Ratio

The pie chart shows the proportion of games won by a sports team.

The sports team won 9 games.

Work out how many games the sports team played.

The ratio of the number of games drawn by the sports team to the number of games lost by the sports team was 2: 1.

Complete the pie chart above.

The ratio 40 grams to 1 kilogram can be written in the form 1: n.

Find the value of n.

There are 483 counters in a bag. The counters are blue, red or yellow.

The ratio of blue counters to red counters is 1: 5. The ratio of red counters to yellow counters is 4: 9.

Work out the number of red counters in the bag.

Three lengths of wood are in the ratio 2: 5: 7. The difference in size between two of the lengths of wood is 30 cm.

Kofi says,

The sum of the three lengths of wood must be at least 120 cm.

Is Kofi correct? Show how you decide.

Kofi is........ because........

The diagram shows a large rectangle made from 10 smaller rectangles of equal area. The large rectangle is divided into two unequal parts, A and B.

Tick (✓) all the correct statements.

The area of Part A is 18 k.

Write an expression, in terms of k, for the area of Part B. Give your answer in its simplest form.

Sasha makes some cupcakes. Each cupcake is topped with red or white or yellow icing. of the cupcakes have red icing. of the cupcakes have white icing.

Work out the fraction of the cupcakes that have yellow icing.

Sasha makes all of the icing using butter and sugar in the ratio 1: 2. Each cupcake has 60 g of icing.

Sasha uses 0.7 kg of butter to make the yellow icing.

Find the total number of cupcakes Sasha makes. You must show your working.

The ratio 40 grams to 1 kilogram can be written in the form 1: n.

Find the value of n.

Three lengths of wood are in the ratio 2: 5: 7. The difference in size between two of the lengths of wood is 30 cm.

Kofi says,

The sum of the three lengths of wood must be at least 120 cm.

Is Kofi correct? Show how you decide.

Kofi is........ because........

A bag contains only round tiles and square tiles. Each tile is either black or white.

The ratio of round tiles to square tiles is 3: 1. 45% of all the tiles are round black tiles. 9% of all the tiles are square white tiles.

Show that the proportion of round tiles that are black is less than the proportion of square tiles

that are black.

Write down an odd number.

Write down a common multiple of 3 and 17.

Write 24: 60 as a ratio in its simplest form.

A recipe for cookies uses only butter, flour and sugar in the ratio 2: 4: 1. Using this recipe, 160 g of butter is needed to make 10 cookies.

Using this recipe, work out how much flour is needed to make 25 cookies.

100 students vote in a school election.

1 vote is spoiled and is not counted. The remaining votes are for Jamal or Layla and are in the ratio 3: 8.

How many more votes does Layla have than Jamal?

A bag contains only blue, green and red counters in the ratio 7: 3: 2. There are 76 more blue counters than green counters in the bag.

Work out the total number of counters in the bag.

There is a total of 354 balls in a bag. There are white balls, red balls and green balls only.

The ratio of white balls to red balls is 3: 4. The ratio of red balls to green balls is 5: 6.

Work out the number of green balls in the bag.

A cylinder has a radius of 8.4 cm. The ratio of the radius of the cylinder to the height of the cylinder is 2: 5.

Find the volume of the cylinder.

A bag only contains red counters and blue counters. of the counters are red. There are 20 blue counters.

Complete the table to show the fraction of the counters that are blue and the number of red counters.

Write the ratio 14: 35 in its simplest form.

The scale of a map is 1: 25 000.

Two castles are 6 kilometres apart on the ground.

Work out how far apart the two castles are on the map. Give your answer in centimetres.

A sports team scored 400 points. The defenders scored of the points. The midfielders and the forwards scored the remainder of the points in the ratio 1: 5.

Find the percentage of the 400 points that were scored by the forwards. You must show your working.

A school is deciding on a charity to support. Each student at the school votes for one of four charities, A, B, C or D. The results are to be shown in a pie chart.

