Estimate & check subtraction
In Year 4 (NSW Stage 2, outcome MA2-AR-01), students learn to estimate and check subtraction. They round each number (including four-digit numbers) to the nearest 10 or 100, subtract the rounded numbers, and use the estimate to decide whether an exact answer is reasonable.
This topic also covers rounding on a number line, working out the exact difference, and checking a subtraction with inverse addition by adding the difference back on. These estimating skills help students judge answers to money, distance and everyday problems, and build strong number sense for later work in Stage 2.
Theory
Estimating and checking subtraction is a Year 4 skill: round each number to the nearest 10 or 100, then subtract the rounded numbers to get a quick estimate of the difference. This page shows how to round, how to use an estimate to check that an answer is reasonable, and how to check a subtraction with inverse addition.
An estimate is a quick, close answer, not the exact one. To estimate a subtraction, round each number to the nearest 10 or the nearest 100, then subtract the rounded numbers. For \(86 - 41\), round to \(90 - 40 = 50\), so the difference is about 50.
To round, look at the digit in the next place. If it is 4 or less, round down; if it is 5 or more, round up. So 86 rounds up to 90 and 41 rounds down to 40. A number exactly halfway, like 65, rounds up to 70.
An estimate lets you check that an exact answer is reasonable: the exact answer should land close to the estimate. You can also check a subtraction with addition, because they are opposites. Add the difference and the number you took away, and you should get back the number you started with.
Estimating a subtraction does not need a formula, but these facts help you round and check.
How to estimate and check a subtraction
- Round each number. Round both numbers to the nearest 10, or to the nearest 100 for larger numbers.
- Subtract the rounded numbers. Take one rounded number from the other to get your estimate of the difference.
- Check it is reasonable. Work out the exact answer, or add the difference back on, and make sure it lands close to your estimate.
| \(86\) | \(\to\) | \(90\) |
| \(41\) | \(\to\) | \(40\) |
| \(90 - 40\) | \(=\) | \(50\) |
The difference is about \(50\).
| \(827\) | \(\to\) | \(800\) |
| \(361\) | \(\to\) | \(400\) |
| \(800 - 400\) | \(=\) | \(400\) |
The difference is about \(400\). (The exact answer is \(466\).)
| \(934\) | \(\to\) | \(900\) |
| \(382\) | \(\to\) | \(400\) |
| \(900 - 400\) | \(=\) | \(500\) |
\(552\) is close to \(500\), so it is reasonable.
| \(255 + 176\) | \(=\) | \(431\) |
Adding the difference and the number taken away gives back \(431\), so \(255\) is correct.
Common pitfalls
Frequently asked questions
How do you estimate a subtraction?
Round each number to the nearest 10 or 100, then subtract the rounded numbers. For \(86 - 41\), round to \(90 - 40\), which is about \(50\).
How do you round a number to the nearest 10?
Look at the ones digit. If it is 4 or less, round down to the lower ten. If it is 5 or more, round up to the higher ten. So \(86\) rounds up to \(90\) and \(41\) rounds down to \(40\).
How does estimating help you check a subtraction?
The exact answer should land close to the estimate. If your answer is far from the estimate, you have probably made a mistake and should work it out again.
How do you check a subtraction is correct?
Add the difference and the number you took away. If you get back the number you started with, the subtraction is correct. For \(431 - 176 = 255\), add \(255 + 176\) to get \(431\).
Is an estimate the same as the exact answer?
No. An estimate is a quick, close answer, not the exact one. For \(86 - 41\) the estimate is \(50\) but the exact answer is \(45\). The estimate just shows if an answer looks about right.
What does a reasonable answer mean in maths?
A reasonable answer is one that is close to a sensible estimate. If you estimate about \(500\) and your answer is \(552\), that is reasonable. An answer like \(52\) or \(952\) would not be.