Fractions

13 Grade 8 Mathematics questions on Fractions, with worked marking schemes. 13 questions are available on this topic in full.

1. Question 1

   3 marks

   A trader had 480 oranges. He sold $\frac{5}{8}$ of them. How many oranges remained?

   (3 marks)

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2. Question 2

   3 marks

   A wire $\frac{3}{4}$ m long is cut into pieces each $\frac{1}{8}$ m long. How many pieces are obtained?

   (3 marks)

   Marking scheme

   Asking how many $\frac{1}{8}$ m pieces fit into $\frac{3}{4}$ m is a division: $\frac{3}{4}÷\frac{1}{8}$. (1)

   Dividing by a fraction is the same as multiplying by its reciprocal: $\frac{3}{4}\times \frac{8}{1}$. (1)

   $\frac{3\times 8}{4}=\frac{24}{4}=6$. (1)

   Final answer: $6$ pieces.

3. Question 3

   1 mark

   Work out: $\frac{3}{4}-\frac{2}{5}$

   A. $\frac{1}{20}$

   B. $\frac{7}{20}$

   C. $\frac{5}{9}$

   D. $\frac{11}{20}$

   (1 mark)

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4. Question 4

   1 mark

   A tank is $\frac{3}{4}$ full. After using $\frac{1}{3}$ of a full tank, what fraction remains?

   A. $\frac{1}{2}$

   B. $\frac{5}{12}$

   C. $\frac{5}{7}$

   D. $\frac{1}{4}$

   (1 mark)

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5. Question 5

   3 marks

   Simplify: $\frac{2}{3}+\frac{3}{4}-\frac{5}{6}$

   (3 marks)

   Marking scheme

   The denominators $3$, $4$ and $6$ all divide into $12$, so $12$ is the lowest common denominator. (1)

   Rewrite each fraction over $12$: $\frac{2}{3}=\frac{8}{12}$, $\frac{3}{4}=\frac{9}{12}$, $\frac{5}{6}=\frac{10}{12}$. (1)

   Now work left to right: $\frac{8+9-10}{12}=\frac{7}{12}$. (1)

   Final answer: $\frac{7}{12}$.

6. Question 6

   1 mark

   Express $\frac{7}{4}$ as a mixed number.

   A. 1 $\frac{1}{4}$

   B. 2 $\frac{1}{4}$

   C. 1 $\frac{3}{4}$

   D. $\frac{7}{4}$

   (1 mark)

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7. Question 7

   1 mark

   Work out: $\frac{2}{3}+\frac{1}{4}$

   A. $\frac{11}{12}$

   B. $\frac{3}{7}$

   C. $\frac{5}{6}$

   D. $\frac{7}{12}$

   (1 mark)

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8. Question 8

   1 mark

   Find $\frac{2}{5}$ of 60.

   A. 12

   B. 24

   C. 30

   D. 150

   (1 mark)

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9. Question 9

   1 mark

   Work out: $\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$

   A. $\frac{3}{11}$

   B. $\frac{1}{2}$

   C. $\frac{5}{6}$

   D. 1

   (1 mark)

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10. Question 10

    1 mark

    Work out: $\frac{3}{5}÷\frac{9}{10}$

    A. $\frac{27}{50}$

    B. $\frac{1}{2}$

    C. $\frac{6}{5}$

    D. $\frac{2}{3}$

    (1 mark)

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11. Question 11

    1 mark

    Which of the following fractions is the largest?

    A. $\frac{2}{3}$

    B. $\frac{5}{8}$

    C. $\frac{3}{5}$

    D. $\frac{7}{12}$

    (1 mark)

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12. Question 12

    1 mark

    Work out: $\frac{2}{3}\times \frac{9}{10}$

    A. $\frac{6}{13}$

    B. $\frac{11}{30}$

    C. $\frac{3}{5}$

    D. $\frac{2}{15}$

    (1 mark)

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13. Question 13

    3 marks

    Simplify: $1\frac{1}{2}+2\frac{1}{3}$

    (3 marks)

    Marking scheme

    Change both mixed numbers to improper fractions: $1\frac{1}{2}=\frac{3}{2}$ and $2\frac{1}{3}=\frac{7}{3}$. (1)

    The lowest common denominator of $2$ and $3$ is $6$: $\frac{3}{2}=\frac{9}{6}$ and $\frac{7}{3}=\frac{14}{6}$. (1)

    Add: $\frac{9+14}{6}=\frac{23}{6}$, and $23÷6=3$ remainder $5$. (1)

    Final answer: $3\frac{5}{6}$.

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