This pie chart shows the sector for charity A. Twice as many students voted for charity C than charity B. Twice as many students voted for charity D than charity C.

Show that the sector for charity B will have an angle of 44°.

Complete the pie chart.

39 students voted for charity A.

Calculate the total number of students at the school.

The school asks 80 of the students to choose a new logo from three designs G, H and J. The same results are shown in a pie chart and in a bar chart.

Give one advantage of using the pie chart rather than the bar chart.

Give one disadvantage of using the pie chart rather than the bar chart.

In a survey, 50 people were asked whether they have a car (C) or a bicycle (B).

The Venn diagram shows some of the results.

The ratio of those that only have a car to those that only have a bicycle is 2: 1.

One of the 50 people is chosen at random.

Find the probability that they have a bicycle. You must show your working.

Finley and Gabi share £14 in the ratio 1: 3.

Write down the letter of the correct calculation to work out Gabi’s share.

Work out Finley’s share.

1 cm on a map represents 150 km in real life.

Below is part of the map showing City A and City B.

Heidi is planning to walk from City A to City B for charity.

Heidi measures the straight-line distance on the map from City A to City B accurately as 5 cm. Heidi says she will walk from City A to City B at an average speed of 2.5 km / h for 10 hours per day.

Use this information to work out how many days Heidi needs to complete the walk from City A to City B.

Explain why the information used in part (i) is likely to give an underestimate for the number of days Heidi needs to complete the walk.

Yoshi writes the scale of the map, 1 cm represents 150 km, as the ratio 1: 150.

Explain Yoshi’s error and write the scale correctly in the form 1: n.

The correct answer is 1:........

A school is deciding on a charity to support. Each student at the school votes for one of four charities, A, B, C or D. The results are to be shown in a pie chart.

This pie chart shows the sector for charity A. Twice as many students voted for charity C than charity B. Twice as many students voted for charity D than charity C.

Show that the sector for charity B will have an angle of 44°.

Complete the pie chart.

39 students voted for charity A.

Calculate the total number of students at the school.

The school asks 80 of the students to choose a new logo from three designs G, H and J. The same results are shown in a pie chart and in a bar chart.

Give one advantage of using the pie chart rather than the bar chart.

Give one disadvantage of using the pie chart rather than the bar chart.

Sasha and Taylor each have a stamp collection.

They organise their stamp collections according to where the stamps come from: United Kingdom (UK), European Union (EU), Other.

The table shows the number of stamps in each collection and the ratio UK: EU: Other.

When they put the two stamp collections together, Sasha and Taylor claim that at least of all the stamps come from the UK.

Are they correct? Show how you decide.

They are........ because........

A bottle contains litres of cordial.

Work out the maximum number of cups that can be filled from the bottle of cordial. You must show your working.

1 cm on a map represents 150 km in real life.

Below is part of the map showing City A and City B.

Heidi is planning to walk from City A to City B for charity.

Heidi measures the straight-line distance on the map from City A to City B accurately as 5 cm. Heidi says she will walk from City A to City B at an average speed of 2.5 km / h for 10 hours per day.

Use this information to work out how many days Heidi needs to complete the walk from City A to City B.

Explain why the information used in part (i) is likely to give an underestimate for the number of days Heidi needs to complete the walk.

Yoshi writes the scale of the map, 1 cm represents 150 km, as the ratio 1: 150.

Explain Yoshi’s error and write the scale correctly in the form 1: n.

The correct answer is 1:........

Two bags of fruit contain only apples and bananas. In bag X, the ratio of apples to bananas is 5: 7. In bag Y, of the fruit are apples.

Finley says

Bag X and bag Y contain the same number of apples.

Tick the correct statement.

Show how you decided.

Finley adds 4 apples to bag X. The ratio of apples to bananas is now 11: 14.

How many bananas are in bag X?

A painter mixes red paint and yellow paint in the ratio 2: 3. They make a total of 1.5 litres of paint.

Work out how much red paint they use. Give your answer in millilitres.

