Fractions

29 Grade 6 Mathematics questions on Fractions, with worked marking schemes. 29 questions are available on this topic in full.

1. Question 1

   1 mark

   A mother divided Ksh 2,400 among her children. The eldest got $\frac{1}{3}$ and the youngest got $\frac{1}{4}$. How much did the two get altogether?

   A. Ksh 1,200

   B. Ksh 1,000

   C. Ksh 1,400

   D. Ksh 1,600

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2. Question 2

   1 mark

   Simplify $\frac{18}{24}$.

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

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

   C. $\frac{6}{8}$

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

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3. Question 3

   1 mark

   Convert $3\frac{2}{5}$ to an improper fraction.

   A. $\frac{17}{5}$

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

   C. $\frac{15}{5}$

   D. $\frac{11}{5}$

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4. Question 4

   1 mark

   Work out: $\frac{2}{3}\times 45$

   A. 30

   B. 40

   C. 22

   D. 15

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5. Question 5

   1 mark

   Divide: $\frac{4}{5}÷\frac{2}{3}$

   A. $\frac{12}{10}$

   B. $\frac{8}{15}$

   C. $\frac{2}{5}$

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

   (1 mark)

   Marking scheme

   D. $\frac{6}{5}$ — dividing by a fraction means multiplying by its reciprocal: $\frac{4}{5}\times \frac{3}{2}=\frac{12}{10}=\frac{6}{5}$. B multiplies straight across without flipping, and A is right but unsimplified.

6. Question 6

   1 mark

   Work out $\frac{3}{4}+\frac{1}{8}$.

   A. ⁴⁄₁₂

   B. 1

   C. ⁷⁄₈

   D. ⁴⁄₈

   Marking scheme

   C. $\frac{7}{8}$ — eighths and quarters need a common denominator, and $8$ works because $4$ divides into it: $\frac{3}{4}=\frac{6}{8}$, so $\frac{6}{8}+\frac{1}{8}=\frac{7}{8}$. The option $\frac{4}{12}$ is the classic error of adding tops and bottoms across the bar — that is never how fractions add.

7. Question 7

   1 mark

   What is $\frac{2}{3}$ of 450?

   A. 150

   B. 225

   C. 350

   D. 300

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8. Question 8

   1 mark

   Work out: $\frac{4}{9}\times \frac{3}{8}$

   A. $\frac{2}{9}$

   B. $\frac{7}{17}$

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

   D. $\frac{12}{72}$

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9. Question 9

   1 mark

   Evaluate: $\frac{3}{4}÷6$

   A. $\frac{1}{8}$

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

   C. $\frac{18}{4}$

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

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10. Question 10

    1 mark

    What fraction of 1 kg is 250 g?

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

    B. $\frac{2}{5}$

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

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

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11. Question 11

    1 mark

    A tank is $\frac{3}{4}$ full. It holds 600 litres when full. How many litres are in the tank?

    A. 400

    B. 500

    C. 300

    D. 450

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12. Question 12

    1 mark

    How many $\frac{1}{4}$ pieces can be cut from a string $3\frac{1}{2}$ m long?

    A. 7

    B. 12

    C. 14

    D. 15

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13. Question 13

    1 mark

    A rope is $4\frac{1}{2}$ metres long. A piece of $1\frac{3}{4}$ metres is cut off. What length remains?

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

    B. 3 $\frac{1}{4}$ m

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

    D. 2 $\frac{3}{4}$ m

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14. Question 14

    1 mark

    Convert $\frac{23}{4}$ to a mixed number.

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

    B. 5 $\frac{3}{4}$

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

    D. 6 $\frac{3}{4}$

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15. Question 15

    1 mark

    Ochieng' spent $\frac{1}{5}$ of his salary on rent and $\frac{3}{10}$ on food. What fraction remained?

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

    B. $\frac{3}{10}$

    C. $\frac{7}{10}$

    D. $\frac{2}{5}$

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16. Question 16

    1 mark

    Wanjala had a piece of land. He gave $\frac{5}{8}$ of the land to the son and $\frac{1}{4}$ to the brother. What fraction of the land did Wanjala give to the son and brother altogether?

    A. ¹⁄₂

    B. ³⁄₈

    C. ¹⁄₈

    D. ⁷⁄₈

    Marking scheme

    D. $\frac{7}{8}$ — eighths are the common denominator: $\frac{1}{4}=\frac{2}{8}$, so $\frac{5}{8}+\frac{2}{8}=\frac{7}{8}$. Adding tops and bottoms across the bar, the commonest error here, would give $\frac{6}{12}$.

17. Question 17

    1 mark

    What is $\frac{7}{10}-\frac{2}{5}$?

