Work out (7)/(8) - (1)/(3). Give your answer as a fraction in its simplest form.

numerator = 13, denominator = 24

Work out (3)/(4) (2)/(5). Give your answer as a single fraction in its simplest form.

numerator = 15, denominator = 8

Work out 2(2)/(5) 1(1)/(6). Give your answer as a mixed number in its simplest form, stating the whole number part, the numerator and the denominator.

whole number part = 2, numerator = 4, denominator = 5

Which of these statements is true?

They cannot be compared without a calculator

A water butt holds 5(5)/(6) litres of water when it is full. It is currently (3)/(4) full. Work out how many litres of water are in it. Give your answer as a mixed number in its simplest form, stating the whole number part, the numerator and the denominator.

whole number part = 4, numerator = 3, denominator = 8

A tap fills a barrel at a steady rate. After (3)/(4) of an hour the barrel is (2)/(5) full. Work out the total time, in hours, that the tap takes to fill the barrel from empty. Give your answer as a mixed number in its simplest form, stating the whole number part, the numerator and the denominator.

whole number part = 1, numerator = 7, denominator = 8

Are fractions Higher tier or Foundation tier content?

Both. Spec points N2 and N8 are crossover content in 1MA1, so the same wording appears in the Foundation and the Higher subject content lists. What changes is the treatment: Higher papers assume the arithmetic is already secure and spend their marks on where it is used, while N8 at Higher also runs on into surds and exact answers in terms of .

How many marks are fraction questions worth on Edexcel Higher?

A standalone calculation with mixed numbers is usually 2-3 marks, and it tends to sit in the first quarter of a paper. Counting only those, expect roughly 3-6 marks across a series. The honest figure is much higher, because fraction arithmetic is the first or last step of probability tree, ratio, sector and compound measure questions that are marked under other spec points.

Can I use the fraction button on my calculator?

On Papers 2 and 3, yes, and it is worth learning the mixed-number key and the toggle between fraction and decimal display. Paper 1 is non-calculator, so nothing there is available to you. Watch the wording either way: when a question says show all your working, a correct answer with a blank space above it can score nothing.

Do I always have to give the answer as a mixed number?

Only when the question says so. Edexcel is explicit, using phrases such as "give your answer as a mixed number" or "in its simplest form", and an unsimplified or improper answer then loses the accuracy mark. If no form is named, any correct equivalent fraction is accepted, though simplest form is still the safer habit.

Fractions - Edexcel GCSE Higher Maths

Typically 3-6 marks per paper, most of them buried inside questions about something else · Spec 1MA1

Fractions sit at spec points N2 and N8 of Edexcel's 1MA1. N2 covers the four operations applied to proper fractions, improper fractions and mixed numbers, positive and negative, by formal written method. N8 asks you to calculate exactly with fractions, and at Higher tier that same point stretches on to surds and multiples of $\pi$ . Both are crossover content: identical wording appears in the Foundation and the Higher lists, so a Higher scheme of work assumes you arrived able to do this rather than setting aside lessons to teach it. That assumption is where the trouble usually starts.

Edexcel does still set the arithmetic on its own, normally as a mixed-number addition, subtraction or division worth 2-3 marks in the first quarter of a paper, carrying an instruction such as "show all your working" or "give your answer as a mixed number in its simplest form". Paper 1 is the non-calculator paper, so that is where a bare fraction calculation is most likely to turn up. On Papers 2 and 3 the fraction key does the arithmetic for you, which is precisely why the marks migrate: into a probability tree where two branch fractions are multiplied, into a ratio question that opens by taking $\frac{3}{8}$ of a total, into a sector that is $\frac{5}{12}$ of the way round a circle, into a compound measure whose numbers happen to be thirds. None of those questions contains the word fraction, and all of them are lost on fraction arithmetic.

