Why Fractions Matter More Than You Think
Fractions turn up on every single GCSE maths paper — sometimes as a straightforward calculation, sometimes hidden inside a ratio question, a percentage problem, or a word problem about sharing amounts. Examiners consistently flag fractions as one of the areas where students drop the most avoidable marks. Not because the questions are tricky, but because the rules get muddled under pressure.
This guide covers every fraction skill you need for GCSE maths: reading and simplifying fractions, adding and subtracting, multiplying and dividing, finding fractions of amounts, and the specific mistakes that examiner reports say cost students marks time and again. Work through the examples, and you'll have a reliable method for every type of fraction question the exam can throw at you.
Types of Fractions and How to Simplify Them
There are three types of fractions you need to recognise.
A proper fraction has a numerator smaller than the denominator — a value less than 1: $\frac{3}{4}$
An improper fraction has a numerator greater than or equal to the denominator — a value of 1 or more: $\frac{9}{4}$
A mixed number combines a whole number and a proper fraction: $2\frac{1}{4}$
You need to convert between improper fractions and mixed numbers in both directions.
Improper fraction → mixed number: Divide the numerator by the denominator. The quotient becomes the whole number and the remainder becomes the new numerator.
$$\frac{11}{4} \rightarrow 11 \div 4 = 2 \text{ remainder } 3 \rightarrow 2\frac{3}{4}$$
Mixed number → improper fraction: Multiply the whole number by the denominator, then add the numerator.
$$2\frac{3}{4} \rightarrow (2 \times 4) + 3 = 11 \rightarrow \frac{11}{4}$$
To simplify a fraction, divide both the numerator and denominator by their highest common factor (HCF).
$$\frac{18}{24}: \text{ HCF of 18 and 24 is 6} \rightarrow \frac{18 \div 6}{24 \div 6} = \frac{3}{4}$$
Always simplify your final answer unless the question tells you otherwise.
Adding and Subtracting Fractions
The key rule: you can only add or subtract fractions when the denominators are the same. If they already match, add the numerators and leave the denominator unchanged.
$$\frac{5}{9} + \frac{2}{9} = \frac{7}{9}$$
When the denominators differ, find the lowest common multiple (LCM) of both denominators and convert each fraction to an equivalent fraction with that denominator.
Worked example: $\dfrac{3}{4} + \dfrac{2}{5}$
The LCM of 4 and 5 is 20.
$$\frac{3}{4} = \frac{15}{20} \qquad \frac{2}{5} = \frac{8}{20}$$
$$\frac{15}{20} + \frac{8}{20} = \frac{23}{20} = 1\frac{3}{20}$$
For mixed numbers, convert to improper fractions before adding or subtracting — it's much harder to make errors that way.
Worked example: $3\frac{1}{2} - 1\frac{2}{3}$
Convert: $3\frac{1}{2} = \frac{7}{2}$ and $1\frac{2}{3} = \frac{5}{3}$
The LCM of 2 and 3 is 6:
$$\frac{7}{2} = \frac{21}{6} \qquad \frac{5}{3} = \frac{10}{6}$$
$$\frac{21}{6} - \frac{10}{6} = \frac{11}{6} = 1\frac{5}{6}$$
One of the most common examiner complaints is students who identify the right LCM but forget to adjust the numerator to match. When you multiply the denominator by a number, you must multiply the numerator by exactly the same number.
Practise adding and subtracting fractions on Bow Tie Maths →
Multiplying Fractions
Multiplying fractions is more straightforward than adding them — no common denominator needed. Multiply the numerators together, then multiply the denominators together, and simplify your answer.
$$\frac{3}{5} \times \frac{4}{7} = \frac{12}{35}$$
It's often quicker to cancel common factors before you multiply. Look for any factor shared between a numerator and a denominator — either pair will do, not just the top and bottom of the same fraction.
Worked example: $\dfrac{4}{9} \times \dfrac{3}{8}$
4 and 8 share a factor of 4; 3 and 9 share a factor of 3. Divide these out first:
$$\frac{4 \div 4}{9 \div 3} \times \frac{3 \div 3}{8 \div 4} = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$$
For mixed numbers, always convert to improper fractions before multiplying.
