Fractions

One day,

a company runs 240 trains

of these trains are late.

The company is charged £350 for each late train.

How much is the company charged that day?

Hot drinks are sold at a station in the ratio

tea: coffee: hot chocolate = 3: 5: 2

2600 hot drinks are sold.

How many coffees are sold?

A sphere has diameter 20 cm

Show that the radius of the sphere is 10 cm

The volume of a sphere is r³ where r is the radius. Work out the volume of a sphere with diameter 20 cm Give your answer in terms of

where a and b are integers.

Work out 80p as a fraction of £1 Give your answer in its simplest form.

The table shows information about two workers on one day.

Margot started work at 10:30 am What time did she finish?

Zeke says he spent more than one quarter of his total working time online.

Is he correct?

Tick a box.

Show working to support your answer.

Jodie makes a sandwich using one type of bread and one filling.

Complete the table of the 6 possible sandwiches they could make. One has been done for you.

What fraction of the possible sandwiches use Cheese?

Ary, Bea and Cat each have an amount of money. Cat has £280

• Cat’s amount is of Bea’s amount.

• Ary’s amount: Bea’s amount = 5: 12

Work out how much money Ary has.

Write 2 weeks as a fraction of 8 days. Give your answer in its simplest form.

Write 56 centimetres: 2.73 metres as a ratio in the form 1: n

7

Write A as a fraction of B.

Ary, Bea and Cat each have an amount of money. Cat has £280

• Cat’s amount is of Bea’s amount.

• Ary’s amount: Bea’s amount = 5: 12

Work out how much money Ary has.

Five identical spheres just fit inside a cylinder. Each sphere has radius r.

What fraction of the space inside the cylinder is filled by the spheres? You must show your working.

7 120 people visit a maze. 80 are children, the rest are adults.

At the start of the maze you can turn left or right. 45 children turn left. 75 people in total turn left.

Complete the frequency tree.

What fraction of the children turn left? Give your answer in its simplest form.

A large circle and a small circle are shown. The radius of the large circle is 12cm

radius of large circle: radius of small circle = 4: 1

Work out the shaded area. Give your answer in terms of π

A large circle and a small circle are shown. The radius of the large circle is 12cm

radius of large circle: radius of small circle = 4: 1

Work out the shaded area. Give your answer in terms of π

Clive owns two coffee shops, A and B. Out of 150 people

18 people use both shops

46% use shop A

Complete the Venn diagram to represent the information.

ξ = 150 people A = people who use shop A B = people who use shop B

Here is a centimetre grid.

What percentage of the grid is shaded?

Kai has shaded two small squares on this centimetre grid.

He wants of the grid to be shaded.

How many more small squares must he shade?

Two friends share £240 in the ratio 1: 3

Work out the larger share.

A tennis player wins or loses matches in the ratio win: lose = 5: 9

What fraction of the matches do they win?

In a house the floor area of the living room is 26 m² the floor area of the kitchen is 16.4m²

Express the area of the living room as a fraction of the area of the kitchen. Give your answer in its simplest form.

In a house the floor area of the living room is 26 m² the floor area of the kitchen is 16.4m²

Express the area of the living room as a fraction of the area of the kitchen. Give your answer in its simplest form.

A sector has radius 12 cm and angle 60 °

Work out the length of the arc. Give your answer in terms of π

A, B and C are numbers. Here is some information about B and C.

Work out C as a fraction of B.

Work out the next term.

Show that the value of 6 sin 30 ° + 2 cos 30 ° × 4 tan 30 ° is an integer.

People in a stadium are in the North Stand, East Stand, South Stand or West Stand. Of the people in the stadium, are in the North Stand are in the East Stand number in South Stand: number in West Stand = 2: 7

There are 4480 people in the West Stand.

How many people are in the stadium?

• A pack of pegs costs 40p

• A bar of soap costs £2.20

• A basket costs £7

Dan buys two packs of pegs, one bar of soap and one basket.

What fraction of the total cost is the cost of the basket?

There are 30 students in a class. 12 of the students have school lunch.

Work out the ratio students having school lunch: students not having school lunch Give your answer in its simplest form.

In a different class students wearing glasses: students not wearing glasses = 3: 8

What fraction of students in this class wear glasses?

The ratio 4: 9 is written in the form 1: n

Work out the value of n.

n =

Write a number in each box to make the calculations correct.

