Fractions

There are 280 chocolates in a box. There are only dark chocolates, milk chocolates and white chocolates. of the 280 chocolates are dark chocolates. The number of milk chocolates: the number of white chocolates = 1: 3 The number of white chocolates: the number of dark chocolates = n: 1

Work out the value of n. You must show all your working.

10 milk chocolates from the box are eaten.

Does this affect your answer to part (a)? Give a reason for your answer.

There are 280 chocolates in a box. There are only dark chocolates, milk chocolates and white chocolates. of the 280 chocolates are dark chocolates. The number of milk chocolates: the number of white chocolates = 1: 3 The number of white chocolates: the number of dark chocolates = n: 1

Work out the value of n. You must show all your working.

10 milk chocolates from the box are eaten.

Does this affect your answer to part (a)? Give a reason for your answer.

∙ ∙ ∙ 13 x = 0.2 y = 0.681 Work out the value of xy. Give your answer as a fraction in its simplest form.

Give your answer in its simplest form.

Work out the value of a and the value of b.

There are 200 counters in a bag. 87 of the counters are green. 24 of the counters are yellow.

What fraction of the counters are green?

What percentage of the counters are yellow?

A team plays 48 games. The team wins of the 48 games. The number of games the team loses is the same as the number of games the team draws. Work out the number of games the team loses.

Milly collects stickers of sports players. She only has stickers of tennis players, football players and cricket players. The incomplete bar chart shows some information about the number of stickers Milly has.

Milly has a total of 40 stickers.

Complete the bar chart.

What fraction of the 40 stickers are stickers of tennis players? Give your fraction in its simplest form.

Ewan also collects stickers. He only has large stickers and small stickers. For Ewan’s stickers, the number of large stickers: the number of small stickers = 5: 4

Write down the fraction of Ewan’s stickers that are large stickers.

Write the ratio 5: 4 in the form n: 1

17Show that simplifies to where k is an integer.

There are 200 people at a party. of the people are children. The rest of the people are adults. 35% of the children are vegetarian. 45% of the adults are vegetarian. How many of the people are not vegetarian?

The diagram shows a triangle and a rectangle.

The perimeter of the rectangle is a quarter of the perimeter of the triangle. Work out the length of the rectangle.

Kasim has some small jars, some medium jars and some large jars. He has a total of 400 jars. of the 400 jars are empty. For the empty jars, number of small jars: number of medium jars = 3: 4 number of medium jars: number of large jars = 1: 2 Work out the percentage of Kasim’s jars that are empty small jars.

Kasim has some small jars, some medium jars and some large jars. He has a total of 400 jars. of the 400 jars are empty. For the empty jars, number of small jars: number of medium jars = 3: 4 number of medium jars: number of large jars = 1: 2 Work out the percentage of Kasim’s jars that are empty small jars.

OAB is a sector of a circle with centre O and radius 6 cm.

The length of the arc AB is 5πcm. Work out, in terms of π, the area of the sector. Give your answer in its simplest form.

Saira buys 24 bars of chocolate. of the 24 bars are white chocolate. The rest of the 24 bars are milk chocolate. Each milk chocolate bar has a weight of 35 grams. Work out the total weight of the milk chocolate bars that Saira buys.

Andy, Luke and Tina share some sweets in the ratio 1: 6: 14 Tina gives of her sweets to Andy. Tina then gives 12 % of the rest of her sweets to Luke. Tina says, “Now all three of us have the same number of sweets.” Is Tina correct? You must show how you get your answer.

Andy, Luke and Tina share some sweets in the ratio 1: 6: 14 Tina gives of her sweets to Andy. Tina then gives 12 % of the rest of her sweets to Luke. Tina says, “Now all three of us have the same number of sweets.” Is Tina correct? You must show how you get your answer.

15Given that a is a prime number, rationalise the denominator of

The diagram shows a circle, radius r cm and two regular hexagons.

Each side of the larger hexagon ABCDEF is a tangent to the circle. Each side of the smaller hexagon PQRSTU is a chord of the circle. By considering perimeters, show that

The circumference of a circle is 10 m. Work out the area of the circle. Give your answer in terms of π.

Find the value of the common ratio the sequence.

You must show all your working.

Here is a grid of squares.

What fraction of the grid is shaded?

There are only red counters, blue counters and green counters in a bag. number of red counters: number of blue counters: number of green counters = 2: 16: 7 What fraction of the counters in the bag are green counters?

What fraction of this shape is shaded?

Last week, 73% of the tickets sold at a cinema were adult tickets.

What percentage of the tickets sold were not adult tickets?

Some people watched a film at the cinema. number of adults: number of children = 2: 5

What fraction of these people were adults?