The bar chart shows the rainfall, in millimetres (mm), for a city in the first three months of the year.

Write down the amount of rainfall in February.

Write in its simplest form the ratio amount of rainfall in February: amount of rainfall in March.

The total amount of rainfall in January and February was the same as the total amount of rainfall in March and April.

Work out the amount of rainfall in April.

A box contains only red, green and black pens. The ratio of red pens to green pens to black pens is 1: 4: 11.

Work out the percentage of the pens that are green.

There are 24 more green pens than red pens.

Work out the total number of pens in the box.

Write this ratio in its simplest form.

4 centimetres: 8 millimetres

The ratio 4: 5 can be written in the form 1: n.

Find the value of n.

Dev and Emma share some money in the ratio 2: 3.

Dev says

What mistake has Dev made? Give the fraction of the money Dev actually receives.

The fraction of the money Dev receives is........

Dev receives £100.

Work out how much money Dev and Emma shared between them.

A box contains only red, green and black pens. The ratio of red pens to green pens to black pens is 1: 4: 11.

Work out the percentage of the pens that are green.

There are 24 more green pens than red pens.

Work out the total number of pens in the box.

A large box of chocolates contains dark, milk and white chocolates. When Riley opens the box, the ratio of dark to milk to white chocolates is 3: 2: 4. Riley’s family eat 6 of the dark chocolates, none of the milk chocolates and all of the white chocolates. The ratio of dark to milk chocolates is now 9: 8.

How many white chocolates did Riley’s family eat?

Eve, Jack and Ling share some money in the ratio 2: 3: 4. Jack gets £720.

Work out how much Ling gets.

Eve, Jack and Ling share some money in the ratio 2: 3: 4. Jack gets £720.

Work out how much Ling gets.

A zoo counts its animals. The ratio of antelope to zebra is 3: 2. The ratio of meerkats to zebra is 7: 3.

Write the number of antelope as a percentage of the number of zebra.

There are 15 more meerkats than antelope.

Work out the number of zebra in the zoo.

A box contains 25 discs. The discs are either blue or yellow in the ratio 4: 1. Two discs are chosen at random from the box without replacement.

Find the probability that the two discs are different colours. You must show your working.

One morning Harper records the first 50 vehicles to pass the school gate. Harper’s results are shown in this table.

Use Harper’s results to estimate the probability that the next vehicle will not be a motorbike.

One afternoon Reece records some vehicles that pass the school gate. of the vehicles they record are cars. For Reece’s results, write down the ratio of cars to not cars. Give your answer in its simplest form.

Eve is counting the photos on her phone. The ratio of the number of photos of her family to photos of her friends is 3: 7. She has 450 photos of her family. 80% of the photos of her friends include Jack.

Work out how many of the photos of her friends include Jack.

A bag contains 35 balls. Each ball is either red or green. The ratio of red balls to green balls is 3: 2.

Work out the smallest number of balls of each colour that have to be added to the bag so that the ratio of red balls to green balls becomes 7: 3. You must show your working.

The diagram shows part of a regular 12-sided polygon.

For this polygon, find the ratio of the size of one exterior angle to the size of one interior angle. Give your answer in its simplest form. You must show your working.

Layla and Jamal open a box of sweets. Layla and Jamal share all of the sweets in the ratio 2: 3.

Write down the fraction of the sweets that Layla receives.

Layla eats some of her sweets. She is then left with 18% of the sweets that were in the box.

Work out the percentage of her sweets that Layla has eaten.

Write 28: 70 as a ratio in its simplest form.

A map has a scale of 8 centimetres represents 1 metre. The scale can be written as a ratio in the form 1: n.

Find the value of n.

A bag contains 35 balls. Each ball is either red or green. The ratio of red balls to green balls is 3: 2.

Work out the smallest number of balls of each colour that have to be added to the bag so that the ratio of red balls to green balls becomes 7: 3. You must show your working.

Layla and Jamal open a box of sweets. Layla and Jamal share all of the sweets in the ratio 2: 3.

