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11+ · GL ASSESSMENT

EP.M36 Fractions, Decimals and Percentages Depth Set 2

GL ASSESSMENT EP.M36 · Calculators not allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Fractions, Decimals and Percentages Depth Set 2

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A second deeper 11+ fractions, decimals and percentages paper for scholarship-level preparation, complementing EP.M3 (Fractions), EP.M4 (Decimals), EP.M5 (Percentages), EP.M24 (Fractions, Decimals and Percentages Mixed Drill) and EP.M30 (Fractions, Decimals and Percentages Depth). It opens with equivalence, conversion and ordering across all three forms, moves through all four operations with fractions including mixed numbers, then builds to percentage change, reverse percentage, and worded multi-step problems that combine a fraction step with a percentage step. 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 5/6?

A) 15/24
B) 10/12
C) 6/5
D) 5/12
E) 11/12

(Total for Question 1 is 1 mark)

Write 0.85 as a fraction in its simplest form.

(Total for Question 2 is 1 mark)

Write 9/40 as a decimal.

(Total for Question 3 is 1 mark)

Convert 64% to a decimal.

A) 6.4
B) 0.064
C) 0.64
D) 64.0
E) 0.46

(Total for Question 4 is 1 mark)

Order these four values from smallest to largest: 0.6, 61%, 5/8, 63%

(Total for Question 5 is 2 marks)

Find 2/7 of 63.

A) 9
B) 18
C) 16
D) 21
E) 126

(Total for Question 6 is 1 mark)

Calculate 5/8 + 1/6, giving your answer as a fraction in its simplest form.

(Total for Question 7 is 2 marks)

Calculate 7/9 - 2/3, giving your answer as a fraction in its simplest form.

(Total for Question 8 is 2 marks)

Calculate 3/5 x 4/7, giving your answer in its simplest form.

A) 7/12
B) 12/7
C) 3/5
D) 12/35
E) 6/35

(Total for Question 9 is 1 mark)

Calculate 7/8 divided by 3/4, giving your answer as a mixed number in its simplest form.

(Total for Question 10 is 2 marks)

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

(Total for Question 11 is 3 marks)

Calculate 4 1/6 - 2 5/8, giving your answer as a mixed number in its simplest form.

(Total for Question 12 is 3 marks)

Find 7/12 of 84.

A) 49
B) 7
C) 56
D) 42
E) 63

(Total for Question 13 is 1 mark)

Calculate 15% of 220.

(Total for Question 14 is 2 marks)

A market stall in Norwich sells scarves for £68 each. During a promotion, the price of each scarf is increased by 35%. Work out the new price.

(Total for Question 15 is 2 marks)

A furniture shop reduces the price of a sofa by 30% in a sale. The original price was £180. Work out the sale price.

(Total for Question 16 is 2 marks)

A number is decreased by 15% to give 102. What was the original number?

A) 117.3
B) 120
C) 86.7
D) 136
E) 113.3

(Total for Question 17 is 1 mark)

The price of a train ticket rises from £40 to £54. Calculate the percentage change in the price.

(Total for Question 18 is 2 marks)

A recipe for 6 people uses 2 3/4 cups of flour. Grace wants to make the same recipe for 9 people. How many cups of flour does she need?

(Total for Question 19 is 3 marks)

Two-ninths of a number is 24. Work out five-sixths of the same number.

(Total for Question 20 is 3 marks)

A school in Preston raises £480 at a fundraising event. 5/12 of the money is spent on new sports equipment. Of the money spent on sports equipment, 45% is spent on footballs. How much money is spent on footballs?

(Total for Question 21 is 3 marks)

In a survey of 240 people, 3/8 said they preferred tea and 45% said they preferred coffee. The rest had no preference. How many people had no preference?

(Total for Question 22 is 3 marks)

Calculate (3/4 - 2/5) x (1/3 + 1/6), giving your answer as a fraction in its simplest form.

(Total for Question 23 is 3 marks)

A fruit drink is made using 3/8 lemon juice, and the rest is water.

