Long addition
Long Addition with Whole Numbers
We show in steps how to add whole numbers (ie "without decimals") using this example 454 + 782.
• Start by stacking the numbers to add and aligning them to the right. So, the digits of the ones (4 and 2) are in the same (first) column, the digits of tens (5 and 8) are in the same (second) column and so on.
| 4 | 5 | 4 | |
| + | 7 | 8 | 2 |
| = |
• We add the digits of the same column starting with the right column (column of ones) and put the result in the bottom of the same column.
4 + 2 = 6
| 4 | 5 | 4 | |
| + | 7 | 8 | 2 |
| = | 6 |
• We continue with the 2nd column (tens place).
5 + 8 = 13
This time the result has 2 digits: we put the ones digit (=3) in the result (bottom of the 2nd column) and we carry the tens digit (=1) to the next column (=3rd column).
| 1 | |||
| 4 | 5 | 4 | |
| + | 7 | 8 | 2 |
| = | 3 | 6 |
• We continue with the 3rd column (hundreds). We add the digits including the carry from the previous step.
1 + 4 + 7 = 12
Since this is the last column: we put the result "as is", i.e. whatever the number of its digits.
| 1 | ||||
| 4 | 5 | 4 | ||
| + | 7 | 8 | 2 | |
| = | 1 | 2 | 3 | 6 |
Long addition of decimal numbers
We show the steps for the following long addition 12.4547 + 3.82 + 878.874
• Start by stacking the numbers to be added and aligning them from the decimal separator. The decimal separators must be aligned in the same column.
| 1 | 2 | . | 4 | 5 | 4 | 7 | ||
| + | 3 | . | 8 | 2 | ||||
| + | 8 | 7 | 8 | . | 8 | 7 | 4 | |
| = |
• Fill the blank places after the decimal separator with zeros.
| 1 | 2 | . | 4 | 5 | 4 | 7 | ||
| + | 3 | . | 8 | 2 | 0 | 0 | ||
| + | 8 | 7 | 8 | . | 8 | 7 | 4 | 0 |
| = |
• We proceed exactly as in the previous case with whole numbers (see 1st paragraph for more details).
The long addition is as follows,
| 1 | 2 | 1 | ||||||
| 1 | 2 | . | 4 | 5 | 4 | 7 | ||
| + | 3 | . | 8 | 2 | 0 | 0 | ||
| + | 8 | 7 | 8 | . | 8 | 7 | 4 | 0 |
| = | 8 | 9 | 5 | . | 1 | 4 | 8 | 7 |
1st column
7 + 0 + 0 = 7
We put 7 in the result.
2nd column
4 + 0 + 4 = 4
We put 4 in the result.
3rd column
5 + 2 + 7 = 14
We put 4 and carry 1.
4th column
1 (carry) + 4 + 8 + 8 = 21
We put 1 and carry 2.
5th column
Column of decimal separators that we keep in the result.
6th column
2 (carry) + 2 + 3 + 8 = 15
We put 5 and carry 1.
7th column
1 (carry) + 1 + 7 = 9
We put 9 in the result.
8th column
We put 8 (the only digit in the column) in the result.
See also
Long Subtraction
Long Multiplication Calculator
Long decimal Division
Long Euclidean Division Calculator
Big numbers Calculator
Number Calculators
Mathematics Calculators