On Friday, 500 people watched a film at the cinema. 70% of these people were children. On Saturd ay, 720 people watched the film at the cinema. of these people were children. Kasim thinks more children watched the film on Friday than on Saturday.

Is Kasim correct? You must show how you get your answer.

Here is a sphere.

of the surface area of this sphere is 75πcm² Find the diameter of the sphere.

13There are 50 teachers in a school. This is of the total number of people in the school. Work out the total number of people in the school.

Elena spent 120 minutes at a sports centre. She played badminton for 50 minutes. She used the swimming pool for of the 120 minutes. She used the gym for 20% of the 120 minutes. She then spent the rest of the 120 minutes in the cafe.

Work out the total time, in minutes, that Elena spent in the cafe.

Elena got to the sports centre at 1.30 pm. She had asked her friend to meet her in the cafe at 3 pm.

Did Elena get to the cafe by 3 pm? Give a reason for your answer.

There are 240 cans of drink on a shelf. Each can contains cola or lemonade or orange. the number of cans the number of cans the number of cans:: = 5: 3: 2 of cola of lemonade of orange of the cans of lemonade and of the cans of orange are removed from the shelf. Work out the number of cans of cola as a percentage of the total number of cans of drink remaining on the shelf.

Rizwan writes down three numbers a, b and c a: b = 1: 3 b: c = 6: 5

Find a:b:c

Express a as a fraction of the total of the three numbers a, b and c

Emma writes down three numbers m, n and p n = 2 m p = 5 n

Find m:p

A car factory is going to make four different car models A, B, C and D. 80 people are asked which of the four models they would be most likely to buy. The table shows information about the results.

The factory is going to make 40 000 cars next year. Work out how many model B cars the factory should make next year.

Rizwan writes down three numbers a, b and c a: b = 1: 3 b: c = 6: 5

Find a:b:c

Express a as a fraction of the total of the three numbers a, b and c

Emma writes down three numbers m, n and p n = 2 m p = 5 n

Find m:p

23Here are the first five terms of a geometric sequence.

Work out the next term of the sequence.

Given that the terms of this sequence are all positive,

work out the first term of this sequence. You must show all your working.

Write the following fractions in order of size. Start with the smallest fraction.

7 208 bars of chocolate were sold from a shop. of these bars of chocolate were large bars. The rest of the bars of chocolate were small bars. All the large bars of chocolate were sold for £1 each. All the small bars of chocolate were sold for 60p each. Work out the total amount of money for which the 208 bars of chocolate were sold. Give your answer in pounds.

There are four boxes on a shelf, A, B, C and D. The total weight of A and B is 3 times the total weight of C and D. The weight of A is of the weight of B. The weight of C is 75% of the weight of D. Find the ratio weight of A: weight of B: weight of C: weight of D

3 can be written in the form where a and b are integers. Work out the value of a and the value of b. You must show all your working.

The centimetre grid shows the plan and the front elevation of a cylinder.

Work out the volume of the cylinder. Give your answer in terms of π

A delivery company has a total of 160 cars and vans. the number of cars: the number of vans = 3: 7 Each car and each van uses electricity or diesel or petrol. of the cars use electricity. 25% of the cars use diesel. The rest of the cars use petrol. Work out the number of cars that use petrol. You must show all your working.

A delivery company has a total of 160 cars and vans. the number of cars: the number of vans = 3: 7 Each car and each van uses electricity or diesel or petrol. of the cars use electricity. 25% of the cars use diesel. The rest of the cars use petrol. Work out the number of cars that use petrol. You must show all your working.

Cormac has some sweets in a bag. The sweets are lime flavoured or strawberry flavoured or orange flavoured. In the bag number of lime number of strawberry number of orange:: = 9: 4: x flavoured sweets flavoured sweets flavoured sweets Cormac is going to take at random a sweet from the bag. The probability that he takes a lime flavoured sweet is Work out the value of x.

The diagram shows three circles, each of radius 4 cm. The centres of the circles are A, B and C such that ABC is a straight line and AB = BC = 4 cm.

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

Write 60 metres as a fraction of 1000 metres. Give your answer in its simplest form.

There are 400 counters in a box. The counters are red or yellow or green. of the counters are red. 82 of the counters are yellow. What percentage of the counters are green?

The pictogram shows information about the number of video games sold in a shop on Monday, on Tuesday and on Wednesday.

How many video games were sold on Monday?

More video games were sold on Tuesday than on Wednesday.

How many more?

On Thursday and Friday, a total of 32 video games were sold in the shop. of these 32 video games were sold in the shop on Thursday.

Complete the pictogram for Thursday and Friday.

