A pizza is cut into 8 equal slices. 5 of the slices have pepperoni on them (shaded).
(a)Write down the fraction of the pizza that has pepperoni on it.(1)
(b)Write down the fraction of the pizza that has no pepperoni on it.(1)
(Total for Question 1 is 2 marks)
2
A tin contains 24 biscuits: 10 are chocolate, 6 are ginger, 4 are shortbread and 4 are oat.
(a)Write down the fraction of biscuits in the tin that are chocolate.(1)
(b)Write your answer to part (a) in its simplest form.(1)
(c)Write down, in its simplest form, the fraction of biscuits that are shortbread.(2)
(Total for Question 2 is 4 marks)
3
Simplify each fraction fully.
(a)14/21(1)
(b)18/24(1)
(c)16/40(1)
(d)27/36(1)
(Total for Question 3 is 4 marks)
4
A number line starts at 0 and ends at 1. It is divided into 12 equal intervals. Point Q is the mark that is 8 intervals from 0.
(a)Write down the fraction, in twelfths, that Point Q represents.(1)
(b)Write your answer to part (a) in its simplest form.(1)
(Total for Question 4 is 2 marks)
5
Circle the correct equivalent fraction in each part.
(a)Which fraction is equivalent to 5/6?(1)
A) 10/18
B) 15/18
C) 8/12
D) 20/36
(b)Which fraction is equivalent to 3/8?(1)
A) 6/20
B) 9/16
C) 12/32
D) 15/32
(Total for Question 5 is 2 marks)
6
Complete the chain of equivalent fractions.
2/3 = ?/9 = 8/? = ?/36
(a)2/3 = ?/9(1)
(b)2/3 = 8/?(1)
(c)2/3 = ?/36(1)
(Total for Question 6 is 3 marks)
7
Write these fractions in order of size, starting with the smallest.
5/11 2/11 9/11 6/11
(Total for Question 7 is 2 marks)
8
Insert <, > or = between each pair of fractions.
(a)2/3 ___ 5/8(1)
(b)3/7 ___ 5/14(1)
(c)6/9 ___ 2/3(1)
(d)7/15 ___ 3/5(1)
(Total for Question 8 is 4 marks)
9
Ffion was asked to simplify 15/20 fully. Her working is shown below.
15/20 = (15 - 5)/(20 - 5) = 10/15 = 2/3
Ffion's final answer is 2/3.
(a)Explain the mistake in Ffion's working.(1)
(b)Work out the correct answer when 15/20 is simplified fully.(2)
(Total for Question 9 is 3 marks)
10
Four friends recorded how far they each swam during a training session.
Ben: 7/8 km Chloe: 3/5 km Dev: 9/10 km Freya: 11/20 km
Write the friends in order of the distance swum, starting with the shortest distance.
(Total for Question 10 is 3 marks)
11
A drama club has 36 members. 21 of them are in the acting group and the rest are in the backstage crew.
(a)Write down the fraction of drama club members who are in the backstage crew.(1)
(b)Write your answer to part (a) in its simplest form.(1)
(c)Write down the fraction of drama club members who are in the acting group, in its simplest form.(1)
(Total for Question 11 is 3 marks)
12
Simplify each fraction fully.
(a)42/56(1)
(b)45/81(1)
(c)32/72(1)
(d)54/90(1)
(Total for Question 12 is 4 marks)
13
A recipe uses 16 ounces of flour from a bag that contains 40 ounces of flour in total. Show that the fraction of the bag used is equivalent to 2/5.
(Total for Question 13 is 2 marks)
14
Noah says that 5/8 is smaller than 7/12. Decide whether Noah is correct. You must show working to support your decision.
(Total for Question 14 is 2 marks)
15
A car park has 84 spaces. On Saturday, 35 spaces are used by staff, 21 spaces are used by visitors and the rest are empty.
(a)Work out the number of empty spaces.(1)
(b)Write the fraction of spaces that were empty, in its simplest form.(2)
(Total for Question 15 is 3 marks)
16
Circle the correct list in each part.
(a)Which list shows 3/5, 1/2, 2/5, 3/4 in order from smallest to largest?(1)
A) 2/5, 1/2, 3/5, 3/4
B) 1/2, 2/5, 3/5, 3/4
C) 3/4, 3/5, 1/2, 2/5
D) 2/5, 3/5, 1/2, 3/4
(b)Which list shows 5/8, 3/4, 1/3, 7/12 in order from largest to smallest?(1)
A) 3/4, 5/8, 7/12, 1/3
B) 1/3, 7/12, 5/8, 3/4
C) 3/4, 7/12, 5/8, 1/3
D) 5/8, 3/4, 7/12, 1/3
(Total for Question 16 is 2 marks)
17
Convert between mixed numbers and improper fractions, and simplify where asked.
(a)Write 31/4 as a mixed number.(1)
(b)Write 6 2/5 as an improper fraction.(1)
(c)Write 38/8 as a mixed number, in its simplest form.(1)
(d)Write 3 5/6 as an improper fraction.(1)
(e)Simplify 108/144 fully.(2)
(Total for Question 17 is 6 marks)
18
Write these numbers in order of size, starting with the smallest.
9/4 11/6 13/8 7/3
(Total for Question 18 is 3 marks)
19
Three of these four fractions are equivalent to 3/5.
