[discia] GCSE Maths › Number › Writing, Simplifying and Ordering Fractions › Practise
  1. Either paper 2 marks
    (a)

    Write \(66\%\) as a decimal.

    (b)

    Write \(66\%\) as a fraction in its simplest form.

    Show answer
    (a) \(0.66\)
    (b) \(\frac{33}{50}\)

    Per cent means "out of 100", so divide by 100:

    \(66 \div 100 = 0.66\)

    \(66\% = \frac{ 66 }{100}\)

    66 and 100 both divide by 2:

    \(\frac{ 66 }{100} = \frac{ 33 }{ 50 }\)

  2. Either paper 1 mark

    Simplify \(\frac{ 22 }{ 24 }\)

    Show answer
    \(\frac{11}{12}\)

    The highest common factor of 22 and 24 is 2.

    \(\frac{ 22 }{ 24 } = \frac{ 22 \div 2 }{ 24 \div 2 } = \frac{ 11 }{ 12 }\)

  3. Either paper 2 marks
    (a)

    Find the missing number.

    \(\frac{ 1 }{ 4 } = \frac{?}{ 20 }\)

    (b)

    Find the missing number.

    \(\frac{ 1 }{ 4 } = \frac{ 7 }{?}\)

    Show answer
    (a) \(5\)
    (b) \(28\)

    \(4 \times 5 = 20\), so multiply the numerator by 5 as well:

    \(1 \times 5 = 5\)

    \(1 \times 7 = 7\), so multiply the denominator by 7 as well:

    \(4 \times 7 = 28\)

  4. Either paper 3 marks

    A bag holds 27 beads. 3 of the beads are blue.

    (a)

    What fraction of the beads are blue? Give your answer in its simplest form.

    (b)

    What fraction of the beads are not blue?

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    (a) \(\frac{1}{9}\)
    (b) \(\frac{8}{9}\)

    3 out of 27 are blue, so the fraction is \(\frac{ 3 }{ 27 }\).

    Divide the numerator and the denominator by 3:

    \(\frac{ 3 }{ 27 } = \frac{ 1 }{ 9 }\)

    The two fractions add up to 1, so

    \(1 - \frac{ 1 }{ 9 } = \frac{ 8 }{ 9 }\)

    • (a) M1fraction \(\frac{ 3 }{ 27 }\)
    • (a) A1simplified to \(\frac{ 1 }{ 9 }\)
  5. Either paper 2 marks
    (a)

    \(\frac{ 25 }{ 3 }\) is an improper fraction.

    Write it as a mixed number.

    (b)

    \(9\frac{7}{8}\) is a mixed number.

    Write it as an improper fraction.

    Show answer
    (a) \(8\frac{1}{3}\)
    (b) \(\frac{79}{8}\)

    3 goes into 25 exactly 8 times, with 1 left over.

    \(\frac{ 25 }{ 3 } = 8\frac{1}{3}\)

    \(9 \times 8 = 72\), then add the 7:

    \(9\frac{7}{8} = \frac{ 72 + 7 }{ 8 } = \frac{ 79 }{ 8 }\)

  6. Either paper 2 marks

    Here are two fractions.

    \(\frac{ 1 }{ 4 } \qquad \frac{ 3 }{ 5 }\)

    Which fraction is greater? You must show your working.

    Show answer
    \(\frac{3}{5}\)

    Write both fractions with a denominator of 20:

    \(\frac{ 1 }{ 4 } = \frac{ 5 }{ 20 } \qquad \frac{ 3 }{ 5 } = \frac{ 12 }{ 20 }\)

    \(\frac{ 12 }{ 20 }\) is the larger, so the greater fraction is \(\frac{3}{5}\).

    • M1common denominator 20, \(\frac{ 5 }{ 20 }\) and \(\frac{ 12 }{ 20 }\)
    • A1greater fraction \(\frac{3}{5}\)
  7. Either paper 3 marks
    (a)

    Write \(0.05\) as a fraction in its simplest form.

    (b)

    Write \(0.05\) as a percentage.

    Show answer
    (a) \(\frac{1}{20}\)
    (b) \(5\%\)

    \(0.05\) is 5 out of 100:

    \(0.05 = \frac{ 5 }{ 100 }\)

    5 and 100 both divide by 5:

    \(\frac{ 5 }{ 100 } = \frac{ 1 }{ 20 }\)

    To turn a decimal into a percentage, multiply by 100:

    \(0.05 \times 100 = 5\%\)

    • (a) M1\(0.05\) written over 100: \(\frac{ 5 }{ 100 }\)
    • (a) A1simplest form \(\frac{ 1 }{ 20 }\)
  8. Either paper 3 marks

    Here are four fractions.

    \(\frac{ 12 }{ 14 }, \quad \frac{ 48 }{ 56 }, \quad \frac{ 60 }{ 70 }, \quad \frac{ 30 }{ 36 }\)

    Three of them are equivalent. One is not.

    (a)

    State the fraction that is not equivalent to the other three.

    (b)

    State the simplest form of the other three.

    Show answer
    (a) \(\frac{ 30 }{ 36 }\)
    (b) \(\frac{ 6 }{ 7 }\)

    Cancel each one down as far as it will go.

    \(\frac{ 12 }{ 14 }\), \(\frac{ 48 }{ 56 }\) and \(\frac{ 60 }{ 70 }\) all cancel to \(\frac{ 6 }{ 7 }\).

    \(\frac{ 30 }{ 36 }\) does not, so it is the odd one out.

    Cancelling \(\frac{ 12 }{ 14 }\) by 2 gives \(\frac{ 6 }{ 7 }\), and it will go no further.

    • (a) M1cancelling to find the other three equal \(\frac{ 6 }{ 7 }\)
    • (a) A1odd one out \(\frac{ 30 }{ 36 }\)
  9. Either paper 3 marks
    Here are three numbers.
    A\(\frac{ 21 }{ 4 }\)
    B\(\frac{ 9 }{ 4 }\)
    C\(2\frac{ 3 }{ 4 }\)

    Write the letters A, B and C in order of size, starting with the smallest.

    Show answer
    B, C, A

    Write all three as improper fractions over 4.

    A and B are already over 4: \(\frac{ 21 }{ 4 }\) and \(\frac{ 9 }{ 4 }\).

    C is \(2\) whole ones and \(\frac{ 3 }{ 4 }\), and one whole one is \(\frac{ 4 }{ 4 }\), so C is \(\frac{ 11 }{ 4 }\).

    The denominators now match, so compare the numerators \(21\), \(9\) and \(11\).

    In order, smallest first: B, C, A

    • M1write all three over 4, \(\frac{ 21 }{ 4 }\), \(\frac{ 9 }{ 4 }\) and \(\frac{ 11 }{ 4 }\)
    • M1compare the numerators, 21, 9 and 11
    • A1order smallest to largest, B, C, A
  10. Either paper 1 mark

    Write \(2.95\) as an improper fraction in its simplest form.

    Show answer
    \(\frac{59}{20}\)

    Write the whole decimal over a power of ten, keeping the whole part:

    \(2.95 = \frac{ 295 }{ 100 }\)

    295 and 100 both divide by 5:

    \(\frac{ 295 }{ 100 } = \frac{ 59 }{ 20 }\)