On a school trip, the ratio of adults to children on a coach is 4:9.
(a)Write the number of adults as a fraction of the number of children.(1)
(b)Write the number of children as a fraction of the total number of people on the coach.(1)
(Total for Question 1 is 2 marks)
2
The ratio of boys to girls in a class is 5:7. Write the number of boys as a fraction of the total number of pupils in the class.
(Total for Question 2 is 1 mark)
3
A ratio is 8:9. Write down the second quantity as a fraction of the first quantity, giving your fraction in its simplest form.
(Total for Question 3 is 1 mark)
4
The ratio of concrete to sand in a mixture is 3:11. Write the amount of sand as a fraction of the total amount of mixture.
(Total for Question 4 is 1 mark)
5
A ratio is 15:20.
(a)Simplify the ratio fully.(1)
(b)Write the first part of your simplified ratio as a fraction of the total.(1)
(Total for Question 5 is 2 marks)
6
Given that x:y = 2:9, write down the value of each of the following fractions.
(a)x/y(1)
(b)y/x(1)
(Total for Question 6 is 2 marks)
7
Given that a:b = 5:1, write a as a fraction of the total a + b.
(Total for Question 7 is 1 mark)
8
In a cafe, the ratio of hot drinks sold that were tea to those that were coffee is 7:5. Write down the fraction of these hot drinks sold that were coffee.
(Total for Question 8 is 1 mark)
9
Given that m:n = 4:7, write n in terms of m as a linear function in the form n = km.
(Total for Question 9 is 1 mark)
10
Given that p:q = 9:2, write p in terms of q as a linear function in the form p = kq.
(Total for Question 10 is 1 mark)
11
A fraction of 3/7 of the plants in a garden are type A and the rest are type B.
(a)Write down the fraction of the plants that are type B.(1)
(b)Write the ratio of type A plants to type B plants in its simplest form.(1)
(Total for Question 11 is 2 marks)
12
In a school, 5/12 of the students are boys. Write the ratio of boys to girls in its simplest form.
(Total for Question 12 is 2 marks)
13
Given that y = 3/5 x, write down the ratio x:y in its simplest form.
(Total for Question 13 is 1 mark)
14
Given that y = 8/3 x, write down the ratio x:y using whole numbers.
(Total for Question 14 is 1 mark)
15
A bag contains only red counters and blue counters. The ratio of red counters to blue counters is 3:5. There are 40 counters in the bag altogether.
(a)Write the number of red counters as a fraction of the total number of counters.(1)
(b)Work out the number of red counters in the bag.(2)
(Total for Question 15 is 3 marks)
16
The ratio of the length to the width of a rectangle is 5:2. The width of the rectangle is 8 cm.
(a)Write the length of the rectangle as a fraction of its width.(1)
(b)Work out the length of the rectangle.(2)
(Total for Question 16 is 3 marks)
17
Salma and Tom share some money in the ratio 3:4. Salma receives 27 pounds.
(a)Write Tom's share as a fraction of Salma's share.(1)
(b)Work out the total amount of money shared between Salma and Tom.(3)
(Total for Question 17 is 4 marks)
18
The ratio of two positive numbers x and y is 2:5. Given that x + y = 84, form and solve a linear equation to find the value of y.
(Total for Question 18 is 3 marks)
19
A printer uses ink such that the number of pages printed, P, and the volume of ink used, I ml, are in the ratio P:I = 40:3.
(a)Write I as a linear function of P, in the form I = kP.(1)
(b)Use your linear function to find the volume of ink used when 500 pages are printed.(2)
(Total for Question 19 is 3 marks)
20
In a survey of 150 people, the ratio of people who prefer tea to those who prefer coffee to those who prefer neither is 5:3:2.
(a)Write the number of people who prefer coffee as a fraction of the number of people who do not prefer tea.(2)
(b)Work out how many more people prefer tea than prefer neither.(3)
(Total for Question 20 is 5 marks)
21
The ratio of a to b is (x + 1):(2x - 1), where x > 1/2. Given that a is 2/5 of the total a + b, form and solve an equation to find the value of x.
(Total for Question 21 is 4 marks)
22
Given that q = 5/2 p, and that p and q are both positive integers less than 30, list all possible pairs of values (p, q) for which the ratio p:q simplifies to 2:5.
(Total for Question 22 is 3 marks)
Mark scheme · 5.1D Writing a Ratio as a Fraction or Linear Function: Fluency and Exam Drill
Question 1
(a) B1 4/9 oe
(a) Answer: 4/9
(b) B1 9/13 oe
(b) Answer: 9/13
Question 2
B1 5/12 oe
Answer: 5/12
Question 3
B1 9/8 cao
Answer: 9/8
Question 4
B1 11/14 oe
Answer: 11/14
Question 5
(a) B1 3:4 cao
(a) Answer: 3:4
(b) B1 3/7 oe ft from (a)
(b) Answer: 3/7
Question 6
(a) B1 2/9 oe
(a) Answer: 2/9
(b) B1 9/2 oe
(b) Answer: 9/2
Question 7
B1 5/6 oe
Answer: 5/6
Question 8
B1 5/12 oe
Answer: 5/12
Question 9
B1 n = 7/4 m oe (k = 7/4)
Answer: n = 7/4 m
Question 10
B1 p = 9/2 q oe (k = 9/2 or 4.5)
Answer: p = 9/2 q
Question 11
(a) B1 4/7 oe
(a) Answer: 4/7
(b) B1 3:4 cao ft from (a)
(b) Answer: 3:4
Question 12
B1 recognises girls = 1 - 5/12 = 7/12
B1 5:7 cao
Answer: 5:7
Question 13
B1 5:3 cao
Answer: 5:3
Question 14
B1 3:8 cao
Answer: 3:8
Question 15
(a) B1 3/8 oe
(a) Answer: 3/8
(b) M1 40 / 8 (= 5), ft their fraction from (a)
(b) A1 15 cao
(b) Answer: 15
Question 16
(a) B1 5/2 oe
(a) Answer: 5/2
(b) M1 5/2 x 8, ft their fraction from (a)
(b) A1 20 cm cao
(b) Answer: 20 cm
Question 17
(a) B1 4/3 oe
(a) Answer: 4/3
(b) M1 27 / 3 (= 9), the value of one part
(b) M1 9 x (3 + 4), ft their value of one part
(b) A1 63 pounds cao
(b) Answer: 63 pounds
Question 18
M1 x = 2k and y = 5k (or equivalent single-variable expressions)