Long addition calculator
4,825 + 3,976 = 8,801 by long addition, with a 1 carried into the tens, the hundreds and the thousands.
Sum
- Carries
- 1 into the tens, hundreds and thousands
- Check
- 8,801 - 3,976 = 4,825
| Column | Digits | Carry in | Column total | Write | Carry |
|---|---|---|---|---|---|
| ones | 5 + 6 | 0 | 11 | 1 | 1 |
| tens | 2 + 7 | 1 | 10 | 0 | 1 |
| hundreds | 8 + 9 | 1 | 18 | 8 | 1 |
| thousands | 4 + 3 | 1 | 8 | 8 | - |
- Columns are added from the right. A column total of 10 or more writes its last digit and carries 1 to the next column left.
How the Long Multiplication Calculator works
Long addition lines the numbers up by place value and adds one column at a time, starting with the ones. When a column adds up to 10 or more, write the last digit of that total under the column and carry the 1 to the top of the next column left.
Worked example: 4,825 + 3,976.
Ones: 5 + 6 = 11. Write 1, carry 1. Tens: 2 + 7 + 1 = 10. Write 0, carry 1. Hundreds: 8 + 9 + 1 = 18. Write 8, carry 1. Thousands: 4 + 3 + 1 = 8. Write 8.
The sum is 8,801.
With two numbers the carry is never more than 1, because the largest possible column total is 9 + 9 + 1 = 19. Adding a long list at once can carry more: a column of five 9s totals 45, so write 5 and carry 4.
Decimals line up on the decimal point rather than on the last digit. 12.5 + 3.75 is written as 12.50 + 3.75: the hundredths are 0 + 5 = 5, the tenths 5 + 7 = 12 (write 2, carry 1), the ones 2 + 3 + 1 = 6, and the sum is 16.25.
Check a sum by subtracting one of the numbers from it: 8,801 - 3,976 = 4,825.
Long Multiplication Calculator FAQ
Why does long addition start from the right?
Because carries move left. A column's carry has to be known before the column to its left can be added, so the ones go first.
What is carrying in addition?
Each place is worth ten times the place to its right, so 10 in one column is 1 in the next column left. Carrying moves that 1 across: a ones total of 11 is 1 ten and 1 one. Schools also call it regrouping.
How do I add numbers with different numbers of digits?
Line up the last digits, or the decimal points, and treat the empty places as zeros. 4,825 + 76: 5 + 6 = 11, 2 + 7 + 1 = 10, 8 + 0 + 1 = 9 and 4 + 0 = 4, so the sum is 4,901.