Fractions, Decimals and Percentages (GCSE Maths) - Worksheets, Questions and Revision

22 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

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2.5 Fractions, Decimals and Percentages

EDEXCEL 1MA1 · Calculator allowed · about 65 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Revision notes: Fractions, Decimals and Percentages

Fractions, decimals and percentages are three ways of writing the same value: a percentage is 'out of 100', a decimal uses place value, and a fraction is a numerator over a denominator. Converting fluently between the three forms is a core GCSE skill used throughout the course.

Fraction to decimal: divide the numerator by the denominator.
Decimal to percentage: multiply by 100 (move the decimal point two places right).
Percentage to decimal: divide by 100 (move the decimal point two places left).
Fraction to percentage: convert the fraction to a decimal first, then convert that decimal to a percentage.
Learn the common conversions by heart: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%, 1/3 = 0.333... = 33.3%.

Worked example. Convert 7/20 to a decimal and a percentage. Then write 0.35 as a fraction in its simplest form.

7/20 as a decimal: 7 divided by 20 = 0.35.
0.35 as a percentage: multiply by 100 = 35%.
0.35 as a fraction: 0.35 = 35/100.
Simplify 35/100: HCF(35,100) = 5, so 35/100 = 7/20.

Answer: 7/20 = 0.35 = 35%; 0.35 = 7/20 in simplest form.

Write these decimals in order of size, starting with the smallest.

0.6 0.06 0.66

(Total for Question 1 is 1 mark)

Which of these is equivalent to 3/4?

A) 0.75
B) 75
C) 0.34
D) 34%

(Total for Question 2 is 1 mark)

The grid below is made up of 10 identical squares. 4 of the squares are shaded grey.

Write down, as a fraction, what proportion of the grid is shaded.

(Total for Question 3 is 1 mark)

Simplify 6/9 fully.

(Total for Question 4 is 1 mark)

Write 0.6 as a fraction in its simplest form.

(Total for Question 5 is 1 mark)

Write 1/5 as a percentage.

(Total for Question 6 is 1 mark)

Write these fractions in order of size, starting with the smallest.

3/4 1/8 1/2 1/4

(Total for Question 7 is 2 marks)

Write 40% as a decimal.

(Total for Question 8 is 1 mark)

Jamal writes down the decimal 0.28.

(a)Write 0.28 as a percentage.(1)

(b)Write 0.28 as a fraction in its simplest form.(2)

(Total for Question 9 is 3 marks)

A sack of potatoes has a mass of 84 kg.

Work out 1/4 of 84 kg.

(Total for Question 10 is 2 marks)

A gym membership costs £60 per month. Members get a voucher for a 15% discount.

Work out 15% of £60.

(Total for Question 11 is 2 marks)

Work out 3/8 of 240.

(Total for Question 12 is 2 marks)

Freya eats 2/7 of a pizza. Her brother eats 3/7 of the same pizza.

Work out what fraction of the pizza they eat altogether.

(Total for Question 13 is 1 mark)

Aisha says that 3/5 is bigger than 55%.

Is Aisha correct? Show working to justify your answer.

(Total for Question 14 is 2 marks)

A jacket normally costs £45. In a sale, the price is reduced by 20%.

Work out the sale price of the jacket.

(Total for Question 15 is 3 marks)

Work out 2/5 x 20.

(Total for Question 16 is 2 marks)

Priya scored 34 marks out of 40 in a Science test.

Work out Priya's score as a percentage.

(Total for Question 17 is 3 marks)

Write these values in order of size, starting with the smallest.

0.7 3/4 68% 13/20

(Total for Question 18 is 3 marks)

Work out 1/3 + 1/4. Give your answer as a single fraction in its simplest form.

(Total for Question 19 is 3 marks)

Express 24 as a percentage of 80.

(Total for Question 20 is 2 marks)

A television costs £320. The price of the television increases by 8%.

Work out the new price of the television.

