Writing a Ratio as a Fraction or Linear Function worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

1. 3 marks

   A box contains only silver, gold and black beads.

   The ratio of silver beads to gold beads to black beads is \(2 : 7 : 8\).

   (a)

   What fraction of the beads in the box are gold?

   (b)

   What fraction of the beads in the box are not black?

2. 4 marks

   In a pencil case, \(\frac{ 4 }{ 7 }\) of the pencils are green. The rest are black.

   (a)

   Write down the ratio of green pencils to black pencils. Give your answer in its simplest form.

   (b)

   There are 24 green pencils in the pencil case.

   Work out how many pencils there are in the pencil case altogether.

3. 3 marks

   In a car park there are only vans and cars.

   The ratio of the number of vans to the number of cars is \(5 : 9\).

   (a)

   Write the number of vans as a fraction of the number of cars.

   (b)

   Write the number of cars as a fraction of the number of vans.

   (c)

   What fraction of the vehicles are vans?

4. 3 marks

   In a fruit bowl the ratio of apples to bananas is \(9 : 4\).

   The ratio of oranges to bananas is \(1 : 8\).

   Find the ratio of apples to bananas to oranges. Give your answer in its simplest form.

5. 4 marks

   \(d = \frac{ 11 }{ 3 }c\)

   (a)

   State the ratio \(c : d\).

   (b)

   \(d\) is 192 more than \(c\).

   Calculate the value of \(c\).

6. 4 marks

   A fruit drink is made from orange juice and mango juice.

   \(V\) is the number of millilitres of orange juice and \(M\) is the number of millilitres of mango juice.

   The ratio \(V : M\) is \(3 : 4\).

   (a)

   Write down a formula for \(M\) in terms of \(V\).

   (b)

   Calculate the value of \(M\) when \(V = 24\).

7. 5 marks

   A bag contains only silver, gold and black beads.

   The ratio of the number of silver beads to the number of gold beads is \(3 : 5\).

   The ratio of the number of gold beads to the number of black beads is \(3 : 1\).

   (a)

   Find the ratio of silver beads to gold beads to black beads. Give your answer in its simplest form.

   (b)

   There are 261 beads altogether.

   Calculate how many of them are black.

8. 3 marks

   Amy and Ben each have some money.

   \(\frac{ 6 }{ 7 }\) of the money Amy has is equal to \(\frac{ 3 }{ 8 }\) of the money Ben has.

   Find the ratio of the money Amy has to the money Ben has. Give your answer in its simplest form.

9. 3 marks

   A car park holds only cars, vans and lorries.

   \(\frac{ 1 }{ 4 }\) of the vehicles are cars.

   The rest are vans and lorries in the ratio \(2 : 5\).

   What fraction of the vehicles are lorries?

10. 4 marks

    \((x + 2) : (x - 13) = 7 : 2\)

    Work out the value of \(x\).

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