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11+ · GL ASSESSMENT

EP.M30 Fractions, Decimals and Percentages Depth

GL ASSESSMENT EP.M30 · Calculators not allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Fractions, Decimals and Percentages Depth

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A deeper 11+ fractions, decimals and percentages paper for scholarship-level preparation, complementing EP.M3 (Fractions), EP.M4 (Decimals), EP.M5 (Percentages) and EP.M24 (Fractions, Decimals and Percentages Mixed Drill). It covers equivalence, ordering across all three forms, all four operations with fractions (including mixed numbers), conversions between forms, finding fractions and percentages of amounts, and worded and multi-step problems. Questions are ramped from straightforward warm-up items to demanding multi-step and reverse-reasoning problems designed to stretch the strongest candidates.

Which fraction is equivalent to 3/4?

A) 9/16
B) 4/3
C) 6/8
D) 3/8
E) 5/6

(Total for Question 1 is 1 mark)

Write 0.35 as a fraction in its simplest form.

A) 35/100
B) 7/20
C) 7/10
D) 3/5
E) 7/2

(Total for Question 2 is 1 mark)

Write 5/8 as a decimal.

A) 0.58
B) 0.85
C) 0.5625
D) 1.6
E) 0.625

(Total for Question 3 is 1 mark)

Convert 8% to a decimal.

A) 0.8
B) 8.0
C) 0.008
D) 0.08
E) 80

(Total for Question 4 is 1 mark)

Order these four values from smallest to largest: 7/10, 68%, 0.72, 71%

(Total for Question 5 is 2 marks)

Which of these is NOT equal to 1/4?

A) 2/8
B) 3/10
C) 25%
D) 5/20
E) 0.25

(Total for Question 6 is 1 mark)

Calculate 2/5 + 1/3, giving your answer as a fraction in its simplest form.

(Total for Question 7 is 2 marks)

Calculate 3/4 - 5/12, giving your answer as a fraction in its simplest form.

(Total for Question 8 is 2 marks)

Calculate 3/4 x 2/9, giving your answer in its simplest form.

A) 5/13
B) 2/3
C) 1/6
D) 1/12
E) 2/9

(Total for Question 9 is 1 mark)

Calculate 5/6 divided by 2/3, giving your answer as a mixed number in its simplest form.

(Total for Question 10 is 2 marks)

Calculate 1 1/2 + 2 2/3, giving your answer as a mixed number in its simplest form.

(Total for Question 11 is 3 marks)

Calculate 3 1/4 - 1 5/6, giving your answer as a mixed number in its simplest form.

(Total for Question 12 is 3 marks)

Find 3/8 of 64.

A) 21
B) 8
C) 40
D) 27
E) 24

(Total for Question 13 is 1 mark)

Find 5/9 of 108.

(Total for Question 14 is 2 marks)

What is 45% of 160?

A) 45
B) 115
C) 72
D) 64
E) 80

(Total for Question 15 is 1 mark)

A jacket costs £85. In a sale, the price is reduced by 20%. Work out the sale price.

(Total for Question 16 is 2 marks)

Priti invests £46. Her investment increases in value by 15%. Work out the new value of her investment.

(Total for Question 17 is 2 marks)

A number is increased by 25% to give 60. What was the original number?

A) 45
B) 48
C) 50
D) 75
E) 44

(Total for Question 18 is 1 mark)

Express 24 as a percentage of 40.

(Total for Question 19 is 2 marks)

Aisha has £120. She spends 3/8 of it on a jacket. She then spends 20% of what remains on a book. How much money does she have left?

(Total for Question 20 is 3 marks)

There are 32 pupils in a class. 3/4 of the pupils walk to school. Of the pupils who do not walk, 5/8 travel by car and the rest travel by bus. How many pupils travel by bus?

(Total for Question 21 is 3 marks)

Which of these fractions is closest in value to 1/2?

A) 9/19
B) 5/9
C) 7/15
D) 4/11
E) 6/13

(Total for Question 22 is 1 mark)

Tom has £200 in a savings account. During January, his savings increase by 10%. During February, his savings then decrease by 10%.

(a)Work out how much money Tom has at the end of February.(3)

(b)Explain why the answer to part (a) is not £200.(1)

(Total for Question 23 is 4 marks)

Calculate 2 3/5 x 1 1/4, giving your answer as a mixed number in its simplest form.

