Enter a set of numbers, and the calculator will calculate their sum step by step using vertical addition.
The calculator automatically handles common delimiters like commas, spaces, semicolons, and line breaks. If using a special delimiter, please enter it. The thousands separator can be left empty, but if present, it must differ from the number separator.
Long addition, also known as "multi-digit addition" or "multi-term addition," is the process of finding the sum of a set of numbers. Because the values are larger, the calculation process is often displayed using vertical addition, ensuring accuracy and transparency in each step. The basic principle of long addition is the same as regular addition: add digits column by column and handle any carrying over. Here's how it works:
Start by aligning all the numbers according to their place values. For integers, align from the rightmost digit (ones place). If there are decimals, ensure the decimal points are aligned.
For example: To calculate the sum of \( 125, 76, 389 \), align the numbers by place value:
| Hundreds | Tens | Ones | |
| 1 | 2 | 5 | |
| 7 | 6 | ||
| + | 3 | 8 | 9 |
Begin adding from the rightmost digits (ones place or decimal part). If the sum of digits exceeds or equals 10, carry over to the next higher place value. Continue leftward until all digits have been added.
As with adding two numbers, if the sum of any column exceeds or equals 10, retain the rightmost digit and carry over the remaining value to the next column.
For example, in the calculation \( 58 + 47 + 35 \):
| Carry | 1 | 2 | |
|---|---|---|---|
| 5 | 8 | ||
| 4 | 7 | ||
| + | 3 | 5 | |
| Sum | 1 | 4 | 0 |
If the numbers include decimals, first ensure that the decimal points are aligned. Then, perform the addition following the same rules as integer addition. Carry over from the decimal part to the integer part if needed.
For example: To calculate \( 12.75 + 8.6 + 3.425 \):
| Tens | Ones | Tenths | Hundredths | Thousandths | ||
| 1 | 2 | . | 7 | 5 | 0 | |
| 8 | . | 6 | 0 | 0 | ||
| + | 3 | . | 4 | 2 | 5 |
Add column by column, paying attention to carrying over from the decimal part.
Solution:
| Carry | 1 | 2 | 2 | |
|---|---|---|---|---|
| 1 | 2 | 3 | ||
| 4 | 5 | |||
| 7 | 8 | 9 | ||
| + | 6 | 7 | ||
| Sum | 1 | 0 | 2 | 4 |
Solution:
| Carry | 1 | 1 | ||||
|---|---|---|---|---|---|---|
| 3 | . | 5 | 0 | 0 | ||
| 2 | . | 7 | 5 | 0 | ||
| + | 4 | . | 6 | 2 | 5 | |
| Sum | 1 | 0 | . | 8 | 7 | 5 |
Solution:
| Carry | 2 | 1 | |||
|---|---|---|---|---|---|
| 1 | 5 | . | 0 | 0 | |
| 3 | . | 7 | 5 | ||
| 9 | . | 3 | 0 | ||
| + | 2 | . | 0 | 0 | |
| Sum | 3 | 0 | . | 0 | 5 |