Add whole numbers (written strategies) - 5-7 digit numbers
Theory
The column algorithm works for numbers of any size. Line up the place values so the ones sit under the ones, then add each column from the right, carrying where a column reaches ten.
A number with five, six or seven digits is added with the same column algorithm as a small one.
Line the numbers up so the ones sit under the ones, then add each column from right to left, carrying whenever a column reaches ten.
Keeping the digits in neat columns is what makes a long sum reliable.
Whatever the size of the numbers, the columns are the same idea — each is worth ten times the one on its right:
| Millions | HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|---|
| — | 2 | 3 | 4 | 5 | 6 | 7 |
| — | 1 | 2 | 3 | 4 | 5 | 6 |
| — | 3 | 5 | 8 | 0 | 2 | 3 |
How to add large numbers
- Line up the numbers by place value, ones under ones.
- Add each column from the right, carrying where a column reaches ten.
- Continue to the last column, adding a new column at the front if the final carry needs one.
Add each column, carrying where needed.
| \(45\,678 + 32\,145\) | \(=\) | \(77\,823\) |
| \(234\,567 + 123\,456\) | \(=\) | \(358\,023\) |
| \(1\,234\,567 + 2\,345\,678\) | \(=\) | \(3\,580\,245\) |
| \(48\,900 + 35\,750\) | \(=\) | \(84\,650\) |
Combined: \(84\,650\) people.
Common pitfalls
Frequently asked questions
How do you add numbers with many digits?
The same way as small numbers: line them up by place value and add each column from the right, carrying where a column reaches ten. \(234\,567 + 123\,456 = 358\,023\).
Is adding big numbers different from small numbers?
No. The column algorithm is identical — there are just more columns to work through.
How do you keep the columns lined up?
Write ones under ones, tens under tens, and use the spaces (as in \(234\,567\)) to keep each place in its own column.
What happens if the last column carries?
The carry starts a new column at the front, so the answer has one more digit than the numbers you added.