Two accuracy marks account for most of the losses, and both live in the final line rather than in the method. The first is an answer handed in as $\frac{29}{12}$ when the question asked for a mixed number, or as $\frac{30}{12}$ when it asked for simplest form: the method marks survive, the A mark does not. The second belongs to mixed-number subtraction done by splitting off the whole numbers, where the fraction on the left turns out to be smaller than the one on the right and the subtraction quietly reverses, so $5\frac{1}{4} - 1\frac{1}{2}$ is written down as $4\frac{1}{4}$ instead of $3\frac{3}{4}$ . Converting both numbers to improper fractions first costs one line and removes both problems. Practise until you can turn $2\frac{3}{8}$ into $\frac{19}{8}$ without pausing.

Worked example

A tin contains

5\frac{1}{4}

litres of paint. Bea uses

1\frac{1}{2}

litres of the paint on a ceiling. She then uses

\frac{2}{3}

of the paint that is left on a wall. Work out how much paint is now in the tin. Give your answer as a mixed number of litres in its simplest form.

[4 marks]

Write both mixed numbers as improper fractions over a common denominator: $5\frac{1}{4} = \frac{21}{4}$ and $1\frac{1}{2} = \frac{3}{2} = \frac{6}{4}$ .
M1: correct improper fractions with a common denominator. Multiplying 4 by 2 to get 8 is legal but doubles the size of every number that follows.
Subtract to find what is left after the ceiling: $\frac{21}{4} - \frac{6}{4} = \frac{15}{4}$ litres.
A1: $\frac{15}{4}$ . Leave it improper, there is another operation still to come.
The wall takes $\frac{2}{3}$ of $\frac{15}{4}$ . Cancel the 3 into the 15 before multiplying: $\frac{2}{3} \times \frac{15}{4} = \frac{2 \times 5}{4} = \frac{5}{2}$ litres.
M1: multiplying the remaining amount by $\frac{2}{3}$ . Cancelling first keeps the numbers small and avoids simplifying $\frac{30}{12}$ later.
Subtract again: $\frac{15}{4} - \frac{5}{2} = \frac{15}{4} - \frac{10}{4} = \frac{5}{4} = 1\frac{1}{4}$ litres. Quicker route: the wall leaves $\frac{1}{3}$ of $\frac{15}{4}$ , which is $\frac{5}{4}$ in one step.
A1: $1\frac{1}{4}$ . Stopping at $\frac{5}{4}$ loses this mark, because the question named the form it wanted.

Practice questions

These are original questions written in Edexcel 1MA1 Higher style, covering the four operations with mixed numbers, fractions of an amount, working back from a part to the whole, and fraction to decimal to percentage swaps. Work them without a calculator, because Paper 1 is where the bare arithmetic is actually examined. You can type a fraction straight into a numeric box, so 7/12 is a valid answer; where a mixed number is wanted you get three boxes, one for the whole number part and one each for the numerator and denominator of the fraction, all in simplest form.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [2 marks]

Work out $\frac{7}{8} - \frac{1}{3}$ . Give your answer as a fraction in its simplest form.

numerator = denominator =
Question 2 Warm-up [2 marks]

Work out $\frac{3}{4} \div \frac{2}{5}$ . Give your answer as a single fraction in its simplest form.

numerator = denominator =
Question 3 Exam pace [3 marks]

Work out $2\frac{2}{5} \times 1\frac{1}{6}$ . Give your answer as a mixed number in its simplest form, stating the whole number part, the numerator and the denominator.

whole number part = numerator = denominator =
Question 4 Exam pace [2 marks]

Which of these statements is true?

Answer options for question 4
$\frac{4}{7} > \frac{5}{9}$ $\frac{4}{7} < \frac{5}{9}$ $\frac{4}{7} = \frac{5}{9}$ They cannot be compared without a calculator
Question 5 Stretch [3 marks]

A water butt holds $5\frac{5}{6}$ litres of water when it is full. It is currently $\frac{3}{4}$ full. Work out how many litres of water are in it. Give your answer as a mixed number in its simplest form, stating the whole number part, the numerator and the denominator.

whole number part = numerator = denominator =
Question 6 Stretch [4 marks]

A tap fills a barrel at a steady rate. After $\frac{3}{4}$ of an hour the barrel is $\frac{2}{5}$ full. Work out the total time, in hours, that the tap takes to fill the barrel from empty. Give your answer as a mixed number in its simplest form, stating the whole number part, the numerator and the denominator.

whole number part = numerator = denominator =

Common mistakes examiners see

Adding across the top and across the bottom, so $\frac{1}{3} + \frac{1}{4}$ becomes $\frac{2}{7}$ .