Ali has £80 He gives of his money to Joe. Joe spends of this money. He gives the rest back to Ali.

What fraction of the £80 does Ali have now? Give your answer in its simplest form.

Shape B is a sector of a circle with radius 5cm

Which shape has the greater area, A or B? You must show your working.

Shape B is a sector of a circle with radius 5cm

Which shape has the greater area, A or B? You must show your working.

The nth term of a geometric progression is rⁿ where r 0

Work out the third term.

A sauce is made from cream and stock in the ratio cream: stock = 1: 6

How much sauce can be made using 80 millilitres of cream?

A different sauce is made from olive oil and tomato juice in the ratio olive oil: tomato juice = 1: 14

What fraction of this sauce is olive oil?

A box contains 36 chocolates. The chocolates are milk or dark and have hard or soft centres. of the chocolates have soft centres. There are twice as many milk chocolates as dark. 5 of the dark chocolates have soft centres.

Complete the two-way table.

One chocolate is chosen at random.

What is the probability that it is a dark chocolate with a soft centre?

What is the probability that it has a hard centre?

Three shops sell the same type and size of lip balm stick.

Which shop is the best value for 8 sticks and what is the total cost in that shop? Show working to support your answer.

Round 1 of voting for Head Student is taking place in a school.

To reach round 2, a student must receive at least of the votes. What is the largest possible number of students that can reach round 2? Circle your answer.

15 11 3 4

There are 900 votes in round 1 Sean receives 180 votes.

Amy draws a pie chart to represent the results. Here is her method to work out the angle needed for Sean.

Is Amy’s method correct? Tick a box.

Give a reason for your answer.

Three shops sell the same type and size of lip balm stick.

Which shop is the best value for 8 sticks and what is the total cost in that shop? Show working to support your answer.

Round 1 of voting for Head Student is taking place in a school.

To reach round 2, a student must receive at least of the votes. What is the largest possible number of students that can reach round 2? Circle your answer.

15 11 3 4

There are 900 votes in round 1 Sean receives 180 votes.

Amy draws a pie chart to represent the results. Here is her method to work out the angle needed for Sean.

Is Amy’s method correct? Tick a box.

Give a reason for your answer.

An exhibition was open for 240 hours and had 29 760 visitors. For of the time the exhibition was open, there were 172 visitors per hour.

For the remaining time, how many visitors per hour were there?

a is three quarters of c 6 b = 5 c

Work out the ratio a: b: c Give your answer in its simplest form, where a, b and c are integers.

Write 18 out of 30 as a fraction in its simplest form.

Andrew and Bruce share some money in the ratio 5: 6 Bruce gets £96 Andrew gives of his share to Carl. Bruce gives of his share to Carl. How much money does Carl receive?

Give your answer as a mixed number.

Andrew and Bruce share some money in the ratio 5: 6 Bruce gets £96 Andrew gives of his share to Carl. Bruce gives of his share to Carl. How much money does Carl receive?

Match each expression to its value. One has been done for you.

A circle, centre O, has circumference 20 π cm Q is a point on the circle.

Work out the value of a. You must show your working.

There are 1020 books in a box. of the books are blue. How many are blue?

There are green pens and red pens in the box. The ratio of green: red is 4: 3 What fraction of the pens are green?

There are some calculators in the box. 220 are scientific. 30 are not. What percentage of the calculators are scientific?

Three oranges have masses of 60 g, 70 g and 85 g Show that their total mass is between and of a kilogram.

The only animals on a farm are 30 cows and 80 sheep. of the 30 cows are sold and of the 80 sheep are sold. Work out the total number of animals that are sold.

Here is some information about 120 people who visit a shop. of the people buy neither a coat nor a dress. 19 people buy a coat. 14 people buy a dress. Complete this Venn diagram to represent the information. ξ = 120 people who visit the shop C = people who buy a coat D = people who buy a dress

Here is some information about 120 people who visit a shop. of the people buy neither a coat nor a dress. 19 people buy a coat. 14 people buy a dress. Complete this Venn diagram to represent the information. ξ = 120 people who visit the shop C = people who buy a coat D = people who buy a dress

A road has three sections, D, E and F. The lengths of D, E and F are in the ratios D: E = 3: 5 E: F = 7: 4 What fraction of the length of the road is section D?

4 × sin 30 ° × tan 30 ° × cos 30 ° = sin y Work out one possible value of y. You must show your working.

