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

    Write \(15\%\) as a decimal.

    (b)

    Write \(15\%\) as a fraction in its simplest form.

    Show answer
    (a) \(0.15\)
    (b) \(\frac{3}{20}\)

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

    \(15 \div 100 = 0.15\)

    \(15\% = \frac{ 15 }{100}\)

    15 and 100 both divide by 5:

    \(\frac{ 15 }{100} = \frac{ 3 }{ 20 }\)

  2. Non-calculator 1 mark

    Express \(\frac{ 24 }{ 50 }\) as a percentage.

    Show answer
    \(48\%\)

    Make the denominator 100 by multiplying top and bottom by 2:

    \(\frac{ 24 }{ 50 } = \frac{ 48 }{100}\)

    So \(\frac{ 24 }{ 50 } = 48\%\)

  3. Either paper 3 marks

    The table shows some fractions, decimals and percentages that are worth knowing by heart. Three of the boxes are empty.

    FractionDecimalPercentage
    \(\frac{ 9 }{ 10 }\)(a)\(90\%\)
    (b)\(0.7\)\(70\%\)
    \(\frac{ 1 }{ 5 }\)\(0.2\)(c)
    (a)

    Write down the decimal that goes in box (a).

    (b)

    Write down the fraction that goes in box (b). Give it in its simplest form.

    (c)

    Write down the percentage that goes in box (c).

    Show answer
    (a) \(0.9\)
    (b) \(\frac{7}{10}\)
    (c) \(20\%\)

    \(90\%\) means 90 out of 100, so divide by 100:

    \(90 \div 100 = 0.9\)

    \(0.7 = \frac{ 70 }{100}\)

    70 and 100 both divide by 10:

    \(\frac{ 70 }{100} = \frac{ 7 }{ 10 }\)

    Multiply the decimal by 100:

    \(0.2 \times 100 = 20\), so the percentage is \(20\%\).

  4. Either paper 2 marks

    Each part has its own grid of equal squares.

    (a)

    Shade \(\frac{ 9 }{ 10 }\) of the grid. The grid is made of 20 equal squares.

    (b)

    Shade 35% of the grid. The grid is made of 40 equal squares.

    You cannot draw on this page. Draw this on paper, then show the answer and check your drawing against the model.

    Show answer
    (a) Any 18 of the 20 squares shaded
    (b) Any 14 of the 40 squares shaded
    (a)
    (b)

    The grid has \(4 \times 5 = 20\) squares.

    \(\frac{ 9 }{ 10 } \times 20 = 20 \div 10 \times 9 = 2 \times 9 = 18\)

    Shade any 18 squares.

    The grid has \(8 \times 5 = 40\) squares.

    \(35\% \text{ of } 40 = \frac{ 35 }{100} \times 40 = 14\)

    Shade any 14 squares.

    • (a) B118 squares shaded, no more and no fewer
    • (b) B114 squares shaded, no more and no fewer
  5. Either paper 1 mark

    Two of these six numbers are equal.

    \(\frac{4}{3} \qquad 0.75 \qquad 75\% \qquad \frac{3}{40} \qquad 75 \qquad 750\%\)

    Write down the two numbers.

    Show answer
    The decimal and the percentage: the two numbers with the value \(\frac{3}{4}\) = \(0.75\) = \(75\%\)

    The numbers are in three different forms, so compare them as decimals. Divide the top of a fraction by its bottom, and divide a percentage by 100.

    \(\frac{3}{4} = 0.75\) and \(75\% = 0.75\), so this value appears twice in the list: as a decimal and as a percentage.

    The other numbers do not match. Three of them have the decimal point in the wrong place, with values \(0.075\), \(7.5\) and \(75\), and \(\frac{4}{3}\) is \(\frac{3}{4}\) turned upside down.

  6. Either paper 1 mark

    Work out \(\frac{ 1 }{ 20 } + 0.39\)

    Give your answer as a decimal.

    Show answer
    \(0.44\)

    Write the fraction as a decimal first: \(\frac{ 1 }{ 20 } = 0.05\)

    \(0.05 + 0.39 = 0.44\)

  7. Either paper 3 marks
    (a)

    Write \(0.425\) as a fraction.

    Give your answer in its simplest form.

    (b)

    Write \(0.425\) as a percentage.

    Show answer
    (a) \(\frac{17}{40}\)
    (b) \(42.5\%\)

    \(0.425\) is 425 out of 1000:

    \(0.425 = \frac{ 425 }{ 1000 }\)

    425 and 1000 both divide by 25:

    \(\frac{ 425 }{ 1000 } = \frac{ 17 }{ 40 }\)

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

    \(0.425 \times 100 = 42.5\%\)

    • (a) M1\(0.425\) written over 1000: \(\frac{ 425 }{ 1000 }\)
    • (a) A1simplest form \(\frac{ 17 }{ 40 }\)
  8. Either paper 2 marks
    (a)

    Write \(\frac{ 3 }{ 20 }\) as a decimal.

    (b)

    Write \(\frac{ 3 }{ 20 }\) as a percentage.

    Show answer
    (a) \(0.15\)
    (b) \(15\%\)

    A fraction is a division — 3 shared between 20:

    \(3 \div 20 = 0.15\)

    Multiply the decimal by 100:

    \(0.15 \times 100 = 15\%\)

  9. Either paper 2 marks

    Write these numbers in order of size, starting with the smallest.

    \(\frac{7}{20} \qquad 0.25 \qquad 20\% \qquad \frac{1}{10}\)

    Write each number as a percentage.

    Show answer
    \(10\%,\ 20\%,\ 25\%,\ 35\%\)

    Numbers written in three different ways cannot be compared as they stand, so change them all into the same form. Percentages are the easiest here, because every one of them is a whole number.

    \(\frac{7}{20} = 35\%\), \(0.25 = 25\%\), \(20\%\) is already a percentage, and \(\frac{1}{10} = 10\%\).

    Now put them in order, smallest first:

    \(10\%,\ 20\%,\ 25\%,\ 35\%\)

    • M1all four numbers written in the same form, e.g. as percentages \(35\%\), \(25\%\), \(20\%\), \(10\%\)
    • A1correct order, smallest first \(10\%,\ 20\%,\ 25\%,\ 35\%\)
  10. Either paper 2 marks

    Pace Sports takes \(\frac{ 9 }{ 20 }\) off the price of a pair of running shoes.

    Rundale Sports takes \(39\%\) off the price of the same pair of running shoes.

    Which shop gives the bigger discount? You must show your working.

    Show answer
    Pace Sports

    The two offers are written in different forms, so change one of them. As a percentage,

    \(\frac{ 9 }{ 20 } \times 100\% = 45\%\)

    The two discounts are \(45\%\) and \(39\%\). The bigger of these is \(45\%\), so Pace Sports gives the bigger discount and Rundale Sports gives the smaller one.

    • M1converts \(\frac{ 9 }{ 20 }\) and \(39\%\) to the same form
    • A1Pace Sports