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11+ · GL ASSESSMENT

EP.M65 Fractions: Practice Set 4

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 65 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Fractions: Practice Set 4

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A fourth original 11+ fractions practice set, complementing EP.M3 (Fractions), EP.M3B (Fractions: Practice Set 2), EP.M30 and EP.M36 (Fractions, Decimals and Percentages Depth) and EP.M47 (Fractions: Practice Set 3). It covers equivalence, simplifying, ordering, converting between mixed numbers and improper fractions, all four operations with proper fractions and mixed numbers, finding fractions of an amount, and worded and multi-step reasoning problems. Questions are ramped from straightforward warm-up items to demanding multi-step problems designed to stretch the strongest candidates.

Simplify 27/36 fully.

A) 3/4
B) 9/12
C) 3/5
D) 4/3
E) 2/3

(Total for Question 1 is 1 mark)

Which of these fractions is NOT equivalent to 5/9?

A) 10/18
B) 15/27
C) 20/36
D) 24/36
E) 25/45

(Total for Question 2 is 1 mark)

Find the missing number: 4/7 = ?/35

A) 20
B) 24
C) 28
D) 16
E) 25

(Total for Question 3 is 1 mark)

Write 52/7 as a mixed number in its simplest form.

A) 7 3/7
B) 7 4/7
C) 6 3/7
D) 8 3/7
E) 7 5/7

(Total for Question 4 is 1 mark)

Write 9 4/11 as an improper fraction.

A) 103/11
B) 99/11
C) 104/11
D) 94/11
E) 103/9

(Total for Question 5 is 1 mark)

Write these fractions in order of size, smallest first: 3/4, 2/5, 7/10, 9/20

(Total for Question 6 is 2 marks)

Which of these is closest in value to 1/3?

A) 3/8
B) 5/16
C) 2/7
D) 4/11
E) 7/20

(Total for Question 7 is 1 mark)

Find 7/15 of 225.

A) 90
B) 100
C) 105
D) 120
E) 135

(Total for Question 8 is 2 marks)

Work out 7/9 + 5/12, giving your answer as a mixed number in its simplest form.

(Total for Question 9 is 2 marks)

Work out 5/6 - 7/15, giving your answer in its simplest form.

(Total for Question 10 is 2 marks)

Work out 3 2/5 + 2 5/6, giving your answer as a mixed number in its simplest form.

(Total for Question 11 is 2 marks)

Work out 6 1/4 - 2 5/9, giving your answer as a mixed number in its simplest form.

(Total for Question 12 is 2 marks)

Work out 5/8 x 4/15, giving your answer in its simplest form.

(Total for Question 13 is 2 marks)

Work out 2 1/3 x 1 5/7, giving your answer in its simplest form.

(Total for Question 14 is 2 marks)

Work out 5/6 / 3/10, giving your answer as a mixed number in its simplest form.

(Total for Question 15 is 2 marks)

Work out 3 3/4 / 1 1/2, giving your answer as a mixed number in its simplest form.

(Total for Question 16 is 2 marks)

Find 9/13 of 143.

A) 88
B) 91
C) 99
D) 108
E) 117

(Total for Question 17 is 2 marks)

Meera, a tailor in Derby, buys 96 metres of fabric. She uses 5/8 of the fabric to make curtains. How many metres of fabric does she use for the curtains?

(Total for Question 18 is 2 marks)

Kwame has £120. He spends 2/5 of it on trainers. He then spends 1/4 of what remains on a football shirt. How much money does Kwame have left?

(Total for Question 19 is 3 marks)

A warehouse in Swansea has 275 kg of flour. On Monday, 3/11 of the flour is used. Of the flour that remains, 2/5 is used on Tuesday. How many kilograms of flour are left after Tuesday?

(Total for Question 20 is 4 marks)

3/7 of a number is 108. Find 5/6 of the same number.

(Total for Question 21 is 4 marks)

Show that 5/6 - 1/3 + 1/4 = 3/4

(Total for Question 22 is 3 marks)

Calculate (7/10 - 2/5) / (5/6 + 1/4), giving your answer as a fraction in its simplest form.

(Total for Question 23 is 4 marks)

Calculate (5/8 + 1/6) x (3/4 - 1/3), giving your answer as a fraction in its simplest form.

(Total for Question 24 is 4 marks)

A sequence of fractions begins 2/3, 5/8, 8/13, 11/18, ... Write the next two terms, and give a rule for the nth term.

(Total for Question 25 is 3 marks)

At a carnival in Ipswich, 3/10 of the visitors arrive before 1pm. Of the visitors who arrive at 1pm or later, 2/7 arrive between 1pm and 4pm, and the rest arrive after 4pm. Given that 150 visitors arrive after 4pm, work out the total number of visitors at the carnival.

