A rectangle is divided into 10 equal parts. 7 of the parts are shaded grey.
(a)Write down the fraction of the rectangle that is shaded.(1)
(b)Write down the fraction of the rectangle that is not shaded.(1)
(Total for Question 1 is 2 marks)
2
Tomasz has a bag of 12 counters. 5 of the counters are red, 4 are blue and 3 are green.
(a)Write down the fraction of the counters that are red.(1)
(b)Write down the fraction of the counters that are blue.(1)
(c)Simplify your answer to part (b) fully.(1)
(Total for Question 2 is 3 marks)
3
Simplify each fraction fully.
(a)6/8(1)
(b)10/15(1)
(c)12/18(1)
(d)20/45(1)
(Total for Question 3 is 4 marks)
4
Circle the correct equivalent fraction in each part.
(a)Which fraction is equivalent to 3/4?(1)
A) 6/9
B) 9/12
C) 8/10
D) 12/20
(b)Which fraction is equivalent to 2/5?(1)
A) 4/15
B) 6/20
C) 8/20
D) 10/20
(Total for Question 4 is 2 marks)
5
Find the missing number in each pair of equivalent fractions.
(a)3/4 = ?/20(1)
(b)5/6 = 15/?(1)
(c)2/9 = 8/?(1)
(d)?/7 = 12/21(1)
(Total for Question 5 is 4 marks)
6
Write these fractions in order of size, starting with the smallest.
5/9 2/9 7/9 4/9
(Total for Question 6 is 2 marks)
7
Write these fractions in order of size, starting with the smallest.
1/2 3/8 5/6
(Total for Question 7 is 3 marks)
8
Insert <, > or = between each pair of fractions.
(a)3/5 ___ 7/10(1)
(b)5/6 ___ 7/9(1)
(c)4/8 ___ 1/2(1)
(d)5/12 ___ 3/8(1)
(Total for Question 8 is 4 marks)
9
In Mrs Ahmed's class of 30 pupils, 18 are girls.
(a)Write down the fraction of pupils who are girls.(1)
(b)Write your answer to part (a) in its simplest form.(1)
(c)Write down the fraction of pupils who are boys, in its simplest form.(1)
(Total for Question 9 is 3 marks)
10
Simplify each fraction fully.
(a)36/48(1)
(b)28/70(1)
(c)32/40(1)
(d)63/81(1)
(Total for Question 10 is 4 marks)
11
A recipe book lists the amount of flour needed for four different cakes.
Cake A: 3/4 kg Cake B: 5/8 kg Cake C: 2/3 kg Cake D: 7/12 kg
Write the cakes in order of the amount of flour used, starting with the least amount.
(Total for Question 11 is 3 marks)
12
Aisha says that 1/3 is bigger than 3/10. Decide whether Aisha is correct. You must show working to support your decision.
(Total for Question 12 is 2 marks)
13
At a coffee morning attended by 40 people, 25 people chose tea and the rest chose coffee.
(a)Write down the fraction of people who chose coffee.(1)
(b)Write your answer to part (a) in its simplest form.(1)
(Total for Question 13 is 2 marks)
14
Circle the correct list in each part.
(a)Which list shows 1/4, 1/3, 1/2, 2/3 in order from smallest to largest?(1)
A) 1/4, 1/2, 1/3, 2/3
B) 1/4, 1/3, 1/2, 2/3
C) 2/3, 1/2, 1/3, 1/4
D) 1/3, 1/4, 1/2, 2/3
(b)Which list shows 5/6, 2/3, 3/4, 1/2 in order from largest to smallest?(1)
A) 5/6, 3/4, 2/3, 1/2
B) 1/2, 2/3, 3/4, 5/6
C) 5/6, 2/3, 3/4, 1/2
D) 3/4, 5/6, 2/3, 1/2
(Total for Question 14 is 2 marks)
15
Grace runs a bake sale and sells 60 cakes in total. 24 of the cakes are chocolate, 15 are lemon and the rest are vanilla.
(a)Work out the number of vanilla cakes.(1)
(b)Write the fraction of cakes that were vanilla, in its simplest form.(2)
(Total for Question 15 is 3 marks)
16
Convert between mixed numbers and improper fractions, and simplify where asked.
(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)
(d)Write 5 2/9 as an improper fraction.(1)
(e)Simplify 84/126 fully.(2)
(Total for Question 16 is 6 marks)
17
Write these numbers in order of size, starting with the smallest.
7/4 8/5 5/3 11/6
(Total for Question 17 is 3 marks)
18
Show that 15/18 and 5/6 are equivalent fractions.
