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11+ · Number, Fractions and Decimals

EP.M84 Fractions and Decimals: Practice Set 5

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Fractions and Decimals: Practice Set 5

Revision Library

A fifth original 11+ practice set combining fractions and decimals, complementing EP.M3 (Fractions), EP.M3B (Fractions: Practice Set 2), EP.M4 and EP.M4B (Decimals), EP.M30 and EP.M36 (Fractions, Decimals and Percentages Depth), EP.M47 (Fractions: Practice Set 3), EP.M48 (Decimals: Practice Set 3) and EP.M65 (Fractions: Practice Set 4). It covers simplifying and ordering fractions, converting between fractions, decimals and percentages, all four operations with fractions and decimals, place value and rounding, fractions of an amount, and worded and multi-step reasoning problems that draw on both fractions and decimals together. Questions are ramped from straightforward warm-up items to demanding multi-step problems designed to stretch the strongest candidates.

Simplify 32/48 fully.

A) 8/12
B) 4/6
C) 2/3
D) 3/4
E) 4/3

(Total for Question 1 is 1 mark)

Which of these fractions is NOT equivalent to 4/11?

A) 8/22
B) 16/44
C) 24/60
D) 20/55
E) 28/77

(Total for Question 2 is 1 mark)

Find the missing number: 5/8 = ?/56

A) 30
B) 40
C) 35
D) 42
E) 28

(Total for Question 3 is 1 mark)

In the number 84.396, what is the value of the digit 9?

A) 9
B) 0.9
C) 0.09
D) 0.009
E) 90

(Total for Question 4 is 1 mark)

Write these numbers in order, starting with the largest: 0.502, 0.05, 0.525, 0.52

(Total for Question 5 is 1 mark)

Write 8 3/11 as an improper fraction.

A) 91/11
B) 88/11
C) 90/11
D) 35/11
E) 91/8

(Total for Question 6 is 1 mark)

Write 11/40 as a decimal.

(Total for Question 7 is 2 marks)

Write 0.28 as a fraction in its simplest form.

(Total for Question 8 is 2 marks)

Complete each conversion below.

(a)Write 0.6 as a percentage.(1)

(b)Write 15% as a decimal.(1)

(c)Write 3/8 as a decimal.(1)

(Total for Question 9 is 3 marks)

Work out 3/5 + 7/15, giving your answer as a mixed number in its simplest form.

(Total for Question 10 is 2 marks)

Work out 11/12 - 5/8, giving your answer in its simplest form.

(Total for Question 11 is 2 marks)

Owen buys a jigsaw puzzle for £6.75 and a board game for £9.40 at a toy shop in Norwich. He pays with a £20 note. Work out how much change he receives.

(Total for Question 12 is 2 marks)

Find 5/9 of 162.

A) 72
B) 90
C) 108
D) 54
E) 126

(Total for Question 13 is 2 marks)

Work out 3/10 x 5/6, giving your answer in its simplest form.

(Total for Question 14 is 2 marks)

Work out 7/8 / 2/3, giving your answer as a mixed number in its simplest form.

(Total for Question 15 is 2 marks)

Work out 1.5 x 3.4.

(Total for Question 16 is 2 marks)

Work out 15.68 / 8.

(Total for Question 17 is 2 marks)

The number 24.6857 is to be rounded.

(a)Round 24.6857 to the nearest whole number.(1)

(b)Round 24.6857 to 1 decimal place.(1)

(c)Round 24.6857 to 2 decimal places.(1)

(Total for Question 18 is 3 marks)

Put these in order of size, smallest first: 46%, 9/20, 0.435, 11/25

(Total for Question 19 is 3 marks)

Tariq has £150. He spends 3/10 of it on a helmet and lock for his bicycle. He then spends 2/5 of what remains on a bike light. How much money does Tariq have left?

(Total for Question 20 is 3 marks)

A charity shop in Truro sells 3 identical umbrellas for a total of £11.85. Priya buys one of these umbrellas and a raincoat costing £14.20. She pays with a £20 note. Work out how much change she receives.

(Total for Question 21 is 4 marks)

7/9 of a number is 168. Find 5/12 of the same number.

(Total for Question 22 is 4 marks)

Calculate (3/4 + 1/6) / (7/9 - 5/12), giving your answer as a fraction in its simplest form.

