Add whole numbers (written strategies) - 5-7 digit numbers
Theory
The column method works for any size of number. This Year 5 maths page shows how to add five-, six- and seven-digit numbers by lining them up on the right, adding each column from the ones and carrying where needed, including sums that make a new place such as \(100\,000\) or \(1\,000\,000\).
Large numbers are added exactly like small ones: line them up on the right, add the ones first, and carry whenever a column reaches ten.
When the numbers have different numbers of digits, the shorter one starts further right. In \(64\,000 + 3215\) the \(3\) goes under the \(4\), because both are thousands.
If the last column carries, the answer has one more digit than the numbers, for example \(73\,465 + 26\,535 = 100\,000\).
In the working, O, T, H, Th, TTh, HTh and M stand for ones, tens, hundreds, thousands, ten thousands, hundred thousands and millions.
Estimate first so you know roughly what to expect:
How to add large numbers
- Estimate by rounding each number.
- Line up on the right, using the gaps between groups of three to keep places in line.
- Add each column from the ones, carrying when a column reaches ten.
- Compare your answer with the estimate.
| \(\text{O: }9 + 6\) | \(=\) | \(15\ (\text{carry } 1)\) |
| \(\text{T: }8 + 3 + 1\) | \(=\) | \(12\ (\text{carry } 1)\) |
| \(\text{H: }7 + 4 + 1\) | \(=\) | \(12\ (\text{carry } 1)\) |
| \(\text{Th: }6 + 7 + 1\) | \(=\) | \(14\ (\text{carry } 1)\) |
| \(\text{TTh: }5 + 2 + 1\) | \(=\) | \(8\) |
The answer is \(84\,225\).
| \(\text{O: }8 + 4\) | \(=\) | \(12\ (\text{carry } 1)\) |
| \(\text{T: }7 + 8 + 1\) | \(=\) | \(16\ (\text{carry } 1)\) |
| \(\text{H: }6 + 5 + 1\) | \(=\) | \(12\ (\text{carry } 1)\) |
| \(\text{Th: }5 + 6 + 1\) | \(=\) | \(12\ (\text{carry } 1)\) |
| \(\text{TTh: }4 + 1 + 1\) | \(=\) | \(6\) |
| \(\text{HTh: }3 + 2\) | \(=\) | \(5\) |
The answer is \(562\,262\).
| \(\text{O: }5 + 6\) | \(=\) | \(11\ (\text{carry } 1)\) |
| \(\text{T: }3 + 8 + 1\) | \(=\) | \(12\ (\text{carry } 1)\) |
| \(\text{H: }1 + 9 + 1\) | \(=\) | \(11\ (\text{carry } 1)\) |
| \(\text{Th: }8 + 7 + 1\) | \(=\) | \(16\ (\text{carry } 1)\) |
| \(\text{TTh: }6 + 5 + 1\) | \(=\) | \(12\ (\text{carry } 1)\) |
| \(\text{HTh: }4 + 3 + 1\) | \(=\) | \(8\) |
| \(\text{M: }2 + 1\) | \(=\) | \(3\) |
The answer is \(3\,826\,121\).
Line up on the right: the \(3\) of \(3215\) sits under the \(4\) of \(64\,000\).
| \(\text{O: }0 + 5 + 8\) | \(=\) | \(13\ (\text{carry } 1)\) |
| \(\text{T: }0 + 1 + 1 + 1\) | \(=\) | \(3\) |
| \(\text{H: }0 + 2 + 4\) | \(=\) | \(6\) |
| \(\text{Th: }4 + 3\) | \(=\) | \(7\) |
| \(\text{TTh: }6\) | \(=\) | \(6\) |
The total is \(67\,633\).
| \(\text{O: }5 + 5\) | \(=\) | \(10\ (\text{carry } 1)\) |
| \(\text{T: }6 + 3 + 1\) | \(=\) | \(10\ (\text{carry } 1)\) |
| \(\text{H: }4 + 5 + 1\) | \(=\) | \(10\ (\text{carry } 1)\) |
| \(\text{Th: }3 + 6 + 1\) | \(=\) | \(10\ (\text{carry } 1)\) |
| \(\text{TTh: }7 + 2 + 1\) | \(=\) | \(10\) |
Every column carries, so the answer is \(100\,000\).
| \(\text{O: }0 + 0\) | \(=\) | \(0\) |
| \(\text{T: }5 + 5\) | \(=\) | \(10\ (\text{carry } 1)\) |
| \(\text{H: }9 + 0 + 1\) | \(=\) | \(10\ (\text{carry } 1)\) |
| \(\text{Th: }8 + 1 + 1\) | \(=\) | \(10\ (\text{carry } 1)\) |
| \(\text{TTh: }7 + 2 + 1\) | \(=\) | \(10\ (\text{carry } 1)\) |
| \(\text{HTh: }3 + 4 + 1\) | \(=\) | \(8\) |
The total is \(\$800\,000\).
| \(1\,000\,000 - 645\,300\) | \(=\) | \(354\,700\) |
The missing number is \(354\,700\).
Common pitfalls
Frequently asked questions
How do you add numbers with millions?
Use the same column method: line the numbers up on the right, add each column from the ones and carry when a column reaches ten. \(2\,468\,135 + 1\,357\,986 = 3\,826\,121\).
How do you line up numbers with different numbers of digits?
Line them up on the right so the ones are in the same column. In \(64\,000 + 3215\) the \(3\) goes under the \(4\) because both are thousands.
Why can the answer have more digits than the numbers?
If the last column adds to ten or more, the carry starts a new place. \(73\,465 + 26\,535 = 100\,000\).
How can I check a large addition?
Round each number and add to get an estimate. Your answer should be close to it.
How do you find a missing number in a large addition?
Subtract the known number from the total. \(1\,000\,000 - 645\,300 = 354\,700\).