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

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

    C. $\frac{3}{10}$

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

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18. Question 18

    1 mark

    Wanjala had a piece of land. He gave $\frac{5}{8}$ to his son and $\frac{1}{4}$ to his brother. What fraction did he give out altogether?

    A. $\frac{7}{8}$

    B. $\frac{1}{8}$

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

    D. $\frac{3}{8}$

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19. Question 19

    1 mark

    Arrange from smallest: $\frac{2}{3},\frac{3}{5},\frac{5}{6}$

    A. $\frac{3}{5}$, $\frac{2}{3}$, $\frac{5}{6}$

    B. $\frac{5}{6}$, $\frac{2}{3}$, $\frac{3}{5}$

    C. $\frac{2}{3}$, $\frac{5}{6}$, $\frac{3}{5}$

    D. $\frac{2}{3}$, $\frac{3}{5}$, $\frac{5}{6}$

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20. Question 20

    1 mark

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

    A. 4 $\frac{1}{12}$

    B. 3 $\frac{7}{12}$

    C. 3 $\frac{4}{7}$

    D. 4 $\frac{1}{7}$

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    Marking scheme

    A. $4\frac{1}{12}$ — add whole numbers and fractions separately: $2+1=3$, and $\frac{1}{3}+\frac{3}{4}=\frac{4}{12}+\frac{9}{12}=\frac{13}{12}$. That improper fraction carries one more whole, giving $4\frac{1}{12}$. B forgets to carry it.

21. Question 21

    1 mark

    Which fraction is in its simplest form?

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

    B. $\frac{10}{15}$

    C. $\frac{6}{9}$

    D. $\frac{4}{8}$

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22. Question 22

    1 mark

    Multiply: $\frac{3}{5}\times \frac{5}{9}$

    A. $\frac{1}{3}$

    B. $\frac{8}{14}$

    C. $\frac{15}{45}$

    D. $\frac{3}{9}$

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23. Question 23

    1 mark

    Work out $\frac{3}{4}+\frac{1}{8}$.

    A. $\frac{4}{8}$

    B. 1

    C. $\frac{4}{12}$

    D. $\frac{7}{8}$

    (1 mark)

    Marking scheme

    D. $\frac{7}{8}$ — eighths and quarters need a common denominator, and $8$ works because $4$ divides into it: $\frac{3}{4}=\frac{6}{8}$, so $\frac{6}{8}+\frac{1}{8}=\frac{7}{8}$. The option $\frac{4}{12}$ is the classic error of adding tops and bottoms across the bar — that is never how fractions add.

24. Question 24

    1 mark

    Wanjala had a piece of land. He gave $\frac{5}{8}$ of the land to the son and $\frac{1}{4}$ to the brother. What fraction of the land did Wanjala give to the son and brother altogether?

    A. ¹⁄₂

    B. ³⁄₈

    C. ¹⁄₈

    D. ⁷⁄₈

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25. Question 25

    1 mark

    Which is greater: $\frac{3}{5}$ or $\frac{5}{8}$?

    A. They are equal

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

    C. Cannot tell

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

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26. Question 26

    1 mark

    Work out $\frac{3}{4}+\frac{1}{8}$.

    A. ⁴⁄₁₂

    B. 1

    C. ⁷⁄₈

    D. ⁴⁄₈

    Marking scheme

    C. $\frac{7}{8}$ — eighths and quarters need a common denominator, and $8$ works because $4$ divides into it: $\frac{3}{4}=\frac{6}{8}$, so $\frac{6}{8}+\frac{1}{8}=\frac{7}{8}$. The option $\frac{4}{12}$ is the classic error of adding tops and bottoms across the bar — that is never how fractions add.

27. Question 27

    1 mark

    Subtract: $\frac{5}{6}-\frac{1}{3}$

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

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

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

    D. $\frac{4}{6}$

    (1 mark)

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28. Question 28

    1 mark

    A recipe needs $\frac{3}{4}$ cup of flour. How many cups are needed for 5 batches?

    A. 4

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

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

    D. 3 $\frac{1}{2}$

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29. Question 29

    1 mark

    Subtract: $5\frac{1}{4}-2\frac{2}{3}$

    A. 3 $\frac{7}{12}$

    B. 2 $\frac{5}{12}$

    C. 3 $\frac{1}{12}$

    D. 2 $\frac{7}{12}$

    (1 mark)

    Marking scheme

    D. $2\frac{7}{12}$ — twelfths are the common denominator: $5\frac{3}{12}-2\frac{8}{12}$. Since $3$ cannot take $8$, borrow a whole to make $4\frac{15}{12}$, giving $2\frac{7}{12}$. Subtracting the fractions the wrong way round is what produces the other options.

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