(Total for Question 24 is 3 marks)

Priya scored 68 out of 80 in a maths test and 54 out of 60 in a science test. Write each score as a percentage, state which test Priya scored higher in, and find the difference between the two percentages.

(Total for Question 25 is 4 marks)

A water tank is 3/8 full. After 45 litres of water are added, the tank becomes 5/8 full. Work out the total capacity of the tank.

(Total for Question 26 is 3 marks)

Mark scheme · EP.M30 Fractions, Decimals and Percentages Depth

Question 1

B1 C (6/8) cao
Answer: C) 6/8

Question 2

B1 B (7/20) cao
Answer: B) 7/20

Question 3

B1 E (0.625) cao
Answer: E) 0.625

Question 4

B1 D (0.08) cao
Answer: D) 0.08

Question 5

M1 converts all four values to the same format, e.g. decimals 0.70, 0.68, 0.72, 0.71
A1 68%, 7/10, 71%, 0.72 cao
Answer: 68%, 7/10, 71%, 0.72

Question 6

B1 B (3/10) cao
Answer: B) 3/10

Question 7

M1 correct common denominator 15 with equivalent fractions 6/15 and 5/15
A1 11/15 cao
Answer: 11/15

Question 8

M1 correct common denominator 12, e.g. 9/12 - 5/12
A1 1/3 cao (simplified from 4/12)
Answer: 1/3

Question 9

B1 C (1/6) cao
Answer: C) 1/6

Question 10

M1 correctly inverts and multiplies, e.g. 5/6 x 3/2
A1 1 1/4 cao (oe 5/4)
Answer: 1 1/4

Question 11

M1 converts both to improper fractions: 3/2 and 8/3
M1 correct common denominator 6, e.g. 9/6 + 16/6
A1 4 1/6 cao
Answer: 4 1/6

Question 12

M1 converts both to improper fractions: 13/4 and 11/6
M1 correct common denominator 12, e.g. 39/12 - 22/12
A1 1 5/12 cao
Answer: 1 5/12

Question 13

B1 E (24) cao
Answer: E) 24

Question 14

M1 108 / 9 = 12
A1 60 cao
Answer: 60

Question 15

B1 C (72) cao
Answer: C) 72

Question 16

M1 finds 20% of £85 = £17, oe (e.g. uses 0.8 x 85)
A1 £68 cao
Answer: £68

Question 17

M1 finds 15% of £46 = £6.90, oe (e.g. uses 1.15 x 46)
A1 £52.90 cao
Answer: £52.90

Question 18

B1 B (48) cao
Answer: B) 48

Question 19

M1 24/40 converted to a fraction out of 100, or equivalent method
A1 60% cao
Answer: 60%

Question 20

M1 3/8 of £120 = £45, so £75 remains after the jacket
M1 20% of £75 = £15
A1 £60 cao
Answer: £60

Question 21

M1 3/4 of 32 = 24 walk, so 8 do not walk
M1 5/8 of 8 = 5 travel by car
A1 3 cao
Answer: 3 pupils

Question 22

B1 A (9/19) cao
Answer: A) 9/19

Question 23

(a) M1 finds the value after January: 200 x 1.1 = 220 (oe 200 + 20)
(a) M1 applies the 10% February decrease to 220, e.g. 220 x 0.9
(a) A1 £198 cao
(a) Answer: £198
(b) B1 correct explanation that the 10% decrease is taken from the larger amount, £220, removing £22, which is more than the £20 added by the 10% increase on £200, oe
(b) Answer: The 10% decrease in February is worked out on £220 (removing £22), which is more than the £20 added by the 10% increase in January, so the two changes do not cancel out.

Question 24

M1 converts both to improper fractions: 13/5 and 5/4
M1 multiplies correctly: 65/20
A1 3 1/4 cao
Answer: 3 1/4

Question 25

M1 maths: 68/80 = 85%
M1 science: 54/60 = 90%
A1 correctly identifies science as the higher percentage
A1 difference = 5 percentage points cao
Answer: Science is higher (90% compared with 85%); the difference is 5 percentage points.

Question 26

M1 recognises that 45 litres represents 5/8 - 3/8 = 1/4 of the tank's capacity
M1 sets up 1/4 x capacity = 45, oe (e.g. capacity = 45 / (1/4))
A1 180 litres cao
Answer: 180 litres

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