(Total for Question 23 is 4 marks)

At a food festival in Chester, 1/5 of the visitors arrive before 11am. Of the visitors who arrive at 11am or later, 3/8 arrive between 11am and 2pm, and the rest arrive after 2pm. Given that 175 visitors arrive after 2pm, work out the total number of visitors at the festival.

(Total for Question 24 is 5 marks)

Mark scheme · EP.M84 Fractions and Decimals: Practice Set 5

Question 1

B1 C) 2/3 cao (HCF of 32 and 48 is 16)
Answer: C) 2/3

Question 2

B1 C) 24/60 cao (24/60 = 2/5, not 4/11)
Answer: C) 24/60

Question 3

B1 C) 35 cao
Answer: C) 35

Question 4

B1 C) 0.09 cao
Answer: 0.09

Question 5

B1 0.525, 0.52, 0.502, 0.05 cao
Answer: 0.525, 0.52, 0.502, 0.05

Question 6

B1 A) 91/11 cao
Answer: 91/11

Question 7

M1 1/40 = 0.025 seen, or equivalent complete method
A1 0.275 cao
Answer: 0.275

Question 8

M1 28/100 seen
A1 7/25 oe cao
Answer: 7/25

Question 9

(a) B1 60% cao
(a) Answer: 60%
(b) B1 0.15 cao
(b) Answer: 0.15
(c) B1 0.375 cao
(c) Answer: 0.375

Question 10

M1 both fractions converted to a common denominator, e.g. 9/15 + 7/15
A1 1 1/15 cao
Answer: 1 1/15

Question 11

M1 both fractions converted to a common denominator, e.g. 22/24 - 15/24
A1 7/24 cao
Answer: 7/24

Question 12

M1 6.75 + 9.40 (= 16.15) seen, or equivalent complete method
A1 £3.85 cao
Answer: £3.85

Question 13

M1 162 / 9 (= 18) seen
A1 B) 90 cao
Answer: B) 90

Question 14

M1 3/10 x 5/6 = 15/60 seen (or equivalent unsimplified fraction)
A1 1/4 cao
Answer: 1/4

Question 15

M1 7/8 x 3/2 seen (flip and multiply)
A1 1 5/16 cao
Answer: 1 5/16

Question 16

M1 15 x 34 (= 510) seen, or equivalent complete method
A1 5.1 cao
Answer: 5.1

Question 17

M1 1568 / 8 (= 196) seen, or equivalent complete method
A1 1.96 cao
Answer: 1.96

Question 18

(a) B1 25 cao
(a) Answer: 25
(b) B1 24.7 cao
(b) Answer: 24.7
(c) B1 24.69 cao
(c) Answer: 24.69

Question 19

M1 at least three values correctly converted to a common form (e.g. decimals: 0.46, 0.45, 0.435, 0.44)
A1 all four values correctly converted
A1 0.435, 11/25, 9/20, 46% cao, in this order
Answer: 0.435, 11/25, 9/20, 46%

Question 20

M1 amount spent on the helmet and lock found, 3/10 x 150 = 45, and £105 remaining
M1 2/5 x 105 (= 42) found, ft from the remaining amount
A1 £63 cao
Answer: £63

Question 21

M1 11.85 / 3 (= 3.95) seen, or equivalent method to find the cost of one umbrella
M1 3.95 + 14.20 (= 18.15) seen
dM1 20.00 - 18.15, dependent on the previous marks
A1 £1.85 cao
Answer: £1.85

Question 22

M1 168 / 7 x 9, or equivalent complete method to find the whole number
A1 216 identified as the number
M1 5/12 x 216, ft from the number found
A1 90 cao
Answer: 90

Question 23

M1 3/4 + 1/6 (= 11/12) evaluated correctly
M1 7/9 - 5/12 (= 13/36) evaluated correctly
M1 11/12 x 36/13 seen (flip and multiply)
A1 33/13 oe 2 7/13 cao
Answer: 33/13 (2 7/13)

Question 24

M1 fraction not arriving before 11am found, e.g. 1 - 1/5 = 4/5
M1 fraction arriving 11am to 2pm found in terms of the whole, e.g. 3/8 x 4/5 = 3/10
M1 fraction arriving after 2pm found, e.g. 4/5 - 3/10 = 1/2
M1 equation set up correctly, e.g. 1/2 x T = 175
A1 350 cao
Answer: 350 visitors

Fractions and Decimals: Practice Set 5 - Worksheets, Questions and Revision