(Total for Question 21 is 3 marks)

The same pair of speakers costs £80 in two different shops.

Shop A reduces the price by 30%.
Shop B reduces the price by 1/4.

Work out which shop offers the cheaper price for the speakers, and by how much. You must show all your working.

(Total for Question 22 is 4 marks)

Mark scheme · 2.5 Fractions, Decimals and Percentages

Question 1

B1 0.06, 0.6, 0.66 in this order oe
Answer: 0.06, 0.6, 0.66

Question 2

B1 A cao
Answer: A (0.75)

Question 3

B1 4/10 oe (e.g. 2/5)
Answer: 4/10 (oe 2/5)

Question 4

B1 2/3 cao
Answer: 2/3

Question 5

B1 3/5 cao
Answer: 3/5

Question 6

B1 20% cao
Answer: 20%

Question 7

M1 evidence of converting to a common denominator, e.g. 6/8, 1/8, 4/8, 2/8
A1 1/8, 1/4, 1/2, 3/4 cao (correct order)
Answer: 1/8, 1/4, 1/2, 3/4

Question 8

B1 0.4 cao
Answer: 0.4

Question 9

(a) B1 28% cao
(a) Answer: 28%
(b) M1 28/100 oe seen
(b) A1 7/25 cao
(b) Answer: 7/25

Question 10

M1 84 divided by 4 (=21) oe
A1 21 kg cao
Answer: 21 kg

Question 11

M1 0.15 x 60 oe (e.g. 10% + 5% method: 6 + 3)
A1 £9 cao
Answer: £9

Question 12

M1 240 divided by 8 (=30) oe
A1 90 cao
Answer: 90

Question 13

B1 5/7 cao
Answer: 5/7

Question 14

M1 3/5 converted to 60% oe (or 55% converted to 11/20)
A1 correct conclusion that Aisha is correct, since 60% > 55% ft
Answer: Yes, Aisha is correct: 3/5 = 60%, and 60% is greater than 55%.

Question 15

M1 10% of 45 (=4.5) found, or equivalent method to find 20% of 45
M1 20% of 45 (=9) subtracted from 45, i.e. 45 - 9 oe
A1 £36 cao
Answer: £36

Question 16

M1 20 divided by 5 (=4) oe, or 2 x 20 (=40) seen
A1 8 cao
Answer: 8

Question 17

M1 34/40 written or 34 divided by 40 (=0.85) oe
M1 0.85 x 100 oe
A1 85% cao
Answer: 85%

Question 18

M1 at least 3 of the values correctly converted to a common form, e.g. decimals 0.7, 0.75, 0.68, 0.65
M1 all 4 values correctly ordered as decimals (0.65, 0.68, 0.7, 0.75)
A1 13/20, 68%, 0.7, 3/4 cao (correct order using original labels)
Answer: 13/20, 68%, 0.7, 3/4

Question 19

M1 common denominator of 12 identified oe
M1 4/12 + 3/12 oe seen
A1 7/12 cao (already in simplest form)
Answer: 7/12

Question 20

M1 24/80 written or 24 divided by 80 (=0.3) oe
A1 30% cao
Answer: 30%

Question 21

M1 8% of 320 (=25.6) found oe
M1 320 + 25.6 oe
A1 £345.60 cao
Answer: £345.60

Question 22

M1 30% of 80 (=24) found, leading to Shop A price of 56 oe
M1 1/4 of 80 (=20) found, leading to Shop B price of 60 oe
A1 both prices correct: £56 (Shop A) and £60 (Shop B)
C1 correct conclusion stated clearly: Shop A is cheaper, by £4 ft from their prices
Answer: Shop A is cheaper, by £4 (Shop A: £56, Shop B: £60).

Question 22

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Fractions, Decimals and Percentages (GCSE Maths) - Worksheets, Questions and Revision

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2.5 Fractions, Decimals and Percentages

Revision notes: Fractions, Decimals and Percentages

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