Only multiplication works term by term. For a sum or a difference, rewrite both fractions over the lowest common multiple of the denominators first: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$ . A sanity check catches it instantly, since $\frac{2}{7}$ is smaller than $\frac{1}{3}$ and adding a positive amount cannot shrink a number.
Subtracting mixed numbers by handling the whole parts and the fraction parts separately, then reversing the fraction subtraction when it would go negative: $5\frac{1}{4} - 1\frac{1}{2}$ written as $4\frac{1}{4}$ from $4$ and $\frac{1}{2} - \frac{1}{4}$ .

Convert both to improper fractions before you subtract anything: $\frac{21}{4} - \frac{6}{4} = \frac{15}{4} = 3\frac{3}{4}$ . If you prefer the split method, borrow one whole first, so $5\frac{1}{4}$ becomes $4\frac{5}{4}$ and the fraction on the left is now the bigger one.
Flipping the first fraction instead of the second when dividing, so $\frac{3}{4} \div \frac{2}{5}$ becomes $\frac{4}{3} \times \frac{2}{5} = \frac{8}{15}$ , or flipping both.

Only the divisor turns over: keep the first, change the sign to $\times$ , flip the second. Check the size of the answer against the question. Dividing by a number below 1 must make the answer bigger, so $\frac{3}{4} \div \frac{2}{5} = \frac{15}{8}$ is plausible and $\frac{8}{15}$ is not.
Getting the arithmetic right and then ignoring the instruction, handing in $\frac{71}{12}$ or $\frac{30}{12}$ on a question that said "as a mixed number in its simplest form".

Read the last line of the stem again before you write your answer on the line. Divide the numerator by the denominator to get the whole number part, cancel the fraction that is left, and write both. On Edexcel schemes this is the single accuracy mark on a 3-mark question, so every method mark can be earned and still leave you on 2.
Working backwards the wrong way: told that $\frac{3}{8}$ of a number is 51, multiplying to get $51 \times \frac{3}{8} = 19.125$ instead of finding the whole.

Undo the operation. Divide the part by the numerator to find one eighth ( $51 \div 3 = 17$ ), then multiply by the denominator ( $17 \times 8 = 136$ ). Equivalently, multiply by the reciprocal: $51 \times \frac{8}{3} = 136$ . Test it at the end, because $\frac{3}{8}$ of 136 should give you back 51.

Frequently asked questions

Are fractions Higher tier or Foundation tier content?: Both. Spec points N2 and N8 are crossover content in 1MA1, so the same wording appears in the Foundation and the Higher subject content lists. What changes is the treatment: Higher papers assume the arithmetic is already secure and spend their marks on where it is used, while N8 at Higher also runs on into surds and exact answers in terms of $\pi$ .
How many marks are fraction questions worth on Edexcel Higher?: A standalone calculation with mixed numbers is usually 2-3 marks, and it tends to sit in the first quarter of a paper. Counting only those, expect roughly 3-6 marks across a series. The honest figure is much higher, because fraction arithmetic is the first or last step of probability tree, ratio, sector and compound measure questions that are marked under other spec points.
Can I use the fraction button on my calculator?: On Papers 2 and 3, yes, and it is worth learning the mixed-number key and the toggle between fraction and decimal display. Paper 1 is non-calculator, so nothing there is available to you. Watch the wording either way: when a question says show all your working, a correct answer with a blank space above it can score nothing.
Do I always have to give the answer as a mixed number?: Only when the question says so. Edexcel is explicit, using phrases such as "give your answer as a mixed number" or "in its simplest form", and an unsimplified or improper answer then loses the accuracy mark. If no form is named, any correct equivalent fraction is accepted, though simplest form is still the safer habit.

Fractions - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics