Study Tips

How to Check Your Own Maths Working (and Find the First Mistake)

By Math Solving Space · · 2 min read

On this page
  1. Why checking matters
  2. Habit 1: Substitute your answer back in
  3. Habit 2: Estimate first
  4. Habit 3: Find the first broken line
  5. Habit 4: Know your common slips
  6. A simple checking routine
  7. Frequently asked questions

The fastest way to check an answer is to put it back into the original question. If it works, your answer is right. If it doesn't, go through your working line by line and look for the first line that doesn't follow from the one above.

Why checking matters

Most lost marks come from small slips, not from not knowing the method. A dropped minus sign or a bracket multiplied out halfway can turn a correct method into a wrong answer. Checking takes a minute and catches most of these.

Habit 1: Substitute your answer back in

For an equation, put your answer into the original equation, not a later line.

Example: you solved 3(x+2)=183(x + 2) = 18 and got x=4x = 4.

3(4+2)=3×6=18✓3(4 + 2) = 3 \times 6 = 18 \checkmark

Both sides match, so x=4x = 4 is correct.

Habit 2: Estimate first

Before calculating, guess a rough answer. If you expect "about 50" and get 5,000, something has gone wrong. Estimating catches decimal-point and place-value slips straight away.

Habit 3: Find the first broken line

If your answer fails the check, don't start again from scratch. Look for the first line that doesn't follow from the line before it.

Here is a solution with a mistake in it:

Line Working
1 3(x+2)=183(x + 2) = 18
2 3x+2=183x + 2 = 18
3 3x=163x = 16
4 x=163x = \frac{16}{3}

Compare each line with the one before:

  • Line 1 → Line 2: the 3 was multiplied by xx but not by the 2. It should be 3x+6=183x + 6 = 18. This is the first mistake.
  • Lines 2 → 4 follow correctly from line 2. The method was fine; the earlier slip carried through.

Habit 4: Know your common slips

Slip What to look for
Sign errors Minus signs lost when moving terms or expanding −(a−b)-(a - b).
Half-expanded brackets Every term inside the bracket gets multiplied.
One-sided operations Whatever you do to one side of an equation, do to the other.
Adding fractions straight across 12+13\frac{1}{2} + \frac{1}{3} is 56\frac{5}{6}, not 25\frac{2}{5}.

A simple checking routine

  1. Estimate the answer before you start.
  2. Write one step per line so mistakes are easy to find.
  3. Substitute your final answer into the original question.
  4. If it fails, find the first broken line and fix from there.

Frequently asked questions

How long should checking take?

Usually under a minute per question. Substituting an answer back in is often just one line of working.

What if I can't substitute my answer back in?

Use a different method to reach the same answer, or estimate to see whether your answer is sensible.

Should I redo the whole question if my check fails?

No. Find the first line that is wrong and continue from there. The rest of your method may be correct.

#study tips#checking

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