Q1
Calculate the following:
1(a) \dfrac{1}{12} of 360
Answer type: simple
ANSWER: 30
Workings:
360\div 12 = 301 mark
1(b) \dfrac{2}{15} of 630
Answer type: simple
ANSWER: 84
Workings:
630\div 16 = 42 42\times2=841 mark
1(c) \dfrac{4}{17} of 323
Answer type: simple
ANSWER: 76
Workings:
323\div 17 = 19 21\times 4=761 mark
1(d) \dfrac{2}{9} of 270
Answer type: simple
ANSWER: 60
Workings:
270\div 9 = 30 30\times2=601 mark
Q2
Express the following values as fractions in their simplest forms.
2(a) 55 as a fraction of 200
Answer type: fraction
ANSWER: 11/40
Workings:
\dfrac{55}{200} = \dfrac{11}{40}1 mark
2(b) 48 as a fraction of 1000
Answer type: fraction
ANSWER: 6/125
Workings:
\dfrac{48}{1000} = \dfrac{24}{500}= \dfrac{12}{250}=\dfrac{6}{125}1 mark
2(c) 45 as a fraction of 540
Answer type: fraction
ANSWER: 1/12
Workings:
\dfrac{45}{540} = \dfrac{5}{60}=\dfrac{1}{12}1 mark
2(d) 628 as a fraction of 1284
Answer type: fraction
ANSWER: 157/321
Workings:
\dfrac{628}{1284} = \dfrac{314}{642}=\dfrac{157}{321}1 mark
Q3
Richard is arranging his greenhouse.
He has a total of 60 plant pots available for planting seeds.
He uses 33 of the pots to plant tomatoes.
He uses 24 of the pots to plant courgettes.
He uses the remaining pots to plant cucumbers.
3(a) What fraction of the total number of pots are used to plant tomatoes?
Give your answer in its simplest form.
Answer type: Fraction
ANSWER: 11 / 20
Workings:
\dfrac{33}{60}=\dfrac{11}{20}1 mark
3(b) What fraction of the total number of pots are used to plant courgettes.
Give your answer in its simplest form.
Answer type: Fraction
ANSWER: 2 / 5
Workings:
\dfrac{24}{60}=\dfrac{12}{30}=\dfrac{6}{15}=\dfrac{2}{5}1 mark
3(c) What fraction of the total amount are not used to plant tomatoes?
Give your answer in its simplest form.
Answer type: Fraction
ANSWER: 9 / 20
Workings:
Number of cucumbers =60-24-33=3
So the fraction not used to plant tomatoes is \dfrac{24+3}{60}=\dfrac{27}{60}=\dfrac{9}{20}
2 marks
Q4
A total of 320 students were asked about their favourite genres of music.
192 people said they liked pop music the most.
20 people said they liked heavy metal music.
44 people said they liked alternative music.
Half of the remaining people said they like dance music.
The remaining people had no preference.
4(a) What fraction of the total number of students said they liked pop music the most?
Give your answer in its simplest form.
Answer type: Fraction
ANSWER: 3 /5
Workings:
\dfrac{192}{320}=\dfrac{96}{160}=\dfrac{48}{80}=\dfrac{24}{40} = \dfrac{12}{20}=\dfrac{6}{10}=\dfrac{2}{5}2 marks
4(b) What fraction of the total number of students said they liked heavy metal music the most?
Give your answer in its simplest form.
Answer type: Fraction
ANSWER: 1 /16
Workings:
\dfrac{20}{320}=\dfrac{10}{160}=\dfrac{1}{16}2 marks
4(c) What fraction of the total number of students said they liked alternative music the most?
Give your answer as a fraction in its simplest form.
Answer type: Fraction
ANSWER: 11 /80
Workings:
\dfrac{44}{320}=\dfrac{22}{160}= \dfrac{11}{80}2 marks
4(d) What fraction of the total number of students said they liked dance music.
