Fractions can be written in different equivalent forms.
(a)Find the missing number: 3/4 = ?/20(1)
(b)Find the missing number: 5/6 = 20/?(1)
(c)Which fraction is larger, 3/5 or 7/10?(1)
A) 3/5
B) 7/10
C) They are equal
(Total for Question 2 is 3 marks)
3
Write these fractions in order of size, smallest first: 3/8, 1/2, 2/3, 5/6
(Total for Question 3 is 2 marks)
4
Convert between mixed numbers and improper fractions.
(a)Write 17/5 as a mixed number.(1)
(b)Write 4 3/7 as an improper fraction.(1)
(c)Write 29/6 as a mixed number in its simplest form.(1)
(Total for Question 4 is 3 marks)
5
Work out each answer, giving each fraction in its simplest form.
(a)2/9 + 5/9(1)
(b)7/8 - 3/8(1)
(c)1/3 + 1/4(2)
(d)5/6 - 2/9(2)
(Total for Question 5 is 6 marks)
6
Work out each answer, giving each as a mixed number in its simplest form.
(a)2 1/4 + 1 5/6(3)
(b)5 1/3 - 2 3/4(3)
(Total for Question 6 is 6 marks)
7
Work out each answer, giving each in its simplest form.
(a)2/3 x 3/5(2)
(b)4/7 x 14/16(2)
(c)1 1/2 x 2 2/3(3)
(Total for Question 7 is 7 marks)
8
Work out each answer, giving each in its simplest form.
(a)3/4 / 2/5(2)
(b)2 1/2 / 1 1/4(3)
(Total for Question 8 is 5 marks)
9
Work out each fraction of an amount.
(a)Find 3/8 of 48 kg.(2)
(b)Find 5/6 of 42 km.(2)
(Total for Question 9 is 4 marks)
10
A bakery in Leeds bakes 240 loaves one morning. By 10am, 3/8 of the loaves have been sold. Of the loaves that remain, 1/3 are sold by noon. How many loaves are left after noon?
(Total for Question 10 is 4 marks)
11
Fractions, decimals and percentages are linked.
(a)Write 3/8 as a decimal.(1)
(b)Write 0.35 as a fraction in its simplest form.(2)
(c)Write 7/20 as a percentage.(1)
(Total for Question 11 is 4 marks)
12
Priya, from Cardiff, makes a fruit punch using 2/5 orange juice. Layla makes her punch using 5/12 orange juice. Who has the higher proportion of orange juice in her punch? Show working to justify your answer.
(Total for Question 12 is 3 marks)
13
A sequence of fractions begins 1/2, 2/3, 3/4, 4/5, ...
(Total for Question 13 is 3 marks)
14
A patchwork quilt is made from 24 equal squares. 9 squares are coloured red, 8 squares are coloured white and the rest are coloured blue.
(a)What fraction of the quilt is blue? Give your answer in its simplest form.(2)
(b)What fraction of the quilt is red? Give your answer in its simplest form.(2)
(Total for Question 14 is 4 marks)
15
Which of the following fractions is NOT equivalent to 3/4?
A) 6/8
B) 9/12
C) 12/15
D) 15/20
(Total for Question 15 is 1 mark)
16
Put these in order of size, smallest first: 7/10, 68%, 0.72, 3/4
(Total for Question 16 is 3 marks)
17
On a school trip organised from a school in Bristol, 2/5 of the students travel by coach. Of the students who do not travel by coach, 1/4 walk and the rest cycle. Given that 18 students cycle, work out the total number of students who went on the trip.
(Total for Question 17 is 5 marks)
18
Show that 3/4 - 2/5 + 1/10 = 9/20
(Total for Question 18 is 3 marks)
19
3/5 of a number is 45. Find 2/7 of the same number.
(Total for Question 19 is 4 marks)
20
Calculate (2/3 + 1/6) / (5/9 - 1/3), giving your answer as a fraction in its simplest form.
