Writing a Ratio as a Fraction or Linear Function
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Either paper 5 marks
Here is a triangle.
(a)Work out the length of the shortest side as a fraction of the length of the longest side.
Give your answer as a fraction in its simplest form.
(b)Here is a different triangle.
\(x = 3y\)
Work out the size of angle \(y\).
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Either paper 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?
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Either paper 1 mark
\(v : u = 1 : 4\)
Circle the correct equation.
\(v = u - 3\) \(v = \frac{ u }{ 4 }\) \(v = u + 3\) \(v = 4u\)
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Either paper 1 mark
\(m : n = 8 : 5\)
Circle the correct statement.
\(n\) is \(\frac{ 8 }{ 13 }\) of \(m\)
\(n\) is \(\frac{ 5 }{ 13 }\) of \(m\)
\(n\) is \(\frac{ 8 }{ 5 }\) of \(m\)
\(n\) is \(\frac{ 5 }{ 8 }\) of \(m\)
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Either paper 4 marks
In a pencil case, \(\frac{ 9 }{ 13 }\) 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 63 green pencils in the pencil case.
Work out how many pencils there are in the pencil case altogether.
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Either paper 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 \(3 : 11\).
(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?
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Either paper 3 marks
In a car park the ratio of hatchbacks to vans is \(5 : 2\).
The ratio of lorries to vans is \(3 : 8\).
Work out the ratio of hatchbacks to vans to lorries. Give your answer in its simplest form.
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Either paper 4 marks
\(b = \frac{ 5 }{ 2 }a\)
(a)Write down the ratio \(a : b\).
(b)\(b\) is 21 more than \(a\).
Calculate the value of \(a\).
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Either paper 4 marks
A builder mixes mortar from cement and sand.
The number of buckets of sand \((y)\) : the number of buckets of cement \((x)\) = \(7 : 5\)
(a)Use this information to draw a graph on the grid to show the relationship between the number of buckets of cement and the number of buckets of sand.
(b)Find the gradient of the line drawn in part (a).
(c)Explain what this gradient represents.
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Either paper 4 marks
A farm keeps sheep and goats.
\(S\) is the number of sheep and \(G\) is the number of goats.
The ratio \(S : G\) is \(6 : 7\).
(a)Write down a formula for \(G\) in terms of \(S\).
(b)Calculate the value of \(G\) when \(S = 66\).
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(a) \(\frac{ 3 }{ 4 }\)
(b) \(20\ \text{degrees}\) -
(a) \(\frac{7}{17}\)
(b) \(\frac{9}{17}\) - \(v = \frac{ u }{ 4 }\)
- \(n\) is \(\frac{ 5 }{ 8 }\) of \(m\)
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(a) \(9 : 4\)
(b) \(91\) -
(a) \(\frac{3}{11}\)
(b) \(\frac{11}{3}\)
(c) \(\frac{3}{14}\) - \(20 : 8 : 3\)
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(a) \(2 : 5\)
(b) \(14\) -
(a) A straight line through \((0, 0)\), \((5, 7)\) and \((10, 14)\)
(b) \(\frac{7}{5}\)
(c) The number of buckets of sand needed for 1 bucket of cement(a) -
(a) \(G = \frac{ 7 }{ 6 }S\)
(b) \(77\)
Takes a couple of seconds the first time a sheet is made.