Add whole numbers (written strategies) - No regrouping
Theory
The column method adds numbers written one under the other, lined up by place value. When every column adds to less than ten, there is no regrouping: each column total is written straight underneath. This Year 5 maths page shows how to set out and add three-, four- and five-digit numbers, add three numbers, find a missing number and solve word problems.
The column method (also called the written algorithm) writes the numbers one under the other so that digits with the same place value line up: ones under ones, tens under tens, and so on. Numbers are lined up on the right.
You add one column at a time, starting with the ones and moving left. The result is the sum or total.
No regrouping means every column adds to \(9\) or less, so each column total is a single digit and nothing is carried.
In the working, O, T, H, Th, TTh, HTh and M stand for ones, tens, hundreds, thousands, ten thousands, hundred thousands and millions.
The column method adds hundreds to hundreds, tens to tens and ones to ones. For \(524 + 263\):
How to add with the column method
- Write the numbers one under the other, lined up on the right by place value.
- Add the ones and write the total under the ones column.
- Move left: add the tens, then the hundreds, and so on.
- Check by estimating, or by adding in a different order.
| \(\text{O: }4 + 3\) | \(=\) | \(7\) |
| \(\text{T: }2 + 6\) | \(=\) | \(8\) |
| \(\text{H: }5 + 2\) | \(=\) | \(7\) |
The answer is \(787\).
| \(\text{O: }2 + 5\) | \(=\) | \(7\) |
| \(\text{T: }3 + 4\) | \(=\) | \(7\) |
| \(\text{H: }1 + 7\) | \(=\) | \(8\) |
| \(\text{Th: }6 + 2\) | \(=\) | \(8\) |
The answer is \(8877\).
| \(\text{O: }3 + 4\) | \(=\) | \(7\) |
| \(\text{T: }0 + 7\) | \(=\) | \(7\) |
| \(\text{H: }2 + 6\) | \(=\) | \(8\) |
| \(\text{Th: }1 + 5\) | \(=\) | \(6\) |
| \(\text{TTh: }4 + 2\) | \(=\) | \(6\) |
The answer is \(66\,877\).
| \(\text{O: }2 + 5 + 1\) | \(=\) | \(8\) |
| \(\text{T: }1 + 2 + 4\) | \(=\) | \(7\) |
| \(\text{H: }3 + 1 + 4\) | \(=\) | \(8\) |
Add all three digits in each column. The total is \(878\).
Line up on the right: the \(3\) goes under the \(1\) (tens), the \(2\) under the \(5\) (ones).
| \(\text{O: }5 + 2\) | \(=\) | \(7\) |
| \(\text{T: }1 + 3\) | \(=\) | \(4\) |
| \(\text{H: }6\) | \(=\) | \(6\) |
\(615 + 32 = 647\). Lining up on the left would wrongly add \(320\).
| \(8760 - 5230\) | \(=\) | \(3530\) |
| \(5230 + 3530\) | \(=\) | \(8760\) |
The missing number is \(3530\).
| \(\text{O: }4 + 3\) | \(=\) | \(7\) |
| \(\text{T: }1 + 0\) | \(=\) | \(1\) |
| \(\text{H: }2 + 6\) | \(=\) | \(8\) |
| \(\text{Th: }5 + 2\) | \(=\) | \(7\) |
There are \(7817\) animals altogether.
Common pitfalls
Frequently asked questions
What is the column method for addition?
Write the numbers one under the other, lined up by place value, and add each column starting from the ones.
Which digits must line up?
Digits with the same place value: ones under ones, tens under tens, hundreds under hundreds.
What does no regrouping mean?
Every column adds to \(9\) or less, so nothing is carried. \(524 + 263\) needs no regrouping.
How do you add three numbers in columns?
Line all three up on the right and add all three digits in each column, for example \(312 + 125 + 441 = 878\).
How do you find a missing number in an addition?
Subtract the number you know from the total. In \(5230 + \square = 8760\), the missing number is \(3530\).
How can I check my answer?
Estimate by rounding, or add the numbers in a different order. You should get the same total.