Estimation and Checking Answers

Why estimate at all?

Calculators and careful working still produce wrong answers — a slipped finger, a missing zero, a decimal point in the wrong place. Estimation is your safety net. By working out roughly what the answer should be, you can instantly spot when something has gone badly wrong.

Estimating means replacing tricky numbers with easy, rounded ones, then calculating in your head. We use the symbol ≈, which means "is approximately equal to."

This skill leans on estimating and rounding, so make sure you can round numbers confidently first.

How to estimate a calculation

The standard method is to round each number to 1 significant figure, then calculate.

Example 1 — Estimate 487 + 312.

1. Round each number to 1 sig fig: 487 ≈ 500 and 312 ≈ 300.
2. Add the easy numbers: 500 + 300 = 800.
3. So 487 + 312 ≈ 800. (The exact answer, 799, is very close.)

Example 2 — Estimate 6.9 × 21.

1. Round: 6.9 ≈ 7 and 21 ≈ 20.
2. Multiply: 7 × 20 = 140.
3. So 6.9 × 21 ≈ 140. (The exact answer is 144.9.)

Calculation	Rounded	Estimate	Exact
387 + 214	400 + 200	600	601
612 − 289	600 − 300	300	323
49 × 31	50 × 30	1,500	1,519
824 ÷ 4	800 ÷ 4	200	206

Notice how every estimate lands in the right "ballpark."

Checking with inverse operations

The second tool is the inverse operation — the operation that undoes the one you just did. If the inverse takes you back to where you started, your answer is right.

Operation done	Check with	Example
Addition	Subtraction	38 + 17 = 55, check 55 − 17 = 38 ✓
Subtraction	Addition	91 − 46 = 45, check 45 + 46 = 91 ✓
Multiplication	Division	12 × 7 = 84, check 84 ÷ 7 = 12 ✓
Division	Multiplication	96 ÷ 8 = 12, check 12 × 8 = 96 ✓

Example 3 — Check 144 ÷ 6 = 24.

1. The inverse of division is multiplication.
2. Calculate 24 × 6 = 144.
3. This matches the number we started with, so the answer is correct.

The "does it make sense?" test

The simplest check of all is common sense. Always pause and ask: does this answer make sense?

• If you share 30 sweets between 5 friends and get 150, something is wrong — sharing makes numbers smaller, not bigger.
• If 7 books cost about £4 each and your total reads £2.80, that is far too small for 7 books.

Why this works: every operation changes the size of a number in a predictable way. Multiplying by a number bigger than 1 grows it; dividing shrinks it. If your answer breaks that expectation, recheck it.

A practice activity

Play "estimate, then prove":

1. Write down five two-number calculations (mix of +, −, ×, ÷).
2. For each, first write a quick estimate using rounded numbers and the ≈ symbol.
3. Then work out the exact answer.
4. Compare: is the exact answer close to your estimate? If not, find the mistake.
5. Challenge: deliberately make one calculation with a misplaced decimal point and see whether your estimate catches it.

Where this leads

Estimation and checking are habits, not one-off tricks. Used on every problem, they catch errors before they cost you marks. Combine them with mental math strategies and you will solve problems faster and more accurately.