Fred bought an apartment for £137 500 He made 8% profit when he sold the apartment. He used all of this profit to pay 40% of the deposit on a house. The deposit was one sixth of the price of the house. Work out the price of the house.

480 people are asked if they eat sushi. 20% say Yes. of the people who say Yes eat sushi at least once a month. Complete the frequency tree.

Joe, Kim and Lisa each have an amount of money. Joe has £72 Joe’s amount: Kim’s amount = 6: 5 Lisa’s amount is times Joe’s amount. Show that, in total, they have less than £250

Joe, Kim and Lisa each have an amount of money. Joe has £72 Joe’s amount: Kim’s amount = 6: 5 Lisa’s amount is times Joe’s amount.

Show that, in total, they have less than £250

In each box, write a fraction less than 1 to make a correct calculation.

In each box, write a decimal less than 1 to make a correct calculation.

What is 0.28 as a fraction of 0.8 ? Circle your answer.

Nihal has savings of £168 He uses of his savings to buy sports equipment.

Assume that he will use of the rest of the money to buy a shirt. How much of his savings, in £, will he have left?

What does this tell you about how much of his savings he has left? Tick one box.

Circle your answer.

Lily’s age is 2 years and 4 months. Hugo’s age is 1 year and 8 months. Write Lily’s age in months as a fraction of Hugo’s age in months. Give your fraction in its simplest form.

Lily’s age is 2 years and 4 months. Hugo’s age is 1 year and 8 months. Write Lily’s age in months as a fraction of Hugo’s age in months. Give your fraction in its simplest form.

The table shows information about how 150 students travel to school.

What fraction of the girls walk to school? Give your answer in its simplest form.

One of the boys is chosen at random. What is the probability that the boy travels to school by bus?

What percentage of the 150 students travel to school by car?

Two wire shapes make an earring. The shapes are a circle with radius 21 mm and a quarter circle.

radius of circle: radius of quarter circle = 7: 2

Show that the radius of the quarter circle is 6 mm

Work out the total length of the wire in the earring. Give your answer in the form a π + b where a and b are integers.

The shorter side of a parallelogram has length 6.5 cm

The length of the shorter side is of the perimeter. Work out the length of the longer side.

Give your answer as an integer.

Members of a club are Senior, Adult or Junior.

Give a reason why there must be a mistake in the report.

An Adult membership fee is £120 A Junior membership fee is of the Adult fee. Work out the total membership fee for 2 Adults and 3 Juniors.

Give your answer as a single fraction in its simplest form.

Her method is divide 6 c by 2 then add 10 Evaluate her method.

Mo played 30 games of chess. He won 18 of these games.

What fraction of the games did he win? Give your answer in its simplest form.

He played 20 more games. He had then won 64% of all of his games. How many of the 20 games did he win?

What is x as a fraction of y ? Circle your answer.

Work out £1.50 as a fraction of 60p Circle your answer.

Beth and Mia translate documents from Spanish into English. A set of documents that would take Beth 8 days would take Mia 10 days. Beth starts to translate the documents. After 2 days Beth and Mia both work on translating the documents. How many more days will it take to complete the work? You must show your working.

where c and d are integers.

Work out the value of w.

The table shows the number of messages Sam received each day for five days.

Sam draws a composite bar chart to represent the data. He has drawn the bar for Monday.

Complete the chart.

In total, what fraction of the messages were emails? Give your answer in its simplest form.

This triangle is equilateral.

Is the perimeter of the triangle greater than one metre? You must show your working.

What is 1.75 kilometres as a fraction of 700 metres? Circle your answer.

Circle your answer.

The height of Zak is 1.86 metres. The height of Fred is 1.6 metres. Write the height of Zak as a fraction of the height of Fred. Give your answer in its simplest form.

The height of Zak is 1.86 metres. The height of Fred is 1.6 metres. Write the height of Zak as a fraction of the height of Fred. Give your answer in its simplest form.

A shopkeeper compares the income from sales of a laptop in March and April.

By what fraction does the income from these sales decrease in April?

Circle your answer. 0.30 0.6 0.75 0.9

There are 720 boys and 700 girls in a school. The probability that a boy chosen at random studies French is The probability that a girl chosen at random studies French is

Work out the number of students in the school who study French.

Work out the probability that a student chosen at random from the whole school does not study French.