Which of these is the fully simplified form of 16/24?
A) 8/12
B) 4/6
C) 3/2
D) 1/2
E) 2/3
(Total for Question 1 is 1 mark)
2
Find the missing number: 5/8 = ?/32
A) 4
B) 20
C) 27
D) 37
E) 40
(Total for Question 2 is 1 mark)
3
Which of these fractions is closest in value to 1/2?
A) 2/5
B) 3/8
C) 5/9
D) 5/12
E) 7/10
(Total for Question 3 is 1 mark)
4
Write these fractions in order of size, smallest first: 2/5, 1/2, 3/10
(Total for Question 4 is 2 marks)
5
Write 45/8 as a mixed number in its simplest form.
A) 5 1/8
B) 6 5/8
C) 5 5/8
D) 4 5/8
E) 5 4/8
(Total for Question 5 is 1 mark)
6
Write 6 2/9 as an improper fraction.
(Total for Question 6 is 1 mark)
7
Which of these fractions is NOT equivalent to 2/3?
A) 4/6
B) 6/9
C) 8/12
D) 10/16
E) 10/15
(Total for Question 7 is 1 mark)
8
Work out 3/8 + 1/6, giving your answer in its simplest form.
(Total for Question 8 is 2 marks)
9
Work out 11/12 - 5/8, giving your answer in its simplest form.
(Total for Question 9 is 2 marks)
10
Work out 3 1/5 + 2 5/6, giving your answer as a mixed number in its simplest form.
(Total for Question 10 is 3 marks)
11
Work out 7 1/4 - 3 5/6, giving your answer as a mixed number in its simplest form.
(Total for Question 11 is 3 marks)
12
Work out 3/5 x 5/9, giving your answer in its simplest form.
A) 1/3
B) 8/14
C) 15/45
D) 1/9
E) 2/3
(Total for Question 12 is 1 mark)
13
Work out 2 1/3 x 1 3/4, giving your answer as a mixed number in its simplest form.
(Total for Question 13 is 3 marks)
14
Work out 4/9 / 2/3, giving your answer in its simplest form.
A) 2/3
B) 8/27
C) 3/2
D) 12/18
E) 2/9
(Total for Question 14 is 1 mark)
15
Work out 3 3/5 / 1 1/5, giving your answer as a whole number.
(Total for Question 15 is 3 marks)
16
At a market stall in Coventry, a jacket costs £96. Find 5/8 of £96.
A) £12
B) £40
C) £60
D) £72
E) £84
(Total for Question 16 is 2 marks)
17
A swimming lesson lasts 156 minutes in total across a half-term block. Find 7/12 of 156 minutes.
(Total for Question 17 is 2 marks)
18
Write 5/8 as a decimal.
A) 0.58
B) 0.625
C) 1.6
D) 0.65
E) 0.85
(Total for Question 18 is 1 mark)
19
Write 0.44 as a fraction in its simplest form.
(Total for Question 19 is 2 marks)
20
Write 9/20 as a percentage.
A) 9%
B) 20%
C) 45%
D) 90%
E) 29%
(Total for Question 20 is 1 mark)
21
Put these in order of size, smallest first: 0.6, 58%, 5/8, 7/10
(Total for Question 21 is 3 marks)
22
A market stall in Newport sells 180 punnets of strawberries one Saturday. By midday, 2/5 of the punnets have been sold. Of the punnets that remain, 1/4 are sold during the afternoon. How many punnets are left unsold at the end of the day?
(Total for Question 22 is 4 marks)
23
2/7 of a number is 26. Find 3/4 of the same number.
(Total for Question 23 is 4 marks)
24
Calculate (3/4 - 1/6) / (5/8 + 1/4), giving your answer as a fraction in its simplest form.
(Total for Question 24 is 4 marks)
25
At a summer fete in Dundee, 3/8 of the visitors arrive before 11am. Of the visitors who arrive at 11am or later, 2/5 arrive between 11am and 1pm, and the rest arrive after 1pm. Given that 42 visitors arrive after 1pm, work out the total number of visitors at the fete.
(Total for Question 25 is 5 marks)
26
A sequence of fractions begins 1/3, 3/5, 5/7, 7/9, ... Write the next two terms, and give a rule for the nth term.