Write down the fraction of the sweets that Layla receives.

Layla eats some of her sweets. She is then left with 18% of the sweets that were in the box.

Work out the percentage of her sweets that Layla has eaten.

Alex and Blake share some money in the ratio 2: 5. Blake receives £150 more than Alex.

How much money does Alex receive?

A local theatre is putting on a show. 50 child tickets are sold. The ratio of the number of child tickets sold to the number of adult tickets sold is 5: 2.

The cost of a child ticket is £2.50. The cost of an adult ticket is £5.00.

Work out the total amount paid for the tickets.

Some students were asked how they travel to school. Each student gave one answer. The pie chart shows the proportion who travel by bus, by train or walk.

All of the remaining students travel to school either by bike or by car. The ratio of the number who travel by bike to the number who travel by car is 2: 3.

Complete the pie chart.

You must show your working.

Which way of travelling to school is the mode?

In a recipe, the ratio of the amount of flour needed to the amount of butter needed is 4: 1. Rowan mixes 4 kg of flour with 1 g of butter.

Explain what Rowan has done wrong.

Azmi gives of their earnings to charity and keeps the remainder. For Azmi’s earnings, find the ratio of the amount they give to charity to the amount they keep.

Give your answer in its simplest form.

A sports club has 250 members.

Some of the members wish to change a club rule. To change a club rule, at least 70% of all the members must vote ‘yes’.

At a meeting of the sports club, 10 members were absent and did not vote. The other members voted yes: no: don’t know in the ratio 11: 3: 1.

Did enough members vote ‘yes’ to change the rule? Show how you decide.

The diagram shows a shaded shape made by removing sector OAB from sector OCD. Both sectors have an angle of 60°. The radius, OA, of the smaller sector is r cm. The ratio of radius OA to radius OC is 2: 3.

Work out, in terms of π and r, the total length of arc AB and arc CD. Give your answer in its simplest form. You must show your working.

Amir, Beth and Charlie work in a cafe. Customers give spare change as tips. At the end of each week, Amir, Beth and Charlie share the total amount of tips between them in the ratio matching the number of hours they worked that week.

This week:

• Amir’s share of the tips was £25.40.

• Beth worked twice as many hours as Amir.

• Charlie worked 5 more hours than Amir.

• The total hours worked by Amir, Beth and Charlie was 85 hours.

Calculate the total amount of tips received this week. You must show your working.

Ben and Sundip are making pancakes using the ingredients below.

The ratio of the amount of water to the amount of milk needed is 75: 200.

Write this ratio in its simplest form.

Ben makes 18 pancakes.

Work out how much flour he needs.

Sundip has 225 g of butter and 10 eggs. She has plenty of the other ingredients.

Work out the maximum number of pancakes that she can make.

In a survey, some students chose their favourite type of film from a list of five. The bar chart shows the results.

(a)(i)........

How many Year 11 students chose Action films?

What type of film was chosen by the most Year 10 students?

How many Year 10 students took part in the survey?

45 students took part in the survey.

Write the ratio

number of Year 10 students taking part: number of Year 11 students taking part

in its simplest form.

Azmi, Beth and Callum share a flat.

The monthly rent is £760. They share the rent in the ratio 2: 3: 3.

How much does Beth pay for rent each month?

Azmi, Beth and Callum also share the fuel bill in the ratio 2: 3: 3. Callum pays £36 for fuel each month.

How much does Azmi pay for fuel each month?

A bag of sweets contains jellies, mints and toffees.

The ratio of jellies to mints is n: 2. The ratio of mints to toffees is 5: 3 n.

Work out the ratio of jellies to toffees. Give your answer in its simplest form.

The diagram shows a quadrilateral ABCD.

AD = 10 cm, angle BAD = 30° and angle ABD = angle BDC = 90°.

The ratio of length BD to length DC is 1: 2.4.

Work out length BC. You must show your working.

A, B, C and D are points on the circumference of a circle.

EF is the tangent to the circle at D.