There are two drama groups in a school. In one group there are 36 boys and 48 girls. In the other group, of the students are boys and the rest of the students are girls. Ann says, “The ratio of the number of boys to the number of girls is the same for both groups.” Is Ann correct? You must show how you get your answer.

15Show that can be written in the form where a, b and c are integers.

Write 17 as a fraction of 30

Rachel, Samina and Tom share £600 between them.

Samina gets of the money that is left over. Tom gets the rest of the money. Tom says, “I would have got more money if we had shared the £600 equally between us.” Is Tom correct? You must show how you get your answer.

A stadium cost £600 million. of this cost was for the building. The rest of the cost was for the land. Work out the cost of the land.

A bag contains red counters and blue counters only. number of red counters: number of blue counters = 3: 4 Write down the fraction of the counters that are red.

Write the ratio 12: 30 in the form 1:n

10Jenny has 12 marbles. of these 12 marbles are large. The rest of these 12 marbles are small. Each large marble has a weight of 70 grams. Each small marble has a weight of 50 grams. Work out the total weight of the 12 marbles.

In a shop, a TV has a normal price of £500 The shop has a sale. On Monday, the normal price of the TV is reduced by to give the sale price. On Tuesday, the sale price of the TV is reduced by 20% Chris wants to buy the TV. He has £400 to spend on the TV. Does Chris have enough money to buy the TV on Tuesday? You must show how you get your answer.

There are four types of cards in a game. Each card has a black circle or a white circle or a black triangle or a white triangle.

Express the total number of cards with a black shape as a fraction of the total number of cards with a triangle.

An exam has two papers, Paper 1 and Paper 2 Paper 1 has 60 marks. Paper 2 has 90 marks. The pass mark is of the total number of marks. Danielle gets 70% of the marks for Paper 1 How many of the marks for Paper 2 must Danielle get in order to get the pass mark?

Adam, Linda and Rytis share an amount of money. Linda gets three times as much money as Rytis gets. Linda gets half as much money as Adam gets. What fraction of the amount of money does Linda get?

What fraction of the shape is shaded? Give your answer in its simplest form.

Give your answer in its simplest form.

Dylan buys 13 bicycle lights for £7.50 each. He pays with five £20 notes.

How much change should Dylan get?

The normal price of a bicycle is £120

Work out the price of the bicycle in the sale.

A group of people went to a restaurant. Each person chose one starter and one main course.

the number of people who chose soup: the number of people who chose prawns = 2: 3

Of those who chose soup, the number of people who chose lasagne: the number of people who chose curry = 5: 3

Of those who chose prawns, the number of people who chose lasagne: the number of people who chose curry = 1: 5

What fraction of the people chose curry? You must show how you get your answer.

Fiona has to work out the exact value of 48 ÷ She writes

Fiona’s reason is, “There are 2 halves in 1, so there will be 24 halves in 48”

Explain what is wrong with Fiona’s reason.

Here are three spheres.

The volume of sphere Q is 50% more than the volume of sphere P. The volume of sphere R is 50% more than the volume of sphere Q. Find the volume of sphere P as a fraction of the volume of sphere R.

Find the exact value of tan 30 sin 60 Give your answer in its simplest form.

The diagram shows a solid shape. The shape is a cone on top of a hemisphere.

The height of the cone is 10 cm. The base of the cone has a diameter of 6 cm. The hemisphere has a diameter of 6 cm. The total volume of the shape is cm³, where k is an integer. Work out the value of k.

Here is the gauge for the fuel tank of a car.

The fuel tank holds 52 litres of fuel when the tank is full. The tank is full of fuel. Work out how many more litres of fuel are needed to fill the tank.

Bill has 400 counters in a bag. He gives 35 of the counters to Sameena 50 of the counters to Henry 75 of the counters to Lucas What fraction of the 400 counters is left in Bill’s bag? Give your fraction in its simplest form.

Ali, Ben and Cathy share an amount of money in the ratio 6: 9: 10 What fraction of the money does Ben get?

Costcorp sells packets of mints to shop owners. On Monday three shop owners buy mints from Costcorp. Each shop owner buys small packets, medium packets and large packets of mints. Alan buys 400 packets of mints. 32 % are small packets. 40 % are large packets. Beryl buys 500 packets of mints.

Charlie buys 150 small packets of mints so that number of small packets: number of medium packets 3: 4 Work out the total number of medium packets of mints these shop owners buy. You must show all your working.

The diagram shows a square ABCD with sides of length 20 cm. It also shows a semicircle and an arc of a circle.

AB is the diameter of the semicircle. AC is an arc of a circle with centre B.

The diagram shows a square ABCD with sides of length 20 cm. It also shows a semicircle and an arc of a circle.

AB is the diameter of the semicircle. AC is an arc of a circle with centre B.

