Example
Say one wants to find the sum of the numbers 653 and 274. Write the second number under the first one, with digits aligned in columns, like so:
| 6 | 5 | 3 |
| 2 | 7 | 4 |
Then draw a line under the second number and put a plus sign. The addition starts with the ones-column. The ones-digit of the first number is 3 and of the second number is 4. The sum of three and four is seven, so write a 7 in the ones-column under the line:
| 6 | 5 | 3 | |
| + | 2 | 7 | 4 |
| 7 |
Next, the tens-column. The tens-digit of the first number is 5, and the tens-digit of the second number is 7, and five plus seven is twelve: 12, which has two digits, so write its last digit, 2, in the tens-column under the line, and write the carry digit on the hundreds-column above the first number:
| 1 | |||
| 6 | 5 | 3 | |
| + | 2 | 7 | 4 |
| 2 | 7 |
Next, the hundreds-column. The hundreds-digit of the first number is 6, while the hundreds-digit of the second number is 2. The sum of six and two is eight, but there is a carry digit, which added to eight is equal to nine. Write the 9 under the line in the hundreds-column:
| 1 | |||
| 6 | 5 | 3 | |
| + | 2 | 7 | 4 |
| 9 | 2 | 7 |
No digits (and no columns) have been left unadded, so the algorithm finishes, and
- 653 + 274 = 927.
Read more about this topic: Elementary Arithmetic, Addition
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