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

Show that $a \% of b = b \% of a$

Rosie says,

“160% of 40 = 140% of 60 because $a \%$ of $b$ = $b \%$ of $a$”

Is she correct? Tick a box.

square Yes square No

Give a reason for your answer.

Railtickets and Cheaptrains are two websites selling train tickets.

Each of the websites adds a credit card charge and a booking fee to the ticket price.

Nadia wants to buy a train ticket. The ticket price is £60 on each website. Nadia will pay by credit card.

Will it be cheaper for Nadia to buy the train ticket from Railtickets or from Cheaptrains?

Ria is going to buy a caravan.

The total cost of the caravan is £7000 plus VAT at 20%.

Ria pays a deposit of £3000 She pays the rest of the total cost in 6 equal monthly payments.

Work out the amount of each monthly payment.

Amrit’s income is 32% more than Bethan’s income. Amrit and Bethan’s combined income is £54868.

Calculate Amrit’s income.

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

A company sells boxes to factories. Fred buys boxes. The boxes are sold in packs of 1000. Each pack costs £193.86

Fred orders 3 packs of boxes. He gets a discount on his total order.

The table shows the discount he will get.

Work out the total cost of the order after the discount. You must show your working.

Tom is a ski jumper.

The maximum length of skis he can use is 145% of his height. Tom's height is 1.80 m.

Work out the maximum length of skis Tom can use.

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

Greg sells car insurance and home insurance.

The table shows the cost of these insurances.

Each month Greg earns

£530 basic pay

5% of the cost of all the car insurance he sells

and 10% of the cost of all the home insurance he sells

In May Greg sold

6 car insurances

and 4 home insurances

Work out the total amount of money Greg earned in May.

George wants to watch all 23 games that a football team will play at home next season.

He can buy

a season ticket costing £425 or 23 separate tickets costing £24 each ticket.

What percentage of the total cost of 23 separate tickets does George save by buying a season ticket?

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

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

The table gives some information about student attendance at a school on Friday.

The school has a target of 94% of students being present each day.

Did the school meet its target on Friday?

Emily buys a pack of 12 bottles of water. The pack costs £5.64

Emily sells all 12 bottles for 50p each.

Work out Emily's percentage profit. Give your answer correct to 1 decimal place.

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

Bill buys and sells laptops.

Last month Bill bought 50 laptops. He paid £400 for each laptop.

He sold

40 of these laptops at a profit of 30% on each laptop 10 of these laptops at a profit of 15% on each laptop

Bill's target last month was to sell all 50 laptops for a total of at least £25 000 Did Bill reach this target?

Gladys buys a table for $465 to sell in her shop.

She sells the table for $520

Work out the percentage profit that Gladys makes from the sale of the table.

Give your answer correct to 3 significant figures.

......................................................%

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

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

Renee buys 5 kg of sweets to sell. She pays £10 for the sweets.

Renee puts all the sweets into bags. She puts 250 g of sweets into each bag. She sells each bag of sweets for 65p.

Renee sells all the bags of sweets.

Work out her percentage profit.

In 2018, the population of Sydney was 5.48 million. This was 22% of the total population of Australia.

Work out the total population of Australia in 2018 Give your answer correct to 3 significant figures.

...................................................... million

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

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.

Work out 320 as a percentage of 80

Circle your answer.

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

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

Work out 40 as a percentage of 10

Circle your answer.

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

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

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.

$0.4 \dot{x}$ 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.

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

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.

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

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

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?

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.

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.

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

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

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

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

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.

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

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

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.

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

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

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.

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

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

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?

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

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