Fractions, Decimals and Percentages (Copy)
Practice Questions – 1.4 Fractions, Decimals and Percentages
Question 1
Write each of the following as a proper fraction in simplest form:
(a) 12/20
(b) 45/60
Question 2
Convert the following into improper fractions:
(a) 3 1/4
(b) 7 2/5
Question 3
Convert the following into mixed numbers:
(a) 29/6
(b) 50/9
Question 4
Express the following as decimals:
(a) 3/4
(b) 7/20
(c) 2/3 (recurring decimal notation required)
Question 5
Write each of the following decimals as fractions in simplest form:
(a) 0.25
(b) 0.125
(c) 0.875
Question 6
Convert the following percentages to fractions in simplest form:
(a) 20%
(b) 35%
(c) 62.5%
Question 7
Convert the following fractions into percentages:
(a) 3/8
(b) 7/16
(c) 5/20
Question 8
Express the following as percentages:
(a) 0.08
(b) 0.375
(c) 1.25
Question 9
Convert the following percentages to decimals:
(a) 45%
(b) 120%
(c) 0.5%
Question 10
Simplify:
(a) 48/64
(b) 84/126
(c) 150/210
Question 11
A shop advertises a 20% discount on a jacket costing Rs. 4,500.
(a) Find the discount.
(b) Find the sale price.
Question 12
A student scored 42 marks out of 60.
Express this score as:
(a) a fraction in simplest form
(b) a decimal
(c) a percentage.
Question 13
Convert the following recurring decimals into fractions:
(a) 0.‾7
(b) 0.‾23
(c) 0.‾123
Question 14
Write each of the following fractions as decimals, giving answers correct to 3 decimal places:
(a) 5/7
(b) 11/30
(c) 29/12
Question 15
The price of a laptop increases from Rs. 60,000 to Rs. 66,000.
(a) Find the percentage increase.
(b) If the price falls back to Rs. 60,000, find the percentage decrease.
Question 16
Write down:
(a) the reciprocal of 2/5
(b) the reciprocal of 1.25
(c) the reciprocal of 25%
Question 17
A recipe needs 0.75 litres of milk. Express this quantity as:
(a) a fraction in simplest form
(b) a percentage of 1 litre.
Question 18
A student invests Rs. 80,000 at 6% simple interest for 3 years.
(a) Find the interest.
(b) Find the total amount.
Question 19
An exam has 80 questions. A candidate answers 60% correctly.
(a) How many questions are correct?
(b) How many are incorrect?
Question 20
Convert the following into percentages:
(a) 7/50
(b) 13/40
(c) 19/25
Answer key and explanations — 1.4 Fractions, Decimals and Percentages
1.
(a) 12/20 = 3/5
(b) 45/60 = 3/4
Explanation: divide numerator and denominator by their highest common factor.
2.
(a) 3 1/4 = (3×4 + 1)/4 = 13/4
(b) 7 2/5 = (7×5 + 2)/5 = 37/5
Explanation: improper fractions are found by multiplying whole number with denominator, then adding numerator.
3.
(a) 29/6 = 4 5/6
(b) 50/9 = 5 5/9
Explanation: divide numerator by denominator to get whole number, remainder becomes fraction part.
4.
(a) 3/4 = 0.75
(b) 7/20 = 0.35
(c) 2/3 = 0.‾6 (recurring)
Explanation: carry out long division if needed.
5.
(a) 0.25 = 25/100 = 1/4
(b) 0.125 = 125/1000 = 1/8
(c) 0.875 = 875/1000 = 7/8
Explanation: write decimal over a power of 10, simplify.
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6.
(a) 20% = 20/100 = 1/5
(b) 35% = 35/100 = 7/20
(c) 62.5% = 62.5/100 = 625/1000 = 5/8
7.
(a) 3/8 = 0.375 = 37.5%
(b) 7/16 = 0.4375 = 43.75%
(c) 5/20 = 1/4 = 25%
8.
(a) 0.08 = 8%
(b) 0.375 = 37.5%
(c) 1.25 = 125%
9.
(a) 45% = 0.45
(b) 120% = 1.20
(c) 0.5% = 0.005
Explanation: divide by 100 to convert percentage to decimal.
10.
(a) 48/64 = 3/4
(b) 84/126 = 2/3
(c) 150/210 = 5/7
Explanation: divide by highest common factor.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
Original price = 4500
Discount = 20% of 4500 = 900
Sale price = 4500 − 900 = 3600
12.
Score = 42/60
(a) Simplest form = 7/10
(b) As decimal = 0.7
(c) As percentage = 70%
13.
(a) 0.‾7 = 7/9
(b) 0.‾23 = 23/99
(c) 0.‾123 = 123/999 = 41/333
Explanation: use method of 10x − x to eliminate recurring part.
14.
(a) 5/7 ≈ 0.714 (3 d.p.)
(b) 11/30 ≈ 0.367 (3 d.p.)
(c) 29/12 ≈ 2.417 (3 d.p.)
15.
Increase from 60000 to 66000 = 6000 increase
(a) % increase = (6000/60000)×100 = 10%
(b) Decrease back from 66000 to 60000 = 6000 decrease
% decrease = (6000/66000)×100 ≈ 9.1%
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
16.
(a) Reciprocal of 2/5 = 5/2
(b) Reciprocal of 1.25 = 1 ÷ 1.25 = 0.8 = 4/5
(c) Reciprocal of 25% = reciprocal of 25/100 = reciprocal of 1/4 = 4
17.
0.75 litres
(a) Fraction = 75/100 = 3/4
(b) Percentage of 1 litre = 75%
18.
Principal = 80 000, rate = 6%, time = 3 years
Interest = P × R × T / 100 = 80 000 × 6 × 3 /100 = 14 400
Total = 80 000 + 14 400 = 94 400
19.
Total = 80, Correct = 60% × 80 = 48
Incorrect = 80 − 48 = 32
20.
(a) 7/50 = 14%
(b) 13/40 = 32.5%
(c) 19/25 = 76%
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course