(Total for Question 26 is 5 marks)

Mark scheme · EP.M65 Fractions: Practice Set 4

Question 1

B1 A) 3/4 cao (HCF of 27 and 36 is 9)
Answer: A) 3/4

Question 2

B1 D) 24/36 cao (24/36 = 2/3, not 5/9)
Answer: D) 24/36

Question 3

B1 A) 20 cao
Answer: A) 20

Question 4

B1 A) 7 3/7 cao
Answer: 7 3/7

Question 5

B1 A) 103/11 cao
Answer: 103/11

Question 6

M1 all four fractions converted to a common denominator (e.g. twentieths: 15/20, 8/20, 14/20, 9/20)
A1 2/5, 9/20, 7/10, 3/4 cao, in this order
Answer: 2/5, 9/20, 7/10, 3/4

Question 7

B1 E) 7/20 cao
Answer: E) 7/20

Question 8

M1 225 / 15 (= 15) seen
A1 C) 105 cao
Answer: C) 105

Question 9

M1 both fractions converted to a common denominator, e.g. 28/36 + 15/36
A1 1 7/36 cao
Answer: 1 7/36

Question 10

M1 both fractions converted to a common denominator, e.g. 25/30 - 14/30
A1 11/30 cao
Answer: 11/30

Question 11

M1 both mixed numbers converted to a common denominator, e.g. 102/30 + 85/30
A1 6 7/30 cao
Answer: 6 7/30

Question 12

M1 both mixed numbers converted to a common denominator, e.g. 225/36 - 92/36
A1 3 25/36 cao
Answer: 3 25/36

Question 13

M1 5/8 x 4/15 = 20/120 seen (or equivalent unsimplified fraction)
A1 1/6 cao
Answer: 1/6

Question 14

M1 both mixed numbers converted to improper fractions and multiplied, e.g. 7/3 x 12/7 = 84/21
A1 4 cao
Answer: 4

Question 15

M1 5/6 x 10/3 seen (flip and multiply)
A1 2 7/9 cao
Answer: 2 7/9

Question 16

M1 both mixed numbers converted to improper fractions and the second flipped, e.g. 15/4 x 2/3
A1 2 1/2 cao
Answer: 2 1/2

Question 17

M1 143 / 13 (= 11) seen
A1 C) 99 cao
Answer: C) 99

Question 18

M1 96 / 8 (= 12) seen
A1 60 metres cao
Answer: 60 metres

Question 19

M1 amount spent on trainers found, 2/5 x 120 = 48, and £72 remaining
M1 1/4 x 72 (= 18) found, ft from the remaining amount
A1 £54 cao
Answer: £54

Question 20

M1 3/11 x 275 (= 75) seen
A1 200 kg remaining after Monday
M1 2/5 x 200 (= 80), ft from the remaining flour
A1 120 kg cao
Answer: 120 kg

Question 21

M1 108 / 3 x 7, or equivalent complete method to find the whole number
A1 252 identified as the number
M1 5/6 x 252, ft from the number found
A1 210 cao
Answer: 210

Question 22

M1 all three fractions converted to a common denominator, e.g. twelfths: 10/12 - 4/12 + 3/12
M1 correct combination shown, e.g. 10/12 - 4/12 + 3/12 = 9/12
A1 9/12 simplified to 3/4, completing the proof
Answer: shown: 5/6 - 1/3 + 1/4 = 3/4

Question 23

M1 7/10 - 2/5 (= 3/10) evaluated correctly
M1 5/6 + 1/4 (= 13/12) evaluated correctly
M1 3/10 x 12/13 seen (flip and multiply)
A1 18/65 cao
Answer: 18/65

Question 24

M1 5/8 + 1/6 (= 19/24) evaluated correctly
M1 3/4 - 1/3 (= 5/12) evaluated correctly
M1 19/24 x 5/12 seen
A1 95/288 cao
Answer: 95/288

Question 25

B1 14/23 cao
B1 17/28 cao
B1 correct rule stated, e.g. nth term = (3n-1)/(5n-2) oe
Answer: next terms: 14/23, 17/28; rule: nth term = (3n-1)/(5n-2)

Question 26

M1 fraction not arriving before 1pm found, e.g. 1 - 3/10 = 7/10
M1 fraction arriving 1pm to 4pm found in terms of the whole, e.g. 2/7 x 7/10 = 1/5
M1 fraction arriving after 4pm found, e.g. 7/10 - 1/5 = 1/2
M1 equation set up correctly, e.g. 1/2 x T = 150
A1 300 cao
Answer: 300 visitors

Fractions: Practice Set 4 - Worksheets, Questions and Revision