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Exam questions · Maths · Number Without a Calculator

Fractions, Decimals and Percentages

  • 7 exam questions
  • 20 marks
  • 10 quick checks
  1. 1 Write [2 marks]

    Write \(0.08\) as a fraction in its simplest form.

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    Model answer

    \(0.08 = \dfrac{8}{100}\). Dividing the top and bottom by 4 gives \(\dfrac{2}{25}\).

    Mark scheme

    • \(\dfrac{8}{100}\) — M1
    • \(\dfrac{2}{25}\) — A1
  2. 2 Work out [3 marks]

    Work out \(45\%\) of \(\pounds 620\).

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    Model answer

    \(10\% = 62\), so \(40\% = 248\). \(5\% = 31\). Then \(45\% = 248 + 31 = \pounds 279\).

    Mark scheme

    • Finds 10% (£62) or 5% (£31) — M1
    • Adds correct parts, such as 248 + 31 — M1
    • \(\pounds 279\) — A1
  3. 3 Work out [3 marks]

    A restaurant bill is \(\pounds 84\) before a service charge. A service charge of \(12.5\%\) is added to the bill. Work out the total amount to pay.

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    Model answer

    \(12.5\% = \dfrac{1}{8}\), and \(84 \div 8 = 10.50\). The total is \(84 + 10.50 = \pounds 94.50\).

    Mark scheme

    • Finds 12.5% of 84, such as \(84 \div 8\), or 10% + 2.5% — M1
    • \(84 + 10.50\) — M1
    • \(\pounds 94.50\) — A1
  4. 4 Work out [3 marks]

    Increase \(\pounds 350\) by \(14\%\).

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    Model answer

    \(10\% = 35\) and \(4\% = 14\), so \(14\% = 49\). The new amount is \(350 + 49 = \pounds 399\).

    Mark scheme

    • Finds 10% (£35) and 1% (£3.50), or 14% as 49 — M1
    • \(350 + 49\) or \(350 \times 1.14\) — M1
    • \(\pounds 399\) — A1
  5. 5 Work out [3 marks]

    The price of a jacket is reduced from \(\pounds 64\) to \(\pounds 48\) in a sale. Work out the percentage reduction.

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    Model answer

    The reduction is \(64 - 48 = \pounds 16\). \(\dfrac{16}{64} = \dfrac{1}{4} = 25\%\).

    Mark scheme

    • \(64 - 48 = 16\) — M1
    • \(\dfrac{16}{64} \times 100\) or \(\dfrac{1}{4}\) — M1
    • 25% — A1
  6. 6 Work out [3 marks]

    Priya invests some money for one year at \(4\%\) interest. At the end of the year she has \(\pounds 1560\). Work out how much she invested.

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    Model answer

    After a \(4\%\) increase, the amount is \(104\%\) of the original. \(104\% = 1560\), so \(1\% = 15\) and \(100\% = \pounds 1500\).

    Mark scheme

    • Recognises that £1560 is 104% of the original — M1
    • \(1560 \div 104 = 15\) or \(1560 \div 1.04\) — M1
    • \(\pounds 1500\) — A1
  7. 7 Explain [3 marks]

    Dev says, ‘If I increase an amount by \(10\%\) and then decrease the result by \(10\%\), I will end up with the amount I started with.’ Is Dev correct? You must show how you decide.

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    Model answer

    No. Take \(\pounds 200\) as an example. A \(10\%\) increase gives \(200 + 20 = 220\). A \(10\%\) decrease of \(220\) is \(22\), giving \(220 - 22 = \pounds 198\), which is not \(\pounds 200\). The second percentage is taken of a bigger number.

    Mark scheme

    • Chooses a starting amount and applies a 10% increase correctly — M1
    • Applies a 10% decrease to the new amount, not the original — M1
    • No, with a correct comparison such as £198 and £200 — 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: \(\dfrac{1}{8}\)

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