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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 \(28\%\) as a fraction in its simplest form.

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    Model answer

    \(28\% = \dfrac{28}{100}\). Dividing the top and bottom by 4 gives \(\dfrac{7}{25}\).

    Mark scheme

    • \(\dfrac{28}{100}\) — M1
    • \(\dfrac{7}{25}\) — A1
  2. 2 Work out [3 marks]

    Work out \(17.5\%\) of \(\pounds 360\).

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    Model answer

    \(10\% = 36\), \(5\% = 18\) and \(2.5\% = 9\), so \(17.5\% = 36 + 18 + 9 = \pounds 63\).

    Mark scheme

    • Finds 10% (\(\pounds 36\)) or 5% (\(\pounds 18\)) — M1
    • Finds 2.5% (\(\pounds 9\)) and adds the parts — M1
    • \(\pounds 63\) — A1
  3. 3 Write [2 marks]

    Write these numbers in order of size. Start with the smallest. \(0.6\) \(\dfrac{5}{8}\) \(62\%\)

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    Model answer

    \(\dfrac{5}{8} = 0.625\) and \(62\% = 0.62\). The order is \(0.6,\ 62\%,\ \dfrac{5}{8}\).

    Mark scheme

    • Converts at least two of the numbers to the same form — M1
    • \(0.6,\ 62\%,\ \dfrac{5}{8}\) — A1
  4. 4 Work out [3 marks]

    A laptop costs \(\pounds 650\) before VAT. VAT at \(20\%\) is added. Work out the total cost of the laptop.

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    Model answer

    \(20\% = 2 \times 10\% = 2 \times 65 = \pounds 130\), so the total is \(650 + 130 = \pounds 780\).

    Mark scheme

    • Finds 10% (\(\pounds 65\)) or 20% (\(\pounds 130\)) — M1
    • \(650 + 130\) or \(650 \times 1.2\) — M1
    • \(\pounds 780\) — A1
  5. 5 Work out [3 marks]

    In a sale, the normal price of a bike is reduced by \(30\%\). The sale price is \(\pounds 56\). Work out the normal price of the bike.

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    Model answer

    The sale price is \(100\% - 30\% = 70\%\) of the normal price. \(70\% = 56\), so \(10\% = 56 \div 7 = 8\) and \(100\% = 8 \times 10 = \pounds 80\).

    Mark scheme

    • Recognises that £56 is 70% of the normal price — M1
    • \(56 \div 7 = 8\) (10%) or \(56 \div 0.7\) — M1
    • \(\pounds 80\) — A1
  6. 6 Work out [3 marks]

    Raj bought a car for \(\pounds 6000\). A year later its value was \(\pounds 4800\). Work out the percentage decrease in the value of the car.

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    Model answer

    The decrease is \(6000 - 4800 = \pounds 1200\). As a fraction of the original value this is \(\dfrac{1200}{6000} = \dfrac{1}{5}\), which is \(20\%\).

    Mark scheme

    • \(6000 - 4800 = 1200\) — M1
    • \(\dfrac{1200}{6000} \times 100\) or \(\dfrac{1200}{6000}\) — M1
    • 20% — A1
  7. 7 Work out [4 marks]

    Two shops sell the same camera. Shop A: normal price \(\pounds 320\), sale price is \(15\%\) off. Shop B: normal price \(\pounds 340\), sale price is \(25\%\) off. Which shop has the cheaper sale price? You must show your working.

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    Model answer

    Shop A: \(10\% = 32\) and \(5\% = 16\), so \(15\% = 48\) and the sale price is \(320 - 48 = \pounds 272\). Shop B: \(25\% = \dfrac{1}{4} \times 340 = 85\), so the sale price is \(340 - 85 = \pounds 255\). Shop B is cheaper.

    Mark scheme

    • Finds 15% of 320 (\(\pounds 48\)) or 25% of 340 (\(\pounds 85\)) — M1
    • Subtracts to get \(\pounds 272\) or \(\pounds 255\) — M1
    • Both sale prices correct — A1
    • States that Shop B is cheaper, consistent with their prices — C1

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: \(\dfrac{1}{8}\)

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