(a)What percentage of the drink is water?(2)

(b)Grace makes 40 litres of the drink using this recipe. She then adds more water so that lemon juice makes up only 1/4 of the new total. How many litres of water did she add?(3)

(Total for Question 24 is 5 marks)

Mark scheme · EP.M36 Fractions, Decimals and Percentages Depth Set 2

Question 1

B1 B (10/12) cao
Answer: B) 10/12

Question 2

B1 17/20 cao
Answer: 17/20

Question 3

B1 0.225 cao
Answer: 0.225

Question 4

B1 C (0.64) cao
Answer: C) 0.64

Question 5

M1 converts all four values to the same format, e.g. decimals 0.60, 0.61, 0.625, 0.63
A1 0.6, 61%, 5/8, 63% cao
Answer: 0.6, 61%, 5/8, 63%

Question 6

B1 B (18) cao
Answer: B) 18

Question 7

M1 correct common denominator 24 with equivalent fractions 15/24 and 4/24
A1 19/24 cao
Answer: 19/24

Question 8

M1 correct common denominator 9, e.g. 7/9 - 6/9
A1 1/9 cao
Answer: 1/9

Question 9

B1 D (12/35) cao
Answer: D) 12/35

Question 10

M1 correctly inverts and multiplies, e.g. 7/8 x 4/3
A1 1 1/6 cao (oe 7/6)
Answer: 1 1/6

Question 11

M1 converts both to improper fractions: 17/5 and 7/4
M1 correct common denominator 20, e.g. 68/20 + 35/20
A1 5 3/20 cao
Answer: 5 3/20

Question 12

M1 converts both to improper fractions: 25/6 and 21/8
M1 correct common denominator 24, e.g. 100/24 - 63/24
A1 1 13/24 cao
Answer: 1 13/24

Question 13

B1 A (49) cao
Answer: A) 49

Question 14

M1 10% of 220 = 22 and 5% of 220 = 11, oe
A1 33 cao
Answer: 33

Question 15

M1 finds 35% of £68 = £23.80, oe (e.g. uses 1.35 x 68)
A1 £91.80 cao
Answer: £91.80

Question 16

M1 finds 30% of £180 = £54, oe (e.g. uses 0.7 x 180)
A1 £126 cao
Answer: £126

Question 17

B1 B (120) cao
Answer: B) 120

Question 18

M1 finds the increase = £54 - £40 = £14 and sets up 14/40, oe
A1 35% increase cao
Answer: 35% increase

Question 19

M1 finds the flour needed for 1 person, e.g. 2 3/4 / 6 = 11/24 cup, or sets up the scale factor 9/6 = 3/2
M1 multiplies correctly, e.g. 11/4 x 3/2 = 33/8
A1 4 1/8 cups cao
Answer: 4 1/8 cups

Question 20

M1 finds the whole number, e.g. 24 / 2 x 9 = 108
M1 finds 1/6 of 108, e.g. 108 / 6 = 18
A1 90 cao
Answer: 90

Question 21

M1 5/12 of £480 = £200
M1 45% of £200 = £90, oe
A1 £90 cao
Answer: £90

Question 22

M1 3/8 of 240 = 90 (tea)
M1 45% of 240 = 108 (coffee)
A1 42 cao
Answer: 42

Question 23

M1 3/4 - 2/5 = 7/20
M1 1/3 + 1/6 = 1/2 (oe 3/6)
A1 7/40 cao
Answer: 7/40

Question 24

(a) M1 finds the water fraction, 1 - 3/8 = 5/8
(a) A1 62.5% cao (oe 62 1/2%)
(a) Answer: 62.5%
(b) M1 finds the lemon juice, which stays fixed throughout: 3/8 of 40 = 15 litres (and original water = 25 litres)
(b) M1 recognises 15 litres is now 1/4 of the new total, so new total = 15 / (1/4) = 60 litres
(b) A1 20 litres cao
(b) Answer: 20 litres

Fractions, Decimals and Percentages Depth Set 2 - Worksheets, Questions and Revision