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Exam questions · Maths · Number Without a Calculator

Fractions, Decimals and Percentages

  • 7 exam questions
  • 17 marks
  • 10 quick checks
  1. 1 Write [1 mark]

    Write \(0.45\) as a percentage.

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    Model answer

    Multiply by 100: \(0.45 \times 100 = 45\%\).

    Mark scheme

    • 45% — B1
  2. 2 Write [2 marks]

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

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    Model answer

    \(\dfrac{3}{20} = \dfrac{15}{100} = 15\%\).

    Mark scheme

    • \(\dfrac{15}{100}\) or \(0.15\) — M1
    • 15% — A1
  3. 3 Work out [3 marks]

    Work out \(35\%\) of 480. You must show your working.

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    Model answer

    \(10\% = 48\), so \(30\% = 144\). \(5\% = 24\). Then \(35\% = 144 + 24 = 168\).

    Mark scheme

    • Finds 10% (48) or 5% (24) — M1
    • Adds correct parts, such as 144 + 24 — M1
    • 168 — A1
  4. 4 Write [2 marks]

    Write these in order of size. Start with the smallest. \(\dfrac{2}{5}\) \(0.38\) \(41\%\)

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    Model answer

    \(\dfrac{2}{5} = 0.4\) and \(41\% = 0.41\). The order is \(0.38,\ \dfrac{2}{5},\ 41\%\).

    Mark scheme

    • At least two converted to a common form — M1
    • \(0.38,\ \dfrac{2}{5},\ 41\%\) — A1
  5. 5 Work out [3 marks]

    A phone costs \(\pounds 250\). In a sale the price is reduced by \(18\%\). Work out the sale price.

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    Model answer

    \(10\% = 25\) and \(8\% = 20\), so \(18\% = 45\). The sale price is \(250 - 45 = \pounds 205\).

    Mark scheme

    • Finds 10% or 1% correctly — M1
    • \(18\% = 45\) or \(250 \times 0.82\) — M1
    • \(\pounds 205\) — A1
  6. 6 Work out [3 marks]

    The price of a ticket rises from \(\pounds 25\) to \(\pounds 28\). Work out the percentage increase.

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    Model answer

    The increase is \(28 - 25 = \pounds 3\). \(\dfrac{3}{25} \times 100 = 12\%\).

    Mark scheme

    • \(28 - 25 = 3\) — M1
    • \(\dfrac{3}{25} \times 100\) or \(\dfrac{3}{25} = 0.12\) — M1
    • 12% — A1
  7. 7 Work out [3 marks]

    After a \(20\%\) increase, a water bill is \(\pounds 144\). Work out the bill before the increase.

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    Model answer

    \(144\) is \(120\%\) of the original bill. \(120\% = 144\), so \(10\% = 12\) and \(100\% = \pounds 120\).

    Mark scheme

    • Recognises that 144 is 120% — M1
    • \(144 \div 12 = 12\) (10%) or \(144 \div 1.2\) — M1
    • \(\pounds 120\) — A1

Quick check

  1. 1

    Which of these fractions is a recurring decimal?

    1. A\(\dfrac{7}{20}\)
    2. B\(\dfrac{1}{6}\)
    3. C\(\dfrac{9}{25}\)
    4. D\(\dfrac{3}{8}\)
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    B: \(\dfrac{1}{6}\)

    6 has the prime factor 3, so \(\dfrac{1}{6} = 0.1\dot{6}\) recurs. The others have denominators with only the prime factors 2 and 5.

  2. 2

    £500 is invested for 4 years at 3% simple interest per year. How much interest is earned in total?

    1. A£62.75
    2. B£15
    3. C£60
    4. D£560
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    C: £60

    3% of £500 is £15 a year, and \(15 \times 4 = £60\).

  3. 3

    Write 0.035 as a percentage.

    1. A350%
    2. B3.5%
    3. C0.35%
    4. D35%
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    B: 3.5%

    Multiply by 100: \(0.035 \times 100 = 3.5\%\).

  4. 4

    Write \(\dfrac{3}{8}\) as a percentage.

    1. A3.8%
    2. B38%
    3. C0.375%
    4. D37.5%
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    D: 37.5%

    \(3 \div 8 = 0.375\), and \(0.375 \times 100 = 37.5\%\).

  5. 5

    What is 15% of 60?

    1. A15
    2. B6
    3. C9
    4. D90
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    C: 9

    10% is 6 and 5% is 3, so 15% is 9.

  6. 6

    What is the multiplier for a decrease of 8%?

    1. A8
    2. B0.92
    3. C1.08
    4. D0.08
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    B: 0.92

    100% − 8% = 92%, which is 0.92.

  7. 7

    Increase £60 by 25%.

    1. A£15
    2. B£75
    3. C£240
    4. D£85
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    B: £75

    25% of 60 is 15, and 60 + 15 = 75.

  8. 8

    After a 20% decrease, a price is £48. What was the original price?

    1. A£57.60
    2. B£60
    3. C£96
    4. D£38.40
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    B: £60

    The sale price is 80% of the original, so the original is 48 ÷ 0.8 = £60.

  9. 9

    A price rises from 40 to 50. What is the percentage increase?

    1. A25%
    2. B20%
    3. C80%
    4. D10%
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    A: 25%

    The change is 10, and \(\dfrac{10}{40} \times 100 = 25\%\). It is divided by the original, not the new price.

  10. 10

    Write 12.5% as a fraction in its simplest form.

    1. A\(\dfrac{1}{8}\)
    2. B\(\dfrac{1}{12}\)
    3. C\(\dfrac{1}{5}\)
    4. D\(\dfrac{5}{8}\)
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    A: \(\dfrac{1}{8}\)

    \(12.5\% = \dfrac{12.5}{100} = \dfrac{1}{8}\).