[discia] GCSE Maths › Number › Fractions

Fractions

discia.org 10 questions · 29 marks
Name Date
  1. Non-calculator 1 mark

    Write down the reciprocal of \(-\frac{7}{8}\)

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    \(-\frac{8}{7}\)
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  2. Non-calculator 4 marks
    (a)

    Find the value of \(\frac{ 1 }{ 2 } + \frac{ 3 }{ 8 }\)

    (b)

    Find the value of \(\frac{ 5 }{ 6 } - \frac{ 1 }{ 12 }\)

    Give your answer in its simplest form.

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    (a) \(\frac{7}{8}\)
    (b) \(\frac{3}{4}\)
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  3. Non-calculator 3 marks

    Joel is working out \(\frac{ 1 }{ 8 } + \frac{ 3 }{ 4 }\)

    He writes \(\frac{ 1 }{ 8 } + \frac{ 3 }{ 4 } = \frac{ 4 }{ 12 }\)

    (a)

    Explain what Joel has done wrong.

    (b)

    Work out the correct answer to \(\frac{ 1 }{ 8 } + \frac{ 3 }{ 4 }\)

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    (a) Joel has added the numerators and added the denominators. Fractions can only be added once they have been rewritten with the same denominator.
    (b) \(\frac{7}{8}\)
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  4. Non-calculator 2 marks

    Work out the value of \(\frac{ 9 }{ 10 } \times \frac{ 1 }{ 6 }\)

    Give your answer in its simplest form.

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    \(\frac{3}{20}\)
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  5. Non-calculator 2 marks
    Here is a grid of squares, 2 rows by 3 columns.
    ◣■■
    ■□◣
    What fraction of the grid is shaded? Give your answer in its simplest form.
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    \(\frac{ 2 }{ 3 }\)
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  6. Non-calculator 3 marks

    Find the value of \(3\frac{3}{4} + 4\frac{1}{2}\)

    Give your answer as a mixed number.

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    \(8\frac{1}{4}\)
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  7. Non-calculator 3 marks

    Work out \(4\frac{1}{6} \times 2\frac{1}{2}\)

    Give your answer as a mixed number.

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    \(10\frac{5}{12}\)
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  8. Non-calculator 5 marks
    (a)

    Work out \(\frac{ 7 }{ 10 } \div \frac{ 7 }{ 8 }\)

    Give your answer in its simplest form.

    (b)

    Work out \(3\frac{5}{6} \div 1\frac{2}{3}\)

    Give your answer as a mixed number.

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    (a) \(\frac{4}{5}\)
    (b) \(2\frac{3}{10}\)
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  9. Non-calculator 3 marks

    \(a\) and \(b\) are positive integers.

    \(\frac{ 1 }{ b } + \frac{ a }{ 5 } = \frac{ 17 }{ 30 }\)

    Work out the values of \(a\) and \(b\).

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    \(a = 2\) and \(b = 6\)
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  10. Non-calculator 3 marks

    Complete the grid so that when you multiply the three numbers in any column, row or diagonal the answer is 1.

    \(\frac{1}{5}\)\(125\)\(A\)
    \(B\)\(1\)\(C\)
    \(25\)\(\frac{1}{125}\)\(5\)

    The empty cells are marked A, B and C. Write the number that goes in each.

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    \(A = \frac{1}{25}, \quad B = \frac{1}{5}, \quad C = 5\)
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discia.org Fractions · sheet 1
Answers Fractions · sheet 1
  1. \(-\frac{8}{7}\)
  2. (a) \(\frac{7}{8}\)
    (b) \(\frac{3}{4}\)
  3. (a) Joel has added the numerators and added the denominators. Fractions can only be added once they have been rewritten with the same denominator.
    (b) \(\frac{7}{8}\)
  4. \(\frac{3}{20}\)
  5. \(\frac{ 2 }{ 3 }\)
  6. \(8\frac{1}{4}\)
  7. \(10\frac{5}{12}\)
  8. (a) \(\frac{4}{5}\)
    (b) \(2\frac{3}{10}\)
  9. \(a = 2\) and \(b = 6\)
  10. \(A = \frac{1}{25}, \quad B = \frac{1}{5}, \quad C = 5\)
discia.org Fractions · sheet 1