Fractions, Decimals & Percentages (Edexcel IGCSE Maths): Exam Questions

Mr Mason asks $240$Year $11$ students what they want to do next year. $15 \%$ of the students want to go to college. $\frac{3}{4}$ of the students want to stay at school. The rest of the students do not know. Work out the number of students who do not know.

Sasha takes a music exam. The table shows the result that Sasha can get for different percentages in her music exam.

Sasha gets 62 out of 80 in her music exam.

What result does Sasha get? You must show your working.

Karen got 32 out of 80 in a maths test. She got 38% in an English test.

Karen wants to know if she got a higher percentage in maths or in English. Did Karen get a higher percentage in maths or in English?

Celina and Zoe both sing in a band.

One evening the band plays for $80$minutes. Celina sings for $65 \%$ of the $80$minutes.

Zoe sings for $\frac{5}{8}$ of the $80$minutes. Celina sings for more minutes than Zoe sings.

Work out for how many more minutes. You must show all your working.

Prove algebraically that the recurring decimal $0.2\overset{.}{5}$ has the value $\frac{23}{90}$

Show that the recurring decimal $0.1\overset{.}{7}\quad =\frac{8}{45}$

Use algebra to show that the recurring decimal $0.3\overset{.}{8}$ $=\frac{7}{18}$

Use algebra to show that the recurring decimal $0.2\overset{.}{6}$ $=\frac{4}{15}$

Use algebra to show that $4. \dot{5} \dot{7} = 4 \frac{19}{33}$

120 children go on an activity holiday. The ratio of the number of girls to the number of boys is $3:5$.

On Sunday, all the children either go sailing or go climbing. $\frac{16}{25}$ of the boys go climbing.

Twice as many girls go sailing as go climbing.

Work out how many children go sailing on Sunday.

The diagram shows three identical rectangles.

$\frac{5}{8}$ of rectangle $A$ is shaded.

80% of rectangle $C$ is shaded.

What fraction of rectangle $B$ is shaded?

Circle the largest number.

Juan wants to buy a ticket to fly from Madrid to Berlin.

He finds two different types of ticket he can buy in a sale, ticket A and ticket B

The sale price of ticket A is 140 euros. The sale price of ticket B is 136 euros.

Work out the difference between the normal price of ticket A and the normal price of ticket B

Mr Brown and his 2 children are going to London by train.

An adult ticket costs £24 A child ticket costs £12

Mr Brown has a Family Railcard.

Work out the total cost of the tickets when Mr Brown uses his Family Railcard.

Write these numbers in order of size. Start with the smallest number.

Prove that the recurring decimal $0.\overset{.}{3}\overset{.}{6}=\frac{4}{11}$

Show that the recurring decimal $0.\overset{.}{3}9\overset{.}{6}$ $=\frac{44}{111}$

Use algebra to show that the recurring decimal $0.\overset{.}{4}1\overset{.}{7}=\frac{139}{333}$

The people working for a company work in Team $A$ or in Team $B$.

number of people in Team $A$ : number of people in Team $B$ = 3 : 4

$\frac{4}{5}$ of Team $A$ work full time. 24% of Team $B$ work full time.

Work out what fraction of the people working for the company work full time. Give your fraction in its simplest form.

Alex makes $80$ cakes to sell. He makes chocolate cakes, lemon cakes and fruit cakes where

Alex sells

all of the chocolate cakes

$\frac{3}{4}$ of the lemon cakes

$\frac{7}{8}$ of the fruit cakes

The profit he makes on each cake he sells is shown in the table.

Work out the total profit that Alex makes from the cakes he sells.

£.............................................

Use algebra to show that the recurring decimal $0.2 \dot{5} \dot{4}$ = $\frac{14}{55}$

Josh buys and sells books for a living.

He buys 120 books for £4 each.

He sells $\frac{1}{2}$ of the books for £5 each.

He sells 40% of the books for £7 each. He sells the rest of the books for £8 each.

Calculate Josh’s percentage profit.

Ahmed, Behnaz and Carmen each have some money. Ahmed has 20% more money than Behnaz.

Carmen has $\frac{7}{8}$ of the amount of money that Behnaz has.

Carmen has 31.50 euros. Work out how much money Ahmed has.

.......................euros

James is taking three examination papers in Spanish. Here are his first two results.

Paper 1: $\frac{43}{80}$ Paper 2: $\frac{38}{65}$

Paper 3 is out of 95. The marks in each of the three papers are added together.

Find the lowest mark that James needs in Paper 3 to achieve 60% of the total marks.

Without using a calculator, show that $0. \dot{1} \dot{9}$ o can be written as $\frac{19}{99}$.

Explain how $\frac{19}{99} = 0. \dot{1} \dot{9}$ can be used to find $\frac{19}{990}$ as a decimal and write down its value.

$\frac{19}{990}$ = ...............

The diagram shows three identical rectangles.

$\frac{5}{8}$of rectangle A is shaded.

80% of rectangle C is shaded.

What fraction of rectangle B is shaded?

Ahmed, Behnaz and Carmen each have some money.

Ahmed has 20% more money than Behnaz.

Carmen has $\frac{7}{8}$ of the amount of money that Behnaz has.

Carmen has 31.50 euros.

Work out how much money Ahmed has.

Express the recurring decimal $0.2\overset{.}{8}\overset{.}{1}$ as a fraction in its simplest form.

$x=0.0\overset{.}{4}\overset{.}{5}$

Prove algebraically that $x$ can be written as $\frac{1}{22}$

Using algebra, prove that $0.1\overset{.}{3}\overset{.}{6}\times0.\overset{.}{2}$ is equal in value to $\frac{1}{33}$

$x=0.4\overset{.}{3}\overset{.}{6}$

Prove algebraically that $x$ can be written as $\frac{24}{55}$

Prove algebraically that the recurring decimal $0.3\overset{.}{1}\overset{.}{8}$ can be written as $\frac{7}{22}$

Show that the recurring decimal $0.0\overset{.}{1}\overset{.}{5}=\frac{1}{66}$

Use algebra to show that the recurring decimal $0.28 \dot{1} \dot{3} = \frac{557}{1980}$

Use algebra to show that $0.7\overset{.}{1}\overset{.}{6}=\frac{709}{990}$

$0.4 \dot{x}$ is a recurring decimal.

$x$ is a whole number such that $1 \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 9$

Find, in terms of $x$, the recurring decimal $0.4 \dot{x}$ as a fraction. Give your fraction in its simplest form. Show clear algebraic working.

Use algebra to show that $0.3 \dot{2} \dot{4} = \frac{107}{330}$

At a country park there is a house, a museum and a garden.

The table shows the prices per person to visit the park.

One day, 480 people visit the park.

67 visit the garden only. 40% visit the house and the museum. $\frac{3}{8}$ visit the house only. The rest visit the museum only.

In total, how much do the 480 people pay to visit the park? You may use the Venn diagram to help you.

Prove algebraically that $2.7 \dot{5}$ converts to the fraction $\frac{124}{45}$

Write $0.4 \dot{1} \dot{6}$ as a fraction in its simplest form. You must show full working in support of your answer.

Use algebra to show that $0.3 \dot{2} \dot{4} = \frac{107}{330}$

Use algebra to show that $0.3 \dot{7} \dot{2} = \frac{41}{110}$