Subtract whole numbers (written strategies) - No regrouping
Theory
The column method for subtraction writes the larger number on top and the smaller number underneath, lined up by place value. When every top digit is at least as big as the digit below it, each column can be subtracted straight away with no trading. This Year 5 maths page shows how to subtract three-, four- and five-digit numbers, check by adding, and solve word problems.
In a subtraction the larger number (the one you start with) goes on top and the number being taken away goes underneath. The answer is the difference.
Subtract one column at a time, starting with the ones: top digit minus bottom digit.
No regrouping means each top digit is at least as large as the digit below it, so no trading is needed.
In the working, O, T, H, Th, TTh, HTh and M stand for ones, tens, hundreds, thousands, ten thousands, hundred thousands and millions.
Addition and subtraction undo each other:
How to subtract with the column method
- Write the larger number on top, lined up on the right.
- Subtract the ones: top minus bottom.
- Move left through the tens, hundreds and so on.
- Check: answer plus the bottom number should equal the top number.
| \(\text{O: }8 - 5\) | \(=\) | \(3\) |
| \(\text{T: }6 - 2\) | \(=\) | \(4\) |
| \(\text{H: }7 - 3\) | \(=\) | \(4\) |
The answer is \(443\).
| \(\text{O: }7 - 2\) | \(=\) | \(5\) |
| \(\text{T: }8 - 5\) | \(=\) | \(3\) |
| \(\text{H: }6 - 3\) | \(=\) | \(3\) |
| \(\text{Th: }9 - 5\) | \(=\) | \(4\) |
The answer is \(4335\).
| \(\text{O: }6 - 3\) | \(=\) | \(3\) |
| \(\text{T: }9 - 7\) | \(=\) | \(2\) |
| \(\text{H: }8 - 5\) | \(=\) | \(3\) |
| \(\text{Th: }7 - 4\) | \(=\) | \(3\) |
| \(\text{TTh: }5 - 2\) | \(=\) | \(3\) |
The answer is \(33\,323\).
| \(\text{O: }6 - 2\) | \(=\) | \(4\) |
| \(\text{T: }0 - 0\) | \(=\) | \(0\) |
| \(\text{H: }9 - 6\) | \(=\) | \(3\) |
The tens are \(0 - 0 = 0\), so a zero holds the tens place: \(304\).
| \(\text{O: }4 + 1\) | \(=\) | \(5\) |
| \(\text{T: }3 + 4\) | \(=\) | \(7\) |
| \(\text{H: }2 + 2\) | \(=\) | \(4\) |
| \(\text{Th: }5 + 3\) | \(=\) | \(8\) |
\(5234 + 3241 = 8475\), the top number, so Mai is correct.
| \(7400 - 4200\) | \(=\) | \(3200\) |
The missing number is \(3200\). Check: \(7400 - 3200 = 4200\).
| \(\text{O: }5 - 1\) | \(=\) | \(4\) |
| \(\text{T: }7 - 3\) | \(=\) | \(4\) |
| \(\text{H: }8 - 4\) | \(=\) | \(4\) |
| \(\text{Th: }6 - 2\) | \(=\) | \(4\) |
There are \(4444\) drinks left.
Common pitfalls
Frequently asked questions
How do you subtract using the column method?
Write the larger number on top and the smaller underneath, lined up on the right. Subtract each column from the ones, top digit minus bottom digit.
Which number goes on top in a subtraction?
The larger number, the one you are taking away from.
What does no regrouping mean in subtraction?
Each top digit is at least as big as the digit under it, so no trading is needed. \(768 - 325\) needs no regrouping.
How do you check a subtraction?
Add the answer to the number you subtracted. For \(768 - 325 = 443\), check \(443 + 325 = 768\).
How do you find a missing number in a subtraction?
For \(7400 - \square = 4200\), subtract the answer from the starting number: \(7400 - 4200 = 3200\).