In a bag of counters, the ratio of red counters to blue counters is 3:5.
(a)Write the number of red counters as a fraction of the number of blue counters.(1)
(b)Write the number of red counters as a fraction of the total number of counters in the bag.(1)
(Total for Question 1 is 2 marks)
2
A ribbon is cut into two pieces so that the length of the first piece to the length of the second piece is in the ratio 2:7.
(a)Write the length of the first piece as a fraction of the length of the second piece.(1)
(b)What fraction of the whole ribbon is the second piece?(1)
(Total for Question 2 is 2 marks)
3
The ratio of the length of Path A to the length of Path B is 15:40.
(a)Simplify the ratio 15:40 fully.(1)
(b)Using your simplified ratio, write the length of Path A as a fraction of the length of Path B.(1)
(Total for Question 3 is 2 marks)
4
At a school, the ratio of teachers to students is 1:18.
(a)Write the number of teachers as a fraction of the number of students.(1)
(b)Write the number of teachers as a fraction of the total number of people (teachers plus students) at the school.(2)
(Total for Question 4 is 3 marks)
5
x and y are two quantities such that x:y = 3:8.
(a)Write y as a fraction of x.(1)
(b)Hence write y as a linear function of x, in the form y = ... x(2)
(Total for Question 5 is 3 marks)
6
Sam's savings, S, and Priya's savings, P, are in the ratio S:P = 5:12.
(a)Write P as a fraction of S.(1)
(b)Write P as a linear function of S.(2)
(Total for Question 6 is 3 marks)
7
a and b are two quantities such that a:b = 4:9.
(a)Write b as a fraction of a.(1)
(b)Hence write b in terms of a.(1)
(c)Given that a = 20, use your function from part (b) to work out the value of b.(2)
(Total for Question 7 is 4 marks)
8
Simplify the ratio 6x:15x fully (x is not zero), and hence write the first quantity as a fraction of the second quantity.
(Total for Question 8 is 2 marks)
9
A shade of grey paint is made by mixing white paint and black paint in the ratio 7:3.
(a)What fraction of the total mixture is black paint?(1)
(b)Write the amount of white paint, W litres, as a linear function of the amount of black paint, B litres.(2)
(Total for Question 9 is 3 marks)
10
On a particular day, the exchange rate between pounds sterling (P) and euros (E) means that the ratio P:E is 4:5 (4 pounds is worth the same as 5 euros).
(a)Write E as a fraction of P.(1)
(b)Write E as a linear function of P.(1)
(c)Use your function to calculate the value in euros of 68 pounds.(2)
(Total for Question 10 is 4 marks)
11
There are 30 students in a class. The ratio of students who walk to school to students who do not walk to school is 2:3.
(a)What fraction of the class walks to school?(1)
(b)Work out how many students walk to school.(2)
(Total for Question 11 is 3 marks)
12
In a jar of sweets, the fraction of sweets that are strawberry flavoured is 3/7.
(a)Write the ratio of strawberry sweets to non-strawberry sweets in its simplest form.(2)
(b)Write the number of non-strawberry sweets, N, as a linear function of the number of strawberry sweets, S.(2)
(Total for Question 12 is 4 marks)
13
Two investments, A and B, are in the ratio A:B = 3:7. Investment A is worth 210 pounds.
(a)Write investment B as a fraction of investment A.(1)
(b)Write B as a linear function of A.(1)
(c)Calculate the value of investment B.(2)
(Total for Question 13 is 4 marks)
14
In a fun run, the ratio of the number of adults to the number of children taking part is 9:4.
(a)What fraction of the participants are children?(1)
(b)There are 351 participants in total. Work out how many of the participants are adults.(3)
(Total for Question 14 is 4 marks)
15
y is directly proportional to x. When x = 6, y = 15.
(a)Write down the ratio x:y in its simplest form.(2)
(b)Write y as a linear function of x.(2)
(c)Use your function to find the value of y when x = 9.(1)
(Total for Question 15 is 5 marks)
16
A cuboid has length l, width w and height h. The ratio l:w:h is 2:3:5.
(a)Write the width as a fraction of the height.(1)
(b)Write the height, h, as a linear function of the length, l.(2)
(c)The length of the cuboid is 8 cm. Work out the height.(2)
(Total for Question 16 is 5 marks)
17
a and b are two quantities such that a:b = (x + 1):(2x), where x is a positive number.
(Total for Question 17 is 2 marks)
18
A baker uses flour and sugar in the ratio flour:sugar = 5:2 to make a batch of biscuits.
(a)Write the amount of sugar, S grams, as a linear function of the amount of flour, F grams.(2)
(b)The baker has 750 g of flour and wants to use all of it. Calculate how much sugar is needed.(2)
(c)The baker only has 180 g of sugar. Work out the maximum amount of flour that can be used while keeping the ratio 5:2.(2)
(Total for Question 18 is 6 marks)
19
Two quantities m and n are in the ratio m:n = 7:4, so that m = kn for some constant k.
(a)State the value of k.(1)
(b)Given also that m - n = 18, find the value of n.(3)
(Total for Question 19 is 4 marks)
20
p and q are two quantities in the ratio p:q = 2:5. It is also known that p + 2q = 96.
(a)Write q as a linear function of p.(1)
(b)Find the value of p.(3)
(Total for Question 20 is 4 marks)
Mark scheme · 5.1 Writing a Ratio as a Fraction or Linear Function
Question 1
(a) B1 3/5 oe
(a) Answer: 3/5
(b) B1 3/8 oe
(b) Answer: 3/8
Question 2
(a) B1 2/7 oe
(a) Answer: 2/7
(b) B1 7/9 oe
(b) Answer: 7/9
Question 3
(a) B1 3:8 cao
(a) Answer: 3:8
(b) B1 3/8 ft from (a)
(b) Answer: 3/8
Question 4
(a) B1 1/18 oe
(a) Answer: 1/18
(b) M1 recognises total parts = 1 + 18 = 19
(b) A1 1/19 oe
(b) Answer: 1/19
Question 5
(a) B1 8/3 oe
(a) Answer: 8/3
(b) M1 sets up y/x = 8/3 or equivalent
(b) A1 y = 8/3 x oe (accept y = 2.67x awrt or y = 2.6 recurring x)
(b) Answer: y = 8/3 x (= 2.6666...x)
Question 6
(a) B1 12/5 oe
(a) Answer: 12/5
(b) M1 sets up P/S = 12/5
(b) A1 P = 12/5 S oe (accept P = 2.4S)
(b) Answer: P = 2.4S
Question 7
(a) B1 9/4 oe
(a) Answer: 9/4
(b) B1 b = 9/4 a ft from (a)
(b) Answer: b = 9/4 a (= 2.25a)
(c) M1 substitutes a = 20 into b = 9/4 a
(c) A1 b = 45 cao
(c) Answer: b = 45
Question 8
M1 divides both parts by common factor 3x to get 2:5