Common Mistakes with Percentages in GCSE Maths

A percentage question can look reassuringly familiar. Then one small decision changes everything: dividing instead of multiplying, treating the final price as the original, or subtracting the same percentage and expecting to return to where you started.

The common mistakes with percentages in GCSE Maths are rarely caused by difficult arithmetic. They usually come from answering a slightly different question from the one on the page. The solution is to identify what represents $100\%$, choose the correct operation and check whether the answer should be larger or smaller.

Imagine a student, Sam, reviewing a marked paper. The calculator work is accurate, but several answers have lost marks. By sorting each error into a clear category, Sam can turn those lost marks into a practical revision list.

A percentage question checklist

Before calculating, ask:

• What amount represents $100\%$?
• Am I finding a percentage, a new amount or an original amount?
• Is the value increasing or decreasing?
• Should my answer be larger or smaller than the amount given?
• Does the question require money to the nearest penny?

This five-question check is useful across foundation and higher tier. Once you can classify the question, the calculation becomes much less mysterious.

If setting up every method feels like a lot, use the Maths Genie percentage lesson and revision resources before applying the checklist in the GCSE Maths Question Bank.

Mistake: turning the percentage into the wrong decimal

Sam sees $7\%$ and writes $0.7$. This is one of the most damaging percentages mistakes because every later step may look perfectly organised.

A percentage means “out of $100$”, so divide by $100$:

$$7\%=\frac{7}{100}=0.07$$

By contrast:

$$70\%=\frac{70}{100}=0.7$$

Worked example

Find $7\%$ of £480£480£480.

Convert the percentage to a decimal and multiply:

$$7\%=0.07$$ $$480\times 0.07=33.6$$

Therefore, the answer is £33.60£33.60£33.60.

A quick sense check helps. Since $10\%$ of £480£480£480 is £48£48£48, an answer of £336£336£336 cannot represent only $7\%$.

Mistake: finding the change but not the new amount

There is an important difference between “find the increase” and “find the price after the increase”. Sam calculates the percentage correctly but stops one step too soon.

Worked example

A bicycle costs £640£640£640 and increases in price by $15\%$. Find the new price.

First find the increase:

$$640\times 0.15=96$$

Then add it to the original price:

$$640+96=736$$

The new price is £736£736£736.

Alternatively, an increase of $15\%$ leaves a total of $115\%$:

$$115\%=1.15$$ $$640\times 1.15=736$$

Both methods are correct. The multiplier method is often quicker, particularly for repeated percentage change.

Mistake: using the wrong percentage multiplier

A multiplier represents the percentage that remains after the change.

For an increase of $r\%$:

$$multiplier=1+\frac{r}{100}$$

For a decrease of $r\%$:

$$multiplier=1-\frac{r}{100}$$

Sam reduces a value by $23\%$ and multiplies by $0.23$. But $0.23$ finds the amount removed. The amount remaining is $77\%$, so the correct multiplier is $0.77$.

Worked example

A coat costing £85£85£85 is reduced by $23\%$.

$$100\%-23\%=77\%$$ $$77\%=0.77$$ $$85\times 0.77=65.45$$

The sale price is £65.45£65.45£65.45.

Two students take the search for an original price rather too literally

Mistake: reversing a percentage by subtracting it

Reverse percentages are a common source of lost marks in percentages GCSE questions. If a final amount is given, that amount is not usually $100\%$.

Suppose a price has risen by $20\%$. The final price is $120\%$ of the original. To recover the original, divide by $1.2$. Do not reduce the final price by $20\%$.

Worked example

After a $20\%$ increase, a laptop costs £780£780£780. Find its original price.

The new price represents $120\%$ of the original:

$$120\%=1.2$$

Let the original price be $x$:

$$1.2x=780$$ $$x=\frac{780}{1.2}=650$$

The original price was £650£650£650.

Check by applying the increase:

$$650\times 1.2=780$$

The reverse percentages lesson explains this distinction, while the reverse percentages revision guide provides a focused recap.

Mistake: assuming equal increases and decreases cancel

Sam thinks that increasing a quantity by $10\%$ and then decreasing it by $10\%$ returns it to its starting value. It does not, because the second percentage is calculated from a different amount.

Worked example

A value of £500£500£500 increases by $10\%$ and then decreases by $10\%$.

After the increase:

$$500\times 1.1=550$$

After the decrease:

$$550\times 0.9=495$$

The final value is £495£495£495, not £500£500£500.

The complete multiplier calculation is:

$$500\times 1.1\times 0.9=495$$

This happens because $10\%$ of £550£550£550 is £55£55£55, whereas the original increase was only £50£50£50. You can practise this idea with the repeated percentage change exam booklet.

Mistake: dividing in the wrong order for percentage change

Percentage change compares the change with the original amount, not the new amount.

$$percentage\; change=\frac{change}{original\; amount}\times 100\%$$

Worked example

A club’s membership rises from $240$ to $276$.

Find the change:

$$276-240=36$$

Divide by the original membership:

$$\frac{36}{240}\times 100\%=15\%$$

The membership increased by $15\%$.

Dividing by $276$ instead would compare the change with the final membership, which is not what percentage change means.

Common mistakes to catch before the exam

Sam’s corrected paper now becomes a checklist rather than a record of failure. The main warning signs are:

• writing $8\%$ as $0.8$ instead of $0.08$;
• giving the percentage change when the question asks for the new amount;
• multiplying by the percentage removed rather than the percentage remaining;
• treating a final amount as $100\%$ in a reverse percentage question;
• expecting equal percentage increases and decreases to cancel;
• dividing percentage change by the final value;
• rounding too early and carrying an inaccurate value forward;
• forgetting units, particularly pounds and pence.

In a multi-step question, keep the full calculator value until the final line. Round money to the nearest penny unless the question gives another instruction.

Exam-style practice

Try these without looking back at the examples.

Question A: Find $18\%$ of £350£350£350.

Question B: A television costing £480£480£480 is reduced by $15\%$. Find its sale price.

Question C: After a $12\%$ increase, a salary is £31,360£31{,}360£31,360. Find the original salary.

Question D: A population falls from $800$ to $728$. Calculate the percentage decrease.

Answers

A: 350×0.18=£63\text{A: } 350 \times 0.18 = £63A: 350×0.18=£63 B: 480×0.85=£408\text{B: } 480 \times 0.85 = £408B: 480×0.85=£408 C: 31,3601.12=£28,000\text{C: } \frac{31{,}360}{1.12} = £28{,}000C: 1.1231,360​=£28,000 $$D:\frac{800-728}{800}\times 100\%=9\%$$

For further exam-style questions with worked solutions and mark-scheme guidance, continue with the reverse percentages Question Bank.

Turn percentage errors into reliable marks

Knowing the method is the first step; recognising it quickly under exam pressure takes practice. Sam’s improvement begins by naming each mistake, correcting it and then answering a fresh question without copying the model. Your turn: start the matching Maths Genie Lessons, then use the Question Bank to practise each percentage method until the choice of operation feels secure.