(Total for Question 20 is 4 marks)
Mark scheme · EP.M3 Fractions
Question 1
(a) B1 2/3 cao
(a) Answer: 2/3
(b) B1 3/8 cao
(b) Answer: 3/8
(c) B1 2/3 cao
(c) Answer: 2/3
Question 2
(a) B1 15 cao
(a) Answer: 15
(b) B1 24 cao
(b) Answer: 24
(c) B1 7/10 cao (option B)
(c) Answer: B) 7/10
Question 3
M1 all four fractions converted to a common denominator (e.g. twenty-fourths: 9/24, 12/24, 16/24, 20/24)
A1 3/8, 1/2, 2/3, 5/6 cao, in this order
Answer: 3/8, 1/2, 2/3, 5/6
Question 4
(a) B1 3 2/5 cao
(a) Answer: 3 2/5
(b) B1 31/7 cao
(b) Answer: 31/7
(c) B1 4 5/6 cao
(c) Answer: 4 5/6
Question 5
(a) B1 7/9 cao
(a) Answer: 7/9
(b) B1 1/2 cao
(b) Answer: 1/2
(c) M1 common denominator of 12 used, e.g. 4/12 + 3/12
(c) A1 7/12 cao
(c) Answer: 7/12
(d) M1 common denominator of 18 used, e.g. 15/18 - 4/18
(d) A1 11/18 cao
(d) Answer: 11/18
Question 6
(a) M1 common denominator of 12 used, e.g. 2 3/12 + 1 10/12
(a) M1 whole numbers and twelfths combined correctly, e.g. 3 13/12
(a) A1 4 1/12 cao
(a) Answer: 4 1/12
(b) M1 common denominator of 12 used, e.g. 5 4/12 - 2 9/12
(b) M1 correct handling of borrowing, e.g. 4 16/12 - 2 9/12
(b) A1 2 7/12 cao
(b) Answer: 2 7/12
Question 7
(a) M1 6/15 seen, or equivalent complete method
(a) A1 2/5 cao
(a) Answer: 2/5
(b) M1 cancelling seen, e.g. 14/7 = 2 or 4/16 = 1/4
(b) A1 1/2 cao
(b) Answer: 1/2
(c) M1 both mixed numbers converted to improper fractions, e.g. 3/2 and 8/3
(c) M1 24/6 seen, or equivalent complete method
(c) A1 4 cao
(c) Answer: 4
Question 8
(a) M1 3/4 x 5/2 seen (flip and multiply)
(a) A1 15/8 oe 1 7/8 cao
(a) Answer: 15/8 (1 7/8)
(b) M1 both mixed numbers converted to improper fractions, e.g. 5/2 and 5/4
(b) M1 5/2 x 4/5 seen (flip and multiply)
(b) A1 2 cao
(b) Answer: 2
Question 9
(a) M1 48 / 8 (= 6) seen
(a) A1 18 (kg) cao
(a) Answer: 18 kg
(b) M1 42 / 6 (= 7) seen
(b) A1 35 (km) cao
(b) Answer: 35 km
Question 10
M1 3/8 x 240 (= 90) seen
A1 150 loaves remaining after 10am
M1 1/3 x 150 (= 50), ft from remaining loaves
A1 100 (loaves) cao
Answer: 100 loaves
Question 11
(a) B1 0.375 cao
(a) Answer: 0.375
(b) M1 35/100 seen
(b) A1 7/20 cao
(b) Answer: 7/20
(c) B1 35% cao
(c) Answer: 35%
Question 12
M1 common denominator of 60 used for both fractions
A1 2/5 = 24/60 and 5/12 = 25/60, both correct
B1 correct conclusion: Layla has the higher proportion of orange juice
Answer: Layla (25/60 > 24/60)
Question 13
B1 5/6 cao
B1 6/7 cao
B1 correct rule stated, e.g. nth term = n/(n+1) oe
Answer: next terms: 5/6, 6/7; rule: nth term = n/(n+1)
Question 14
(a) M1 24 - 9 - 8 (= 7) seen
(a) A1 7/24 cao (already in simplest form)
(a) Answer: 7/24
(b) M1 9/24 seen
(b) A1 3/8 cao
(b) Answer: 3/8
Question 15
B1 C cao (12/15 = 4/5, not 3/4)
Answer: C) 12/15
Question 16
M1 at least three values correctly converted to a common form (e.g. decimals: 0.70, 0.68, 0.72, 0.75)
A1 all four values correctly converted
A1 68%, 7/10, 0.72, 3/4 cao, in this order
Answer: 68%, 7/10, 0.72, 3/4
Question 17
M1 fraction not travelling by coach found, e.g. 1 - 2/5 = 3/5
M1 fraction walking found in terms of the whole, e.g. 1/4 x 3/5 = 3/20
M1 fraction cycling found, e.g. 3/5 - 3/20 = 9/20
M1 equation set up correctly, e.g. 9/20 x T = 18
A1 40 cao
Answer: 40 students
Question 18
M1 common denominator of 20 used for all three fractions, e.g. 15/20, 8/20, 2/20