9/15 12/20 21/35 15/24
Identify the fraction that is NOT equivalent to 3/5, and justify your answer.
(Total for Question 19 is 3 marks)
20
Two rolls of ribbon are compared. Roll A is 5/6 m long. Roll B is 3/4 m long. Callum says that Roll A is more than 1/10 m longer than Roll B. Is Callum correct? You must show your working.
(Total for Question 20 is 3 marks)
Mark scheme · 1.5B Writing, Simplifying and Ordering Fractions (Part 2)
Question 1
(a) B1 5/8 oe
(a) Answer: 5/8
(b) B1 3/8 oe
(b) Answer: 3/8
Question 2
(a) B1 10/24 oe
(a) Answer: 10/24
(b) B1 5/12 ft cao
(b) Answer: 5/12
(c) M1 4/24 seen
(c) A1 1/6 cao
(c) Answer: 1/6
Question 3
(a) B1 2/3 cao
(a) Answer: 2/3
(b) B1 3/4 cao
(b) Answer: 3/4
(c) B1 2/5 cao
(c) Answer: 2/5
(d) B1 3/4 cao
(d) Answer: 3/4
Question 4
(a) B1 8/12 oe
(a) Answer: 8/12
(b) B1 2/3 ft cao
(b) Answer: 2/3
Question 5
(a) B1 B) 15/18
(a) Answer: B) 15/18
(b) B1 C) 12/32
(b) Answer: C) 12/32
Question 6
(a) B1 6 cao
(a) Answer: 6
(b) B1 12 cao
(b) Answer: 12
(c) B1 24 cao
(c) Answer: 24
Question 7
M1 recognising that with a common denominator the order follows the numerators
A1 2/11, 5/11, 6/11, 9/11 cao
Answer: 2/11, 5/11, 6/11, 9/11
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 she subtracted 5 from the numerator and denominator instead of dividing both by a common factor oe
(a) Answer: She subtracted 5 from the top and bottom instead of dividing by a common factor.
(b) M1 identifying that the HCF of 15 and 20 is 5
(b) A1 3/4 cao
(b) Answer: 3/4
Question 10
M1 converting to a common denominator of 40, at least two correct: 35/40, 24/40, 36/40, 22/40
M1 correctly ordering the converted fractions
A1 Freya, Chloe, Ben, Dev cao
Answer: Freya, Chloe, Ben, Dev
Question 11
(a) B1 15/36 oe
(a) Answer: 15/36
(b) B1 5/12 ft cao
(b) Answer: 5/12
(c) B1 7/12 cao
(c) Answer: 7/12
Question 12
(a) B1 3/4 cao
(a) Answer: 3/4
(b) B1 5/9 cao
(b) Answer: 5/9
(c) B1 4/9 cao
(c) Answer: 4/9
(d) B1 3/5 cao
(d) Answer: 3/5
Question 13
M1 dividing numerator and denominator of 16/40 by a common factor, e.g. by 8
A1 cso, fully correct working showing 16/40 = 2/5
Answer: 16/40 = 2/5 (shown)
Question 14
B1 correct working, e.g. converting to a common denominator: 5/8 = 15/24 and 7/12 = 14/24
B1 correct conclusion that Noah is not correct, since 15/24 > 14/24
Answer: Noah is not correct, since 5/8 = 15/24 and 7/12 = 14/24, and 15/24 > 14/24.
Question 15
(a) B1 28 cao
(a) Answer: 28
(b) M1 28/84 ft from part (a)
(b) A1 1/3 cao
(b) Answer: 1/3
Question 16
(a) B1 A) 2/5, 1/2, 3/5, 3/4
(a) Answer: A) 2/5, 1/2, 3/5, 3/4
(b) B1 A) 3/4, 5/8, 7/12, 1/3
(b) Answer: A) 3/4, 5/8, 7/12, 1/3
Question 17
(a) B1 7 3/4 cao
(a) Answer: 7 3/4
(b) B1 32/5 cao
(b) Answer: 32/5
(c) B1 4 3/4 cao
(c) Answer: 4 3/4
(d) B1 23/6 cao
(d) Answer: 23/6
(e) M1 identifying a common factor of 108 and 144, e.g. 4, 9, 12, 18 or 36
(e) A1 3/4 cao
(e) Answer: 3/4
Question 18
M1 converting to a common denominator of 24 or to decimals, at least three correct: 54/24, 44/24, 39/24, 56/24
M1 correctly ordering the converted values
A1 13/8, 11/6, 9/4, 7/3 cao (in original fraction form)
Answer: 13/8, 11/6, 9/4, 7/3
Question 19
M1 attempting to simplify or test the equivalence of at least two of the given fractions
A1 15/24 cao identified as the fraction that is not equivalent to 3/5
B1 correct justification, e.g. 15/24 simplifies to 5/8, which is not equal to 3/5
Answer: 15/24, since 15/24 = 5/8, not 3/5.
Question 20
M1 converting 5/6 and 3/4 to twelfths: 5/6 = 10/12, 3/4 = 9/12
M1 correct difference: 10/12 - 9/12 = 1/12
A1 cso, correct conclusion that Callum is not correct, since 1/12 = 5/60 and 1/10 = 6/60, so 1/12 is less than 1/10
Answer: Callum is not correct; the difference is 1/12 m, which is less than 1/10 m.