Fractions

13 Grade 7 Mathematics questions on Fractions, with worked marking schemes. 13 questions are available on this topic in full.

1. Question 1

   1 mark

   A farmer used $\frac{1}{6}$ of his land for rice on day 1 and $\frac{1}{5}$ of the remainder on day 2. What fraction was used on day 2?

   A. $\frac{1}{5}$

   B. $\frac{1}{30}$

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

   D. $\frac{1}{6}$

   (1 mark)

   Marking scheme

   D. $\frac{1}{6}$ — 'of the remainder' matters: after day 1 there is $\frac{5}{6}$ left, so day 2 uses $\frac{1}{5}\times \frac{5}{6}=\frac{1}{6}$. Taking $\frac{1}{5}$ of the whole field instead would be a different answer.

2. Question 2

   1 mark

   What is $\frac{5}{8}$ of 360?

   A. 200

   B. 225

   C. 270

   D. 180

   (1 mark)

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3. Question 3

   1 mark

   Evaluate: $\frac{3}{4}\times \frac{2}{5}÷\frac{3}{10}$

   A. 1

   B. $\frac{9}{50}$

   C. 2

   D. $\frac{3}{25}$

   (1 mark)

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4. Question 4

   4 marks

   Wanjiru spent $\frac{1}{4}$ of her money on food, $\frac{1}{3}$ on transport, and saved the rest. If she saved Ksh 2,500, how much did she have originally?

   (4 marks)

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5. Question 5

   4 marks

   Three pipes can fill a tank in 6, 8 and 12 hours respectively. If all three are opened together, how long will it take to fill the tank?

   (4 marks)

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6. Question 6

   1 mark

   Evaluate: $\frac{2}{3}+\frac{3}{4}-\frac{1}{6}$

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

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

   C. $\frac{5}{4}$

   D. $\frac{3}{4}$

   (1 mark)

   Marking scheme

   B. $1\frac{1}{4}$ — the lowest common denominator of $3$, $4$ and $6$ is $12$: $\frac{8}{12}+\frac{9}{12}-\frac{2}{12}=\frac{15}{12}=\frac{5}{4}$. C is the same value as an improper fraction, but the mixed number is the required form.

7. Question 7

   5 marks

   A school bought rice for 6 days. On day 1, $\frac{1}{6}$ was used. On day 2, $\frac{1}{5}$ of the remaining was used. The rest was shared equally for 4 days, and on the last day 37.5 kg was used.

   Find the total mass of rice bought.

   (5 marks)

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8. Question 8

   3 marks

   Evaluate: $3\frac{1}{2}-1\frac{3}{4}+\frac{5}{8}$

   (3 marks)

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9. Question 9

   1 mark

   Simplify: $\frac{5}{6}÷\frac{10}{9}$

   A. $\frac{3}{4}$

   B. $\frac{9}{12}$

   C. $\frac{50}{54}$

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

   (1 mark)

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10. Question 10

    1 mark

    Convert $4\frac{3}{7}$ to an improper fraction.

    A. $\frac{19}{7}$

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

    C. $\frac{31}{7}$

    D. $\frac{43}{7}$

    (1 mark)

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11. Question 11

    1 mark

    Multiply: $2\frac{1}{3}\times 1\frac{2}{5}$

    A. 2 $\frac{3}{15}$

    B. 3 $\frac{4}{15}$

    C. 4 $\frac{1}{5}$

    D. 3 $\frac{2}{15}$

    (1 mark)

    Marking scheme

    B. $3\frac{4}{15}$ — change to improper fractions first, since mixed numbers cannot be multiplied part by part: $\frac{7}{3}\times \frac{7}{5}=\frac{49}{15}=3\frac{4}{15}$. Multiplying wholes and fractions separately gives C.

12. Question 12

    4 marks

    Simplify: $\frac{2\frac{1}{2}\times 1\frac{1}{5}}{\frac{3}{4}+\frac{1}{2}}$

    (4 marks)

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13. Question 13

    1 mark

    Which is greater: $\frac{7}{12}$ or $\frac{5}{8}$?

    A. They are equal

    B. Cannot compare

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

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

    (1 mark)

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