Subtract three-digit numbers
Subtracting three-digit numbers finds the difference between amounts in the hundreds. In Tasmanian Year 3 maths this subtopic extends written subtraction to the hundreds column (Australian Curriculum AC9M3N03).
Students use the column method, the split strategy and counting up on a number line. They regroup in the ones, the tens or both, as in \(634 - 258 = 376\), and check an answer by adding it back on. They also learn to spot a common mistake: taking the smaller digit from the larger in every column. Saving for a bike and empty seats at a stadium show where it is used. It is part of Year 3 Subtraction.
Theory
Subtracting three-digit numbers is a Year 3 maths skill: taking one number away from another to find the difference. This page shows the column method with regrouping (borrowing), the split strategy, and counting up on a number line, including how to subtract across a zero and how to check your answer.
Subtraction takes one number away from another. The answer is called the difference. It tells you how many are left, or how much bigger one number is than the other.
To subtract three-digit numbers, line them up so hundreds sit under hundreds, tens under tens and ones under ones. Then subtract each column, starting with the ones. When the top digit is too small, you regroup (some people say borrow): swap 1 ten for 10 ones, or 1 hundred for 10 tens, so there is enough to subtract.
There is more than one way to subtract. The split strategy subtracts the hundreds, tens and ones separately. Counting up finds the difference by jumping from the smaller number up to the larger one. Every answer can be checked by adding it back.
Subtraction has no formula, but these regrouping and checking facts make three-digit subtraction easier.
How to subtract with the column method
- Line up the places. Write the numbers one under the other so hundreds, tens and ones each have their own column.
- Start with the ones. If the top digit is too small, regroup a ten (or a hundred if there are no tens), then subtract the ones.
- Work left. Subtract the tens, then the hundreds, remembering any column you have regrouped.
- Check. Add your answer to the number you took away. If it makes the number you started with, the answer is right.
| \(500 - 300\) | \(=\) | \(200\) |
| \(80 - 40\) | \(=\) | \(40\) |
| \(6 - 2\) | \(=\) | \(4\) |
| \(200 + 40 + 4\) | \(=\) | \(244\) |
No regrouping is needed, so \(586 - 342 = 244\).
| \(\text{ones}\) | \(:\) | \(14 - 8 = 6\) |
| \(\text{tens}\) | \(:\) | \(12 - 6 = 6\) |
| \(\text{hundreds}\) | \(:\) | \(6 - 2 = 4\) |
So \(734 - 268 = 466\).
| \(296 + 4\) | \(=\) | \(300\) |
| \(300 + 41\) | \(=\) | \(341\) |
| \(4 + 41\) | \(=\) | \(45\) |
The two jumps add to \(45\), so \(341 - 296 = 45\).
| \(\text{ones}\) | \(:\) | \(10 - 7 = 3\) |
| \(\text{tens}\) | \(:\) | \(9 - 3 = 6\) |
| \(\text{hundreds}\) | \(:\) | \(5 - 4 = 1\) |
There are no tens, so a hundred becomes 10 tens first. The club needs \(\$163\) more.
Common pitfalls
Frequently asked questions
How do you subtract three-digit numbers?
Line the numbers up so hundreds, tens and ones are in their own columns. Subtract the ones first, then the tens, then the hundreds. If a top digit is too small, regroup a ten or a hundred before subtracting.
What does regrouping or borrowing mean in subtraction?
Regrouping means swapping 1 ten for 10 ones, or 1 hundred for 10 tens, so the top number has enough to subtract. The column you borrowed from goes down by one.
How do you subtract across a zero, like 703 minus 145?
There are no tens to regroup, so first change one hundred into 10 tens. Then regroup one of those tens into 10 ones. Now subtract each column as usual, so \(703 - 145 = 558\).
What is the split strategy for subtraction?
The split strategy subtracts the hundreds, tens and ones separately, then adds the parts back. For \(586 - 342\) you do \(500 - 300 = 200\), \(80 - 40 = 40\), \(6 - 2 = 4\), then \(200 + 40 + 4 = 244\).
How do you find the difference by counting up?
Start at the smaller number and jump up to the larger one, often to the next hundred first. Add the jumps together. For \(341 - 296\), jump \(+4\) to \(300\), then \(+41\) to \(341\), so the difference is \(45\).
How do you check a subtraction answer?
Add your answer back to the number you took away. If the total equals the number you started with, the answer is correct. For \(462 - 137 = 325\), check that \(325 + 137 = 462\).