Gavin, Harry and Isabel each earn the same monthly salary.

Each month,

Gavin saves 28% of his salary and spends the rest of his salary Harry spends of his salary and saves the rest of his salary the amount of salary Isabel saves: the amount of salary she spends = 3: 7

Work out who saves the most of their salary each month. You must show how you get your answer.

There are some chocolates in a box. of the chocolates contain nuts. The rest of the chocolates do not contain nuts.

Write down the ratio of the number of chocolates that contain nuts to the number of chocolates that do not contain nuts. Give your answer in the form 1: n

Find the value of a.

There are only red counters, blue counters and purple counters in a bag. The ratio of the number of red counters to the number of blue counters is 3: 17

Sam takes at random a counter from the bag. The probability that the counter is purple is 0.2

Work out the probability that Sam takes a red counter.

Martin did this question.

Here is how he answered the question.

Martin’s answer is wrong.

Find Martin’s mistake.

Sian did this question.

Here is how she answered the question.

Sian’s answer is wrong.

Find Sian’s mistake.

Last year the cost of a season ticket for a football club was £560 This year the cost of a season ticket for the club has been increased to £600

Write down the increase in the cost of a season ticket as a fraction of last year’s cost.

There are only red buttons, yellow buttons and orange buttons in a jar. The number of red buttons, the number of yellow buttons and the number of orange buttons are in the ratio 7: 4: 9

Work out what percentage of the buttons in the jar are orange.

The diagram shows a logo made from three circles.

Each circle has centre O. Daisy says that exactly of the logo is shaded.

Is Daisy correct? You must show all your working.

The diagram shows a logo made from three circles.

Each circle has centre O. Daisy says that exactly of the logo is shaded.

Is Daisy correct? You must show all your working.

Show that can be written in the form a + b 2 where a and b are integers.

5 60 students were asked how they get to school.

The table shows the results.

What fraction of the 60 students did not walk to school?

Complete the pie chart for the information in the table.

Annie and Lily share some money in the ratio 4: 3

What fraction of the money does Lily get?

Rosie and Dan share some sweets. Dan gets of the sweets.

Write down the ratio of the number of sweets Rosie gets to the number of sweets Dan gets.

There are only blue cubes, yellow cubes and green cubes in a bag.

There are

twice as many blue cubes as yellow cubes and four times as many green cubes as blue cubes.

Hannah takes at random a cube from the bag.

Work out the probability that Hannah takes a yellow cube.

There are only blue cubes, yellow cubes and green cubes in a bag.

There are

twice as many blue cubes as yellow cubes and four times as many green cubes as blue cubes.

Hannah takes at random a cube from the bag.

Work out the probability that Hannah takes a yellow cube.

The pie charts give information about the ages, in years, of people living in two towns, Adley and Bridford.

40 – 59

The ratio of the number of people living in Adley to the number of people living in Bridford is given by the ratio of the areas of the pie charts.

What proportion of the total number of people living in these two towns live in Adley and are aged 0 – 19? Give your answer correct to 3 significant figures.

S is a geometric sequence.

You must show all your working.

Jim thinks of a number.

Work out of Jim’s number.

Sean works for a company. His normal rate of pay is £12 per hour.

When Sean works more than 8 hours a day, he is paid overtime for each hour he works more than 8 hours. Sean’s rate of overtime pay per hour is 1 times his normal rate of pay per hour. On Monday Sean worked for 10 hours.

Work out the total amount of money Sean earned on Monday.

On Saturday, some adults and some children were in a theatre. The ratio of the number of adults to the number of children was 5: 2

Each person had a seat in the Circle or had a seat in the Stalls. of the children had seats in the Stalls. 117 children had seats in the Circle.

There are exactly 2600 seats in the theatre.

On this Saturday, were there people on more than 60% of the seats? You must show how you get your answer.

Find the number.

A path is made of white tiles and grey tiles. of the tiles are white.

Write down the ratio of white tiles to grey tiles.

There is a total of 56 tiles.

Work out the number of grey tiles.

Daniel bakes 420 cakes. He bakes only vanilla cakes, banana cakes, lemon cakes and chocolate cakes. of the cakes are vanilla cakes. 35% of the cakes are banana cakes. The ratio of the number of lemon cakes to the number of chocolate cakes is 4:5

Work out the number of lemon cakes Daniel bakes.

Daniel bakes 420 cakes. He bakes only vanilla cakes, banana cakes, lemon cakes and chocolate cakes. of the cakes are vanilla cakes. 35% of the cakes are banana cakes. The ratio of the number of lemon cakes to the number of chocolate cakes is 4:5

Work out the number of lemon cakes Daniel bakes.