(Total for Question 18 is 2 marks)
19
Ribbon A is 3/5 m long. Ribbon B is 7/10 m long. Priya says that Ribbon B is more than 1/10 m longer than Ribbon A. Is Priya correct? You must show your working.
(Total for Question 19 is 3 marks)
Mark scheme · 1.5 Writing, Simplifying and Ordering Fractions
Question 1
(a) B1 7/10 oe
(a) Answer: 7/10
(b) B1 3/10 oe
(b) Answer: 3/10
Question 2
(a) B1 5/12 oe
(a) Answer: 5/12
(b) B1 4/12 oe
(b) Answer: 4/12
(c) B1 1/3 cao
(c) Answer: 1/3
Question 3
(a) B1 3/4 cao
(a) Answer: 3/4
(b) B1 2/3 cao
(b) Answer: 2/3
(c) B1 2/3 cao
(c) Answer: 2/3
(d) B1 4/9 cao
(d) Answer: 4/9
Question 4
(a) B1 B) 9/12
(a) Answer: B) 9/12
(b) B1 C) 8/20
(b) Answer: C) 8/20
Question 5
(a) B1 15 cao
(a) Answer: 15
(b) B1 18 cao
(b) Answer: 18
(c) B1 36 cao
(c) Answer: 36
(d) B1 4 cao
(d) Answer: 4
Question 6
M1 recognising that with a common denominator the order follows the numerators
A1 2/9, 4/9, 5/9, 7/9 cao
Answer: 2/9, 4/9, 5/9, 7/9
Question 7
M1 converting to a common denominator of 24, at least two correct: 12/24, 9/24, 20/24
M1 correctly ordering the converted fractions
A1 3/8, 1/2, 5/6 cao (in original fraction form)
Answer: 3/8, 1/2, 5/6
Question 8
(a) B1 < cao
(a) Answer: <
(b) B1 > cao
(b) Answer: >
(c) B1 = cao
(c) Answer: =
(d) B1 > cao
(d) Answer: >
Question 9
(a) B1 18/30 oe
(a) Answer: 18/30
(b) B1 3/5 cao
(b) Answer: 3/5
(c) B1 2/5 cao
(c) Answer: 2/5
Question 10
(a) B1 3/4 cao
(a) Answer: 3/4
(b) B1 2/5 cao
(b) Answer: 2/5
(c) B1 4/5 cao
(c) Answer: 4/5
(d) B1 7/9 cao
(d) Answer: 7/9
Question 11
M1 converting to a common denominator of 24, at least three correct: 18/24, 15/24, 16/24, 14/24
M1 correctly ordering the converted values
A1 D, B, C, A cao
Answer: D, B, C, A
Question 12
B1 correct working, e.g. converting to a common denominator: 1/3 = 10/30 and 3/10 = 9/30
B1 correct conclusion that Aisha is correct, since 10/30 > 9/30
Answer: Aisha is correct, since 1/3 = 10/30 and 3/10 = 9/30, and 10/30 > 9/30.
Question 13
(a) B1 15/40 oe
(a) Answer: 15/40
(b) B1 3/8 ft cao
(b) Answer: 3/8
Question 14
(a) B1 B) 1/4, 1/3, 1/2, 2/3
(a) Answer: B) 1/4, 1/3, 1/2, 2/3
(b) B1 A) 5/6, 3/4, 2/3, 1/2
(b) Answer: A) 5/6, 3/4, 2/3, 1/2
Question 15
(a) B1 21 cao
(a) Answer: 21
(b) M1 21/60 ft from part (a)
(b) A1 7/20 cao
(b) Answer: 7/20
Question 16
(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
(d) B1 47/9 cao
(d) Answer: 47/9
(e) M1 identifying a common factor of 84 and 126, e.g. 6, 7, 14, 21 or 42
(e) A1 2/3 cao
(e) Answer: 2/3
Question 17
M1 converting to a common denominator of 60 or to decimals, at least three correct: 105/60, 96/60, 100/60, 110/60
M1 correctly ordering the converted values
A1 8/5, 5/3, 7/4, 11/6 cao (in original fraction form)
Answer: 8/5, 5/3, 7/4, 11/6
Question 18
M1 dividing numerator and denominator of 15/18 by a common factor, e.g. by 3
A1 cso, fully correct working showing 15/18 = 5/6
Answer: 15/18 = 5/6 (shown)
Question 19
M1 converting 3/5 to tenths: 3/5 = 6/10
M1 correct difference: 7/10 - 6/10 = 1/10
A1 cso, correct conclusion that Priya is not correct, since the difference is exactly 1/10 m, not more than 1/10 m
Answer: Priya is not correct; the difference is exactly 1/10 m.