The number of times 5 fits into 24 (4 times) is placed on the right.
-
The number 20 (= 5×4) is placed under 24 and subtracted.
-
A 0 is added between the slashes.
A comma is placed right.
-
The 0 is "added".
-
The number of times 5 fits into 40 (8 times) is placed on the right.
-
The number 40 (= 8×5) is placed under 40 and subtracted.
5 | / | 1 | 2 | 4 | 0 | \ | 24, | 8 |
| | 1 | 0 | | | | |
| | | 2 | 4 | | | |
| | | 2 | 0 | | | |
| | | | 4 | 0 | | |
| | | | 4 | 0 | | |
| | | | | 0 | | |
-
The long division is now finished because the remainder is 0.
The result is 24.8.
5 | / | 1 | 2 | 4 | 0 | \ | 24,8 |
| | 1 | 0 | | | | |
| | | 2 | 4 | | | |
| | | 2 | 0 | | | |
| | | | 4 | 0 | | |
| | | | 4 | 0 | | |
| | | | | 0 | | |
Long division and fractions
Long division can be useful for calculating the decimal notation of a fraction.
Example 1: 1/8 = 0,125
The long division for this fraction:
8 | / | 1 | 0 | 0 | 0 | \ | 0,125 |
| | 0 | | | | | |
| | 1 | 0 | | | | |
| | | 8 | | | | |
| | | 2 | 0 | | | |
| | | 1 | 6 | | | |
| | | | 4 | 0 | | |
| | | | 4 | 0 | | |
| | | | | 0 | | |
Example 2: 1/3 = 0,33333
The long division for this fraction:
3 | / | 1 | 0 | 0 | 0 | 0 | 0 | \ | 0,33333 |
| | 0 | | | | | | | |
| | 1 | 0 | | | | | | |
| | | 9 | | | | | | |
| | | 1 | 0 | | | | | |
| | | | 9 | | | | | |
| | | | 1 | 0 | | | | |
| | | | | 9 | | | | |
| | | | | 1 | 0 | | | |
| | | | | | 9 | | | |
| | | | | | 1 | 0 | | |
| | | | | | | 9 | | |
| | | | | | | 1 | | |