[discia] GCSE Maths › Ratio and Proportion › Writing and Simplifying Ratio

Writing and Simplifying Ratio

discia.org 10 questions · 24 marks
Name Date
  1. Either paper 2 marks

    There are 96 members in a swimming club. 56 of the members are adults. The rest are children.

    Write down the ratio of adults to children. Give your answer in its simplest form.

    Show answer
    \(7 : 5\)
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  2. Either paper 2 marks

    Write each of these ratios in its simplest form.

    (a)

    \(24 : 60\)

    (b)

    \(7 : 63\)

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    (a) \(2 : 5\)
    (b) \(1 : 9\)
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  3. Either paper 3 marks

    Shape \(ABCDE\) is drawn on a centimetre grid.

    xyABCDE
    (a)

    Complete this statement by writing the name of one side of the shape.

    \(AB : \_\_\_\_\_\_ = 4 : 1\)

    (b)

    On the centimetre grid below, draw a rectangle with the same area as shape \(ABCDE\).

    xy
    Show answer
    (a) CD (or DC)
    (b) Any rectangle of area \(18\) cm\(^2\), for example \(6\) cm by \(3\) cm
    (b)xy
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  4. Either paper 2 marks

    A necklace is made with red beads, green beads and silver beads in the ratio \(36 : 54 : 30\).

    Write this ratio in its simplest form.

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    \(6 : 9 : 5\)
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  5. Either paper 2 marks

    Tomas is asked to write the ratio \(12 : 60\) in its simplest form.

    He writes \(12 : 60 = 4 : 20\)

    Explain what Tomas has done wrong, and write \(12 : 60\) in its simplest form.

    Show answer
    Tomas divided both parts by 3, which is not the highest common factor. \(12 : 60 = 1 : 5\)
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  6. Either paper 2 marks

    Omar says that \(5 : 2\) is an equivalent ratio to \(15 : 6\).

    Ella says that \(2.5 : 1\) is an equivalent ratio to \(15 : 6\).

    Who is correct? Tick one box.

    - Both of them - Omar only - Ella only - Neither of them

    Give reasons for your answer.

    Show answer
    Both of them. Omar: dividing 15 and 6 by 3 gives 5 : 2, so Omar is right. Ella: 15 ÷ 6 = 2.5, so 15 : 6 = 2.5 : 1 and Ella is right.
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  7. Either paper 2 marks

    Write the ratio 9 millimetres to 4 centimetres in its simplest form.

    Show answer
    \(9 : 40\)
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  8. Either paper 2 marks

    In a car park the ratio of red cars to blue cars is \(12 : 168\).

    Write this ratio in the form \(1 : n\).

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    \(1 : 14\)
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  9. Either paper 4 marks

    Neither of these ratios is written with whole numbers.

    Write each of them in its simplest form.

    (a)

    \(0.8 : 2.8\)

    (b)

    \(\frac{ 2 }{ 9 } : \frac{ 6 }{ 11 }\)

    Show answer
    (a) \(2 : 7\)
    (b) \(11 : 27\)
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  10. Either paper 3 marks

    A box contains only green, black and pink pencils.

    There are 24 green pencils in the box.

    There are three times as many black pencils as green pencils.

    There are 66 fewer pink pencils than black pencils.

    Write the ratio of green pencils to black pencils to pink pencils in its simplest form.

    Show answer
    \(4 : 12 : 1\)
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discia.org Writing and Simplifying Ratio · sheet 1
Answers Writing and Simplifying Ratio · sheet 1
  1. \(7 : 5\)
  2. (a) \(2 : 5\)
    (b) \(1 : 9\)
  3. (a) CD (or DC)
    (b) Any rectangle of area \(18\) cm\(^2\), for example \(6\) cm by \(3\) cm
    (b)xy
  4. \(6 : 9 : 5\)
  5. Tomas divided both parts by 3, which is not the highest common factor. \(12 : 60 = 1 : 5\)
  6. Both of them. Omar: dividing 15 and 6 by 3 gives 5 : 2, so Omar is right. Ella: 15 ÷ 6 = 2.5, so 15 : 6 = 2.5 : 1 and Ella is right.
  7. \(9 : 40\)
  8. \(1 : 14\)
  9. (a) \(2 : 7\)
    (b) \(11 : 27\)
  10. \(4 : 12 : 1\)
discia.org Writing and Simplifying Ratio · sheet 1