Angle BDF = 70°.

The ratio angle BCD: angle CBD is 5: 2.

Work out angle CBD. You must show your working.

Azmi, Beth and Callum share a flat.

The monthly rent is £760. They share the rent in the ratio 2: 3: 3.

How much does Beth pay for rent each month?

Azmi, Beth and Callum also share the fuel bill in the ratio 2: 3: 3. Callum pays £36 for fuel each month.

How much does Azmi pay for fuel each month?

A bag of sweets contains jellies, mints and toffees.

The ratio of jellies to mints is n: 2. The ratio of mints to toffees is 5: 3 n.

Work out the ratio of jellies to toffees. Give your answer in its simplest form.

Divide 72 in the ratio 4: 5.

In one year, Clara and Dave borrowed books from a library in the ratio 3: 7. Dave borrowed 35 books.

Work out the number of books borrowed by Clara.

Write each of the following ratios in their simplest form.

12: 15

600 g: 1.8 kg

The ratio 45 minutes to 3 hours 45 minutes can be written in the form 1: n.

Find the value of n.

Reece and Sarah share some money in the ratio 9: 16.

Reece says that Sarah gets more than 60% of this money.

Show that Reece is correct.

ABCD is a trapezium.

The perimeter of the trapezium is 56 cm. The ratio AD: AB: DC: BC = 5: 12: 6: 5.

Calculate the area of the trapezium. Show your working.

Bob makes dry concrete by mixing cement, sand and stone in the ratio 1: 2: 3 by weight. He buys the cement, sand and stone in bags as shown in this table.

He packs the dry concrete into 30 kg bags.

Bob buys just enough cement, sand and stone to make 50 bags of dry concrete.

Show that Bob buys 500 kg of sand.

Bob sells the 50 bags of dry concrete for a total of £396.

Calculate Bob’s percentage profit.

Tom buys a radio for £40. Later he sells it and makes a profit of 20%.

Tom says

The ratio of the price I paid for the radio to the price I sold the radio is 5: 6.

Show that Tom is correct.

Bob makes dry concrete by mixing cement, sand and stone in the ratio 1: 2: 3 by weight. He buys the cement, sand and stone in bags as shown in this table.

He packs the dry concrete into 30 kg bags.

Bob buys just enough cement, sand and stone to make 50 bags of dry concrete.

Show that Bob buys 500 kg of sand.

Bob sells the 50 bags of dry concrete for a total of £396.

Calculate Bob’s percentage profit.

A bag of sweets contains only mints, sherberts and toffees.

The ratio of the number of mints to sherberts is 2: 3. The ratio of the number of sherberts to toffees is 7: 5.

What fraction of the sweets are sherberts?

The diagram shows a kite, ABCD. AFE and CEF are equilateral triangles.

Write down a mathematical name for quadrilateral AFCE.

The ratio of angle DAE: angle EAF = 1: 4.

Work out angle x. Write on the diagram the values of any other angles you use in your working.

The scale 1 cm represents 25 m can be written in the form 1: k.

Find the value of k.

The scale drawing represents a harbour.

A boat leaves the harbour from point C and sails on a path that is equidistant from BC and CD. The harbour rules do not allow boats to sail within 75 m of point E.

Find by construction whether the path of the boat will follow the harbour rules. Show all your construction lines.

Delia, Edwin and Freya share some money in the ratio 5: 7: 8. Freya’s share is £1600.

How much money did they share?

Write 6: 14 as a ratio in its simplest form.

The ratio 20: 50 can be written in the form 1: n.

Find the value of n.

A bag contains some counters.

• There are 300 counters in the bag.

• There are only red, white and blue counters in the bag.

• The probability of picking a blue counter is

• The ratio of red counters to white counters is 2: 1.

Calculate the number of red counters in the bag.

The ratio 50 grams to 1 kilogram can be written in the form 1: n.

Find the value of n.

Delia, Edwin and Freya share some money in the ratio 5: 7: 8. Freya’s share is £1600.

