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Exam questions · Maths · Ratio and Proportion

Ratio: Simplifying and Sharing

  • 6 exam questions
  • 18 marks
  • 9 quick checks
  1. 1 Write [2 marks]

    Write the ratio \(18 : 30\) in its simplest form.

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    Model answer

    The highest common factor is 6, so \(18 : 30 = 3 : 5\).

    Mark scheme

    • Divides both by a common factor, such as \(9 : 15\) or \(6 : 10\) — M1
    • \(3 : 5\) — A1
  2. 2 Work out [3 marks]

    Peter and Quinn share \(\pounds 84\) in the ratio \(3 : 4\). Work out Quinn's share.

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    Model answer

    There are \(3 + 4 = 7\) parts, and one part is \(84 \div 7 = 12\). Quinn's share is \(4 \times 12 = \pounds 48\).

    Mark scheme

    • \(3 + 4 = 7\) or \(84 \div 7\) — M1
    • \(4 \times 12\) or \(84 \div 7 \times 4\) — M1
    • \(\pounds 48\) — A1
  3. 3 Work out [3 marks]

    Paint is mixed from blue and yellow in the ratio \(2 : 5\). Lena uses 600 ml of yellow paint. Work out how much blue paint she needs.

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    Model answer

    The yellow is 5 parts, so one part is \(600 \div 5 = 120\) ml. The blue is \(2 \times 120 = 240\) ml.

    Mark scheme

    • \(600 \div 5 = 120\) — M1
    • \(2 \times 120\) — M1
    • 240 ml — A1
  4. 4 Work out [3 marks]

    The ratio of cats to dogs at a rescue centre is \(5 : 3\). There are 16 more cats than dogs. Work out the total number of cats and dogs.

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    Model answer

    The difference is \(5 - 3 = 2\) parts, and \(2\) parts \(= 16\), so one part is 8. The total is \(8\) parts, which is \(8 \times 8 = 64\).

    Mark scheme

    • \(16 \div 2 = 8\) — M1
    • \(8 \times 8\) or \(40 + 24\) — M1
    • 64 — A1
  5. 5 Work out [3 marks]

    Concrete is made from cement, sand and gravel in the ratio \(1 : 3 : 5\). A builder makes 90 kg of concrete. Work out the mass of sand in the concrete.

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    Model answer

    There are \(1 + 3 + 5 = 9\) parts, so one part is \(90 \div 9 = 10\) kg. The sand is \(3 \times 10 = 30\) kg.

    Mark scheme

    • \(1 + 3 + 5 = 9\) or \(90 \div 9\) — M1
    • \(3 \times 10\) — M1
    • 30 kg — A1
  6. 6 Work out [4 marks]

    \(x : y = 3 : 4\) and \(y : z = 6 : 5\). (a) Work out \(x : y : z\). (2 marks) (b) \(x + y + z = 124\). Work out the value of \(z\). (2 marks)

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    Model answer

    (a) Make \(y\) the same in both: the lowest common multiple of 4 and 6 is 12. So \(x : y = 9 : 12\) and \(y : z = 12 : 10\), giving \(x : y : z = 9 : 12 : 10\). (b) There are \(9 + 12 + 10 = 31\) parts, so one part is \(124 \div 31 = 4\) and \(z = 10 \times 4 = 40\).

    Mark scheme

    • (a) \(9 : 12\) or \(12 : 10\) seen — M1
    • (a) \(9 : 12 : 10\) — A1
    • (b) \(124 \div 31 = 4\) — M1
    • (b) 40 — A1

Quick check

  1. 1

    Simplify the ratio \(24 : 36\).

    1. A\(4 : 6\)
    2. B\(2 : 3\)
    3. C\(3 : 2\)
    4. D\(6 : 9\)
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    B: \(2 : 3\)

    The highest common factor of 24 and 36 is 12. Dividing both parts by 12 gives \(2 : 3\).

  2. 2

    Which ratio is equivalent to \(3 : 5\)?

    1. A\(9 : 15\)
    2. B\(9 : 12\)
    3. C\(6 : 8\)
    4. D\(5 : 3\)
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    A: \(9 : 15\)

    Multiplying both parts of \(3 : 5\) by 3 gives \(9 : 15\). The others do not keep the same relationship.

  3. 3

    Write \(40\) cm to \(1.2\) m as a ratio in its simplest form.

    1. A\(40 : 1.2\)
    2. B\(1 : 30\)
    3. C\(3 : 1\)
    4. D\(1 : 3\)
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    D: \(1 : 3\)

    Change to the same unit: \(1.2\) m \(= 120\) cm. Then \(40 : 120 = 1 : 3\).

  4. 4

    \(\pounds 60\) is shared in the ratio \(2 : 3\). How much is the larger share?

    1. A\(\pounds 24\)
    2. B\(\pounds 30\)
    3. C\(\pounds 36\)
    4. D\(\pounds 40\)
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    C: \(\pounds 36\)

    There are \(2 + 3 = 5\) parts, and one part is \(60 \div 5 = 12\). The larger share is \(3 \times 12 = 36\).

  5. 5

    The ratio of boys to girls in a class is \(3 : 5\). There are 12 boys. How many girls are there?

    1. A15
    2. B20
    3. C36
    4. D4
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    B: 20

    One part is \(12 \div 3 = 4\), so the number of girls is \(5 \times 4 = 20\).

  6. 6

    Red and blue beads are in the ratio \(2 : 5\). What fraction of the beads are red?

    1. A\(\dfrac{2}{7}\)
    2. B\(\dfrac{2}{5}\)
    3. C\(\dfrac{5}{7}\)
    4. D\(\dfrac{2}{3}\)
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    A: \(\dfrac{2}{7}\)

    The whole is \(2 + 5 = 7\) parts, so red is \(\dfrac{2}{7}\).

  7. 7

    Orange juice and water are mixed in the ratio \(1 : 4\). There is 250 ml of orange juice. How much water is there?

    1. A750 ml
    2. B1250 ml
    3. C4 ml
    4. D1000 ml
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    D: 1000 ml

    The water is 4 times the juice, so \(4 \times 250 = 1000\) ml.

  8. 8

    Amy and Ben share money in the ratio \(3 : 7\). Ben gets \(\pounds 20\) more than Amy. How much money is shared?

    1. A\(\pounds 35\)
    2. B\(\pounds 80\)
    3. C\(\pounds 50\)
    4. D\(\pounds 20\)
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    C: \(\pounds 50\)

    The difference is \(7 - 3 = 4\) parts, so 4 parts \(= 20\) and one part is 5. The total is \(10 \times 5 = 50\).

  9. 9

    \(A : B = 2 : 3\) and \(B : C = 4 : 5\). Write \(A : B : C\) in its simplest form.

    1. A\(2 : 3 : 5\)
    2. B\(8 : 12 : 15\)
    3. C\(8 : 12 : 20\)
    4. D\(6 : 12 : 15\)
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    B: \(8 : 12 : 15\)

    Make the \(B\) values match. The lowest common multiple of 3 and 4 is 12. Then \(A : B = 8 : 12\) and \(B : C = 12 : 15\), so \(A : B : C = 8 : 12 : 15\).