Revision mat · Fractions: Four Operations

No calculator12 marks

Question mix weighted by 199 real exam questions from 117 GCSE papers (2017–24), so the most common question types get the most space. Show your working.

Add / subtract $\dfrac{a}{b}\pm\dfrac{c}{d}=\dfrac{ad\pm bc}{bd}$Multiply $\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{ac}{bd}$Divide $\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}$Fraction of an amount $\dfrac{a}{b}\text{ of }N=(N\div b)\times a$
Improper <-> mixed≈23% of real exam Qs
1Convert between mixed numbers and improper fractions.
You are given $4\tfrac{1}{4}$ and $\dfrac{14}{5}$.
Write $4\tfrac{1}{4}$ as an improper fraction.
Answer: (1 mark)
2Convert between mixed numbers and improper fractions.
You are given $2\tfrac{3}{5}$ and $\dfrac{16}{3}$.
Write $2\tfrac{3}{5}$ as an improper fraction.
Answer: (1 mark)
Multiply≈15% of real exam Qs
3Work out $2\tfrac{4}{5} \times \dfrac{5}{3}$.
Give your answer as a fraction in its simplest form.
Answer: (2 marks)
Add & subtract≈8% of real exam Qs
4Work out $\dfrac{1}{2} + \dfrac{11}{12}$.
Give your answer as a fraction in its simplest form.
Answer: (2 marks)
Mixed numbers (add/subtract)≈8% of real exam Qs
5Work out $1\tfrac{2}{5} + 2\tfrac{1}{3}$.
Give your answer as a fraction in its simplest form.
Answer: (3 marks)
★ Exam capstonemixed & other forms ≈39% of real exam Qs
6Work out $\dfrac{1}{6} + \dfrac{2}{5} \div \dfrac{1}{2}$.
Give your answer as a fraction in its simplest form.
Answer: (3 marks)

Mark scheme · Fractions: Four Operations

Total: 12 marks

Award the marks shown for each correct step, then add up the total out of 12. A method mark counts even if the final answer is wrong.

1Convert between mixed numbers and improper fractions.
You are given $4\tfrac{1}{4}$ and $\dfrac{14}{5}$.
Write $4\tfrac{1}{4}$ as an improper fraction.[1 mark]
Method
$4\tfrac{1}{4} = \dfrac{4 \times 4 + 1}{4} = \dfrac{17}{4}$.
Answer: $\dfrac{17}{4}$
Marks
✔1 markImproper fraction $\dfrac{17}{4}$
2Convert between mixed numbers and improper fractions.
You are given $2\tfrac{3}{5}$ and $\dfrac{16}{3}$.
Write $2\tfrac{3}{5}$ as an improper fraction.[1 mark]
Method
$2\tfrac{3}{5} = \dfrac{2 \times 5 + 3}{5} = \dfrac{13}{5}$.
Answer: $\dfrac{13}{5}$
Marks
✔1 markImproper fraction $\dfrac{13}{5}$
3Work out $2\tfrac{4}{5} \times \dfrac{5}{3}$.
Give your answer as a fraction in its simplest form.[2 marks]
Method
Write the mixed number as an improper fraction: $2\tfrac{4}{5} = \dfrac{14}{5}$.
Multiply numerators and denominators: $2\tfrac{4}{5} \times \dfrac{5}{3} = \dfrac{14 \times 5}{5 \times 3} = \dfrac{70}{15} = \dfrac{14}{3}$.
Answer: $\dfrac{14}{3}$
Marks
✔1 markMultiply tops and bottoms: $\dfrac{70}{15}$
✔1 markAnswer $\dfrac{14}{3}$
4Work out $\dfrac{1}{2} + \dfrac{11}{12}$.
Give your answer as a fraction in its simplest form.[2 marks]
Method
Common denominator 12: $\dfrac{1}{2} = \dfrac{6}{12}$ and $\dfrac{11}{12} = \dfrac{11}{12}$.
$\dfrac{6}{12} + \dfrac{11}{12} = \dfrac{17}{12}$.
Answer: $\dfrac{17}{12}$
Marks
✔1 markCommon denominator 12 ($\dfrac{6}{12}$ and $\dfrac{11}{12}$)
✔1 markAnswer $\dfrac{17}{12}$
5Work out $1\tfrac{2}{5} + 2\tfrac{1}{3}$.
Give your answer as a fraction in its simplest form.[3 marks]
Method
Write as improper fractions: $1\tfrac{2}{5} = \dfrac{7}{5}$, $2\tfrac{1}{3} = \dfrac{7}{3}$.
Common denominator 15: $\dfrac{21}{15} + \dfrac{35}{15} = \dfrac{56}{15}$.
So the answer is $\dfrac{56}{15} = 3\tfrac{11}{15}$.
Answer: $\dfrac{56}{15}$
Marks
✔1 markBoth as improper fractions $\dfrac{7}{5}$ and $\dfrac{7}{3}$
✔1 markCommon denominator and combine: $\dfrac{56}{15}$
✔1 markAnswer $\dfrac{56}{15}$ (= $3\tfrac{11}{15}$)
6Work out $\dfrac{1}{6} + \dfrac{2}{5} \div \dfrac{1}{2}$.
Give your answer as a fraction in its simplest form.[3 marks]
Method
Do $\times$ / $\div$ first: $\dfrac{2}{5} \div \dfrac{1}{2} = \dfrac{4}{5}$.
Then $\dfrac{1}{6} + \dfrac{4}{5}$: common denominator 30 gives $\dfrac{5}{30} + \dfrac{24}{30} = \dfrac{29}{30}$.
So the answer is $\dfrac{29}{30}$.
Answer: $\dfrac{29}{30}$
Marks
✔1 markMultiply/divide first: $\dfrac{4}{5}$
✔1 markCommon denominator and combine
✔1 markAnswer $\dfrac{29}{30}$
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