Worked example: $1\frac{1}{2} \times 2\frac{2}{3}$
$$\frac{3}{2} \times \frac{8}{3} = \frac{24}{6} = 4$$
Dividing Fractions
To divide by a fraction, flip the second fraction (find its reciprocal) and multiply. A useful prompt: keep, change, flip — keep the first fraction, change $\div$ to $\times$, flip the second fraction.
$$\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} = 1\frac{7}{8}$$
The reciprocal of a whole number $n$ is $\frac{1}{n}$, so dividing by 3 is the same as multiplying by $\frac{1}{3}$.
Worked example: $2\frac{1}{4} \div 1\frac{1}{2}$
Convert to improper fractions first:
$$\frac{9}{4} \div \frac{3}{2} = \frac{9}{4} \times \frac{2}{3} = \frac{18}{12} = \frac{3}{2} = 1\frac{1}{2}$$
The most common error here is flipping the first fraction instead of the second. Only the fraction you're dividing by gets flipped — the first fraction stays exactly as it is.
Fractions of Amounts
Finding a fraction of an amount is a staple of Foundation papers and often appears inside more complex Higher questions too. The method: divide by the denominator, multiply by the numerator.
Find $\dfrac{3}{8}$ of £56:
$$56 \div 8 = 7 \qquad 7 \times 3 = £21$$
At grade 5 and above, you'll also meet reverse fraction problems, where you're given the result and need to find the original value.
Worked example: After a reduction of $\frac{1}{5}$, a jacket costs £52. What was the original price?
If $\frac{1}{5}$ was removed, the £52 represents $\frac{4}{5}$ of the original price.
$$52 \div 4 = 13 \qquad 13 \times 5 = £65$$
The original price was £65.
Reverse fraction questions catch many students out because they try to add $\frac{1}{5}$ of the reduced price back on — but that's $\frac{1}{5}$ of the wrong number. Always identify what fraction the given amount represents, then work from there.
What Examiners Say Students Get Wrong
Examiner reports for AQA and Edexcel consistently flag the same fraction errors. Knowing these in advance means you won't fall into the same traps.
Adding denominators. $\frac{1}{3} + \frac{1}{4}$ is not $\frac{2}{7}$. The denominators tell you the size of the parts — they are never added together. The answer is $\frac{7}{12}$.
Scaling the denominator without scaling the numerator. When converting $\frac{3}{4}$ to twentieths, some students write $\frac{3}{20}$ instead of $\frac{15}{20}$. Both the numerator and denominator must be multiplied by the same number — in this case, 5.
Skipping conversion of mixed numbers. Attempting to multiply or divide mixed numbers without converting to improper fractions first almost always produces the wrong answer.
Not simplifying. Many mark schemes award a method mark and an accuracy mark separately. Leaving your answer as $\frac{6}{8}$ rather than $\frac{3}{4}$ can cost you the accuracy mark.
Flipping the first fraction when dividing. Only the fraction you are dividing by gets flipped. $\frac{2}{3} \div \frac{4}{5}$ becomes $\frac{2}{3} \times \frac{5}{4}$ — the first fraction, $\frac{2}{3}$, stays as it is.
💡 Practise now: Fraction questions on Bow Tie Maths cover every type on this page — adding, subtracting, multiplying, dividing, and fractions of amounts — with fresh numbers every time so you can't just memorise the answers.
Summary
Fractions underpin a huge amount of GCSE maths — not just the dedicated fraction questions, but ratio, percentages, probability, and algebra too. Get the core methods solid (common denominator for adding and subtracting, flip and multiply for division, divide-then-multiply for fractions of amounts) and you'll find that many multi-step questions become straightforward once you identify the fraction skill inside them.
The most effective way to improve on fractions is consistent practice across different question types — a few questions a day beats a long single session.
Ready to test yourself? Try fraction questions on Bow Tie Maths → — unlimited exam-style questions, free to start, with a Topic Radar that shows exactly which fraction skills still need work.