How much money did they share?

An interior angle of an isosceles triangle is p ° and an exterior angle is q °.

It is given that q = 5 p.

Write the ratio p: q in its simplest form.

Work out the two different possible sets of angles for the isosceles triangle.

(b) Triangle 1:........ °,........ °,........ °

Triangle 2:........ °,........ °,........ °

A bag contains some counters.

• There are 300 counters in the bag.

• There are only red, white and blue counters in the bag.

• The probability of picking a blue counter is

• The ratio of red counters to white counters is 2: 1.

Calculate the number of red counters in the bag.

Write 3: 57 as a ratio in its simplest form.

Bob and Chris share some money in the ratio 2: 3. Bob receives £8.

Work out how much Chris receives.

Liu wants to decorate some cakes with shapes.

She has 140 shapes. Each shape is a star or a heart. The ratio of the number of stars: number of hearts is 4: 3. She wants to put 5 stars and 4 hearts on each cake.

How many cakes can Liu decorate? Show full working to support your answer.

Some biscuits contain only three ingredients: flour, butter and sugar.

• The ratio of flour to butter is 5: 4.

• The ratio of butter to sugar is 2: 1.

• The total weight of the flour, butter and sugar is 770 g.

Work out the weight of each of the ingredients.

The table shows the number of computers sold in Tom’s shop each quarter from 2015 to 2017.

Complete this graph using the information for 2017.

Tom adds the three results for quarter 1 and he adds the three results for quarter 4. Tom says

The ratio of the total number of computers sold in quarter 1 compared to quarter 4 is 2: 5.

Is he correct? Show your reasoning.

Make two comments about Tom’s sales over the period 2015 to 2017.

Tom predicts that he will sell more than 60 computers in the 4^th quarter of 2018.

What assumption has he made?

In a dance competition, two judges each award scores out of 30. The scatter diagram shows the scores awarded to the first 10 dancers.

Here are the scores for the next two dancers.

Plot their scores on the scatter diagram.

Dancers who are awarded a score of more than 20 by both judges receive a medal.

For the 12 dancers, express the ratio of medal winners to non-medal winners in its simplest form.

This chart shows the types of dance performed by the 12 dancers.

3 performed a street dance, 8 performed a jazz dance and 1 performed a tap dance.

Why is this diagram misleading?

This map shows part of a village.

Neil knows that Packer Street is 180 m long in real life.

Neil measures the map.

He says

Packer Street is 3.5 cm long. High Street is 11.2 cm long.

Therefore, I calculate that High Street is 576 m long in real life.

Use Neil’s figures to show that the answer to his calculation is correct.

Jodie measures the same map.

She says

I think Packer Street is longer than Neil’s measurement of 3.5 cm. Therefore, High Street must be longer than 576 m in real life.

Is Jodie’s reasoning correct? Show how you decide.

On another map, Packer Street is 2.4 cm long.

Express the scale of this map in the form 1: n.

In a village the ratio of males to females is 2: 1.

40% of the people in the village are right-handed males. 25% of the people in the village are right-handed females.

Show that the proportion of females who are right-handed is greater than the proportion of males

who are right-handed.

The table shows the number of computers sold in Tom’s shop each quarter from 2015 to 2017.

Complete this graph using the information for 2017.

Tom adds the three results for quarter 1 and he adds the three results for quarter 4. Tom says

The ratio of the total number of computers sold in quarter 1 compared to quarter 4 is 2: 5.

Is he correct? Show your reasoning.

Make two comments about Tom’s sales over the period 2015 to 2017.

Tom predicts that he will sell more than 60 computers in the 4^th quarter of 2018.

What assumption has he made?

The cumulative frequency graph shows information about the marks scored by a group of 80 students in a test.

Find the interquartile range.

The ratio of the number of students passing the test compared to failing the test is 4: 1. Find the minimum mark needed to pass the test.

In a dance competition, two judges each award scores out of 30. The scatter diagram shows the scores awarded to the first 10 dancers.

