Homework · Fractions: Four Operations

No calculator9 marks

Answer all questions. Show all your working — you get marks for method.Name: __________ Date: ______

1Work out $\dfrac{5}{8} - \dfrac{1}{4}$.
Give your answer as a fraction in its simplest form.[2 marks]
Answer:
2Work out $3\tfrac{2}{3} + 3\tfrac{1}{2}$.
Give your answer as a fraction in its simplest form.[3 marks]
Answer:
3Work out $\dfrac{1}{3} \times \dfrac{3}{5}$.
Give your answer as a fraction in its simplest form.[2 marks]
Answer:
4Work out $\dfrac{5}{6} \div \dfrac{1}{2}$.
Give your answer as a fraction in its simplest form.[2 marks]
Answer:

Mark scheme · Fractions: Four Operations

Total: 9 marks

Peer marking — award the marks shown for each correct step, then add up the total out of 9. A method mark counts even if the final answer is wrong.

1Work out $\dfrac{5}{8} - \dfrac{1}{4}$.
Give your answer as a fraction in its simplest form.[2 marks]
Method
Common denominator 8: $\dfrac{5}{8} = \dfrac{5}{8}$ and $\dfrac{1}{4} = \dfrac{2}{8}$.
$\dfrac{5}{8} - \dfrac{2}{8} = \dfrac{3}{8}$.
Answer: $\dfrac{3}{8}$
Marks
✔1 markCommon denominator 8 ($\dfrac{5}{8}$ and $\dfrac{2}{8}$)
✔1 markAnswer $\dfrac{3}{8}$
2Work out $3\tfrac{2}{3} + 3\tfrac{1}{2}$.
Give your answer as a fraction in its simplest form.[3 marks]
Method
Write as improper fractions: $3\tfrac{2}{3} = \dfrac{11}{3}$, $3\tfrac{1}{2} = \dfrac{7}{2}$.
Common denominator 6: $\dfrac{22}{6} + \dfrac{21}{6} = \dfrac{43}{6}$.
So the answer is $\dfrac{43}{6} = 7\tfrac{1}{6}$.
Answer: $\dfrac{43}{6}$
Marks
✔1 markBoth as improper fractions $\dfrac{11}{3}$ and $\dfrac{7}{2}$
✔1 markCommon denominator and combine: $\dfrac{43}{6}$
✔1 markAnswer $\dfrac{43}{6}$ (= $7\tfrac{1}{6}$)
3Work out $\dfrac{1}{3} \times \dfrac{3}{5}$.
Give your answer as a fraction in its simplest form.[2 marks]
Method
Multiply numerators and denominators: $\dfrac{1}{3} \times \dfrac{3}{5} = \dfrac{1 \times 3}{3 \times 5} = \dfrac{3}{15} = \dfrac{1}{5}$.
Answer: $\dfrac{1}{5}$
Marks
✔1 markMultiply tops and bottoms: $\dfrac{3}{15}$
✔1 markAnswer $\dfrac{1}{5}$
4Work out $\dfrac{5}{6} \div \dfrac{1}{2}$.
Give your answer as a fraction in its simplest form.[2 marks]
Method
Dividing means multiply by the reciprocal: $\dfrac{5}{6} \div \dfrac{1}{2} = \dfrac{5}{6} \times \dfrac{2}{1}$.
$= \dfrac{10}{6} = \dfrac{5}{3}$.
Answer: $\dfrac{5}{3}$
Marks
✔1 markMultiply by the reciprocal: $\dfrac{5}{6}$ x $\dfrac{2}{1}$
✔1 markAnswer $\dfrac{5}{3}$
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