(Total for Question 26 is 3 marks)
Mark scheme · EP.M3B Fractions: Practice Set 2
Question 1
B1 E) 2/3 cao (HCF of 16 and 24 is 8)
Answer: E) 2/3
Question 2
B1 B) 20 cao
Answer: B) 20
Question 3
B1 C) 5/9 cao
Answer: C) 5/9
Question 4
M1 all three fractions converted to a common denominator (e.g. tenths: 4/10, 5/10, 3/10)
A1 3/10, 2/5, 1/2 cao, in this order
Answer: 3/10, 2/5, 1/2
Question 5
B1 C) 5 5/8 cao
Answer: 5 5/8
Question 6
B1 56/9 cao
Answer: 56/9
Question 7
B1 D) 10/16 cao (10/16 = 5/8, not 2/3)
Answer: D) 10/16
Question 8
M1 common denominator of 24 used, e.g. 9/24 + 4/24
A1 13/24 cao
Answer: 13/24
Question 9
M1 common denominator of 24 used, e.g. 22/24 - 15/24
A1 7/24 cao
Answer: 7/24
Question 10
M1 common denominator of 30 used, e.g. 3 6/30 + 2 25/30
M1 whole numbers and thirtieths combined correctly, e.g. 5 31/30
A1 6 1/30 cao
Answer: 6 1/30
Question 11
M1 common denominator of 12 used, e.g. 7 3/12 - 3 10/12
M1 correct handling of borrowing, e.g. 6 15/12 - 3 10/12
A1 3 5/12 cao
Answer: 3 5/12
Question 12
B1 A) 1/3 cao
Answer: 1/3
Question 13
M1 both mixed numbers converted to improper fractions, e.g. 7/3 and 7/4
M1 49/12 seen, or equivalent complete method
A1 4 1/12 cao
Answer: 4 1/12
Question 14
B1 A) 2/3 cao
Answer: 2/3
Question 15
M1 both mixed numbers converted to improper fractions, e.g. 18/5 and 6/5
M1 18/5 x 5/6 seen (flip and multiply)
A1 3 cao
Answer: 3
Question 16
M1 96 / 8 (= 12) seen
A1 C) £60 cao
Answer: £60
Question 17
M1 156 / 12 (= 13) seen
A1 91 (minutes) cao
Answer: 91 minutes
Question 18
B1 B) 0.625 cao
Answer: 0.625
Question 19
M1 44/100 seen
A1 11/25 cao
Answer: 11/25
Question 20
B1 C) 45% cao
Answer: 45%
Question 21
M1 at least three values correctly converted to a common form (e.g. decimals: 0.6, 0.58, 0.625, 0.7)
A1 all four values correctly converted
A1 58%, 0.6, 5/8, 7/10 cao, in this order
Answer: 58%, 0.6, 5/8, 7/10
Question 22
M1 2/5 x 180 (= 72) seen
A1 108 punnets remaining after midday
M1 1/4 x 108 (= 27), ft from remaining punnets
A1 81 (punnets) cao
Answer: 81 punnets
Question 23
M1 26 / 2 x 7, or equivalent complete method to find the whole number
A1 91 identified as the number
M1 3/4 x 91, ft from the number found
A1 273/4 oe 68 1/4 cao
Answer: 273/4 (68 1/4)
Question 24
M1 3/4 - 1/6 (= 7/12) evaluated correctly
M1 5/8 + 1/4 (= 7/8) evaluated correctly
M1 7/12 x 8/7 seen (flip and multiply)
A1 2/3 cao
Answer: 2/3
Question 25
M1 fraction not arriving before 11am found, e.g. 1 - 3/8 = 5/8
M1 fraction arriving 11am to 1pm found in terms of the whole, e.g. 2/5 x 5/8 = 1/4
M1 fraction arriving after 1pm found, e.g. 5/8 - 1/4 = 3/8
M1 equation set up correctly, e.g. 3/8 x T = 42
A1 112 cao
Answer: 112 visitors
Question 26
B1 9/11 cao
B1 11/13 cao
B1 correct rule stated, e.g. nth term = (2n-1)/(2n+1) oe
Answer: next terms: 9/11, 11/13; rule: nth term = (2n-1)/(2n+1)