Here are the scores for the next two dancers.

Plot their scores on the scatter diagram.

Dancers who are awarded a score of more than 20 by both judges receive a medal.

For the 12 dancers, express the ratio of medal winners to non-medal winners in its simplest form.

This chart shows the types of dance performed by the 12 dancers.

3 performed a street dance, 8 performed a jazz dance and 1 performed a tap dance.

Why is this diagram misleading?

This map shows part of a village.

Neil knows that Packer Street is 180 m long in real life.

Neil measures the map.

He says

Packer Street is 3.5 cm long. High Street is 11.2 cm long.

Therefore, I calculate that High Street is 576 m long in real life.

Use Neil’s figures to show that the answer to his calculation is correct.

Jodie measures the same map.

She says

I think Packer Street is longer than Neil’s measurement of 3.5 cm. Therefore, High Street must be longer than 576 m in real life.

Is Jodie’s reasoning correct? Show how you decide.

On another map, Packer Street is 2.4 cm long.

Express the scale of this map in the form 1: n.

In a box of mixed nuts, the total number of almonds, cashews and peanuts is 1025. The ratio of almonds to cashews is 1: 3. The ratio of cashews to peanuts is 5: 7.

Calculate the number of cashews in the box.

Write 12: 54 as a ratio in its simplest form.

The ratio 400 g: 1 kg can be written in the form 1: n.

Find the value of n.

Amanda and Wim share some money in the ratio 2: 5. Wim receives £115.

Calculate how much money was shared.

Elise wants to divide a sum of money between Hannah and Adil in the ratio 2: 3.

Elise says: Hannah will get of the money.

Explain why Elise is not correct.

George has a different sum of money. He divides the money between Siobhan and Iwan. Iwan receives of the money. Write the ratio of the money that Siobhan receives to the money that Iwan receives.

A recipe for flapjacks uses only oats, butter and syrup, in the ratio 3: 2: 1.

Pirin makes 1.5 kg of flapjacks. He uses 600 g of butter.

Has Pirin followed this recipe? Show how you decide.

Using this recipe, 200 g of syrup are needed to make 10 flapjacks. Find the mass of oats needed to make 15 of these flapjacks.

A box contains only red, blue and green pens. The ratio of red pens to blue pens is 5: 9. The ratio of blue pens to green pens is 1: 4.

Calculate the percentage of pens that are blue.

The ratio 2 centimetres to 5 metres can be written in the form 1: n.

Find the value of n.

Jay, Sheila and Harry share £7200 in the ratio 1: 2: 5.

How much does Harry receive?

The diagram shows a cylinder and a cone.

The cylinder has radius 2 cm and height 9 cm. The cone has radius r cm and height h cm.

The ratio r: h is 1: 4. The volume of the cone is equal to the volume of the cylinder.

Work out the value of r.

A box contains only red, blue and green pens. The ratio of red pens to blue pens is 5: 9. The ratio of blue pens to green pens is 1: 4.

Calculate the percentage of pens that are blue.

Leo, Kush and Mai share some money in the ratio 3: 5: 8. Kush receives £750 more than Leo.

Calculate the total amount of money that they shared.

Maria mixes white paint and red paint in the ratio 2: 3. She makes a total of 15 litres of paint.

How much more red paint does she need to add to the mixture so that the ratio of white paint to red paint becomes 1: 5?

This pie chart shows how the employees of a business travel to work.

Find the ratio of the number of employees who cycle to work to the number of employees who walk to work. Give your answer in its simplest form.

80 employees travel to work by car.

Work out the number of employees who cycle to work and the number of employees who walk to work.

ABCD and PQRS are rectangles. O is the centre of both rectangles.

AC is a straight line passing through P, O and R. BD is a straight line passing through Q, O and S.

PQ = 6 cm and QR = 2 cm. The perimeter of rectangle ABCD is 40 cm.

Work out the length and width of rectangle ABCD.

The angles in a triangle are in the ratio 1: 2: 3.