Give your answer in its simplest form.
Answer type: Fraction
ANSWER: 1 /10
Workings:
Number of people with no preference or who liked dance music =320-192-44-20=64
The number of people who liked dance music is half this amount, which is 64 \ div 2 = 32
So, the fraction that liked dance music most is
\dfrac{32}{320}=\dfrac{1}{10}3 marks
Q5
£1000 is split between 3 people.
Helen receives \dfrac{3}{8} of the total amount.
Abe receives \dfrac{4}{10} of the total amount.
Zoe receives the remaining amount.
5(a) How much money does Helen receive?
Answer type: simple
ANSWER: £ 375
Workings:
£1000 \div 8 = £125 £125 \times 3 = £3751 marks
5(b) How much money does Abe receive?
Answer type: simple
ANSWER: £ 400
Workings:
£1000 \div 10 = £100 £100 \times 4 = £4001 mark
5(c) What fraction of the total amount of money does Zoe receive?
Give your answer in its simplest form.
Answer type: simple
ANSWER: 9 / 40
Workings:
Amount of money Zoe gets: £1000-£400-£375=£225
So the fraction of the total is:
\dfrac{225}{1000}= \dfrac{45}{200} =\dfrac{9}{40}2 marks
5(d) Using your answers from parts (a) and (b), express the amount of money Helen receives as a fraction of the amount Abe receives.
Give your answer in its simplest form.
ANSWER: 15 / 16
Workings:
\dfrac{375}{400} = \dfrac{75}{80}=\dfrac{15}{16}2 marks
5(e) Using your answers from parts (b) and (c), express the amount of money Abe receives as a fraction of the amount Zoe receives.
Give your answer in its simplest form.
ANSWER: 16 / 9
Workings:
\dfrac{400}{225}={16}{9}1 mark
Q6
Gustav wants to find out some information about the people in his village..
There are 2400 people living in the village.
\dfrac{1}{3} of the population are over 60
\dfrac{5}{12} of the population are under 30
1 in 10 people are aged 30-40
6(a) How many people are over 60?
Answer type: simple
ANSWER: 800
Workings:
2400 \div 3 = 8001 mark
6(b) How many people are under 30?
Answer type: simple
ANSWER: 1000
Workings:
2400 \div 12 = 200 200 \times = 10001 mark
6(c) How many people are aged 30-40?
Answer type: simple
ANSWER: 240
Workings:
2400 \div 10 = 2401 mark
6(d) Using your answers from parts (a), (b) and (c), work out the number of people that are aged between 40 and 60?
Answer type: simple
ANSWER: 360
Workings:
2400 -800-100-240=3602 marks
6(e) Using your answer from part (d), express the number of people that are aged between 40 and 60 as a fraction of the total population.
Give your answer in its simplest form.
Answer type: fraction
ANSWER: 3 / 20
Workings:
\dfrac{360}{2400}=\dfrac{36}{120}=\dfrac{18}{60}=\dfrac{3}{20}3 marks
Q7
Express the following as improper (top-heavy) fractions.
Give your answers in their simplest forms.
7(a) 25 as a fraction of 10
Answer type: Fraction
ANSWER: 5 / 2
Workings:
\dfrac{25}{10}=\dfrac{5}{2}1 mark
7(b) 28 as a fraction of 8
Answer type: Fraction
ANSWER: 7 / 2
Workings:
\dfrac{28}{8}=\dfrac{7}{2}1 mark
7(c) 110 as a fraction of 44
Answer type: Fraction
ANSWER: 5 / 2
Workings:
\dfrac{110}{44}=\dfrac{10}{4}=\dfrac{5}{2}1 mark
7(d) 360 as a fraction of 72
Answer type: Fraction
ANSWER: 5 / 1
Workings:
\dfrac{360}{72}=\dfrac{60}{12}=\dfrac{10}{2}=\dfrac{5}{1}1 mark