Show that the triangle is a right-angled triangle.

The hypotenuse of the triangle is 15 cm long.

Calculate the length of the shortest side in the triangle.

There is a total of 250 men, women and children on a train. The ratio of men to women is 4: 5. The ratio of women to children is 10: 7.

How many men are on the train?

Lucy and Ben share £42. Lucy’s share is £30.

Write the ratio Lucy’s share: Ben’s share in its simplest form.

The ratio 2.5 metres to 70 centimetres can be written in the form 1: n.

Find the value of n.

Water flows at a steady rate from a tap. It takes 50 seconds to fill a 5 litre watering can from this tap.

The rate at which water flows from the tap is halved.

Complete.

Find the rate at which the water is now flowing from the tap. Give your answer in cubic centimetres per second (cm³/s).

Two bags each contain only red counters and yellow counters.

In Bag A, the ratio of red counters to yellow counters is 1: 4.

Sharon says

The proportion of the counters that are red is the same in both bags.

Explain why Sharon is not correct.

The number of counters in the two bags is the same.

Complete the table below to show how many counters of each colour could be in the bags.

In another bag, Bag C, the ratio of red counters to yellow counters is 3: 4. If 3 of the red counters are removed from Bag C, the ratio of red counters to yellow counters is 3: 5.

How many yellow counters are in Bag C?

PQRS is a square. G is the midpoint of PQ and H is the midpoint of QR. Triangle GHS is shaded.

Find the ratio shaded area: area of square in its simplest form. Show all your working.

Maria mixes white paint and red paint in the ratio 2: 3. She makes a total of 15 litres of paint.

How much more red paint does she need to add to the mixture so that the ratio of white paint to red paint becomes 1: 5?

The angles in a triangle are in the ratio 1: 2: 3.

Show that the triangle is a right-angled triangle.

The hypotenuse of the triangle is 15 cm long.

Calculate the length of the shortest side in the triangle.

There is a total of 250 men, women and children on a train. The ratio of men to women is 4: 5. The ratio of women to children is 10: 7.

How many men are on the train?

Two bags each contain only red counters and yellow counters.

In Bag A, the ratio of red counters to yellow counters is 1: 4.

Sharon says

The proportion of the counters that are red is the same in both bags.

Explain why Sharon is not correct.

The number of counters in the two bags is the same.

Complete the table below to show how many counters of each colour could be in the bags.

In another bag, Bag C, the ratio of red counters to yellow counters is 3: 4. If 3 of the red counters are removed from Bag C, the ratio of red counters to yellow counters is 3: 5.

How many yellow counters are in Bag C?

The ratio 20 minutes to 1 hour can be written in the form 1: n.

Find the value of n.

The scale on a map is 1: 25 000.

How many kilometres on the ground is represented by 6 cm on the map?

Kiri and Peter share some sweets in the ratio 6: 7.

What fraction of the sweets does Kiri receive?

Last year, Katie earned £16 200. Her total loan repayments were £6400.

Katie estimates that the ratio of her loan repayments to her earnings is approximately 3: 8.

Is she correct? Show your reasoning.

The population of a village is in the following ratios.

• men: children = 11: 3

• women: children = 5: 2

Find the ratio men: women. Give your answer in its simplest form.

There are 36 children in the village.

Find the total population of the village.

Complete this table of fractions, decimals and percentages.

Write 45% as a fraction in its simplest form.

Alan and Brian share a sum of money in the ratio 1: 4.

What fraction of the money does Alan receive?

Last year, Katie earned £16 200. Her total loan repayments were £6400.

Katie estimates that the ratio of her loan repayments to her earnings is approximately 3: 8.

Is she correct? Show your reasoning.

The population of a village is in the following ratios.

• men: children = 11: 3

• women: children = 5: 2

Find the ratio men: women. Give your answer in its simplest form.

There are 36 children in the village.

Find the total population of the village.

Of those students who study a language, study Spanish. Find the ratio of students who study Spanish to students who do not study Spanish.