Converting between units

Change 60 millimetres into centimetres.

A road has a length of 1.6 kilometres. The road is shown on a map with a scale of 1: 20 000 Work out the length, in centimetres, of this road on the map.

Change 3 weeks into days.

Jamie drives his van for 150 minutes. He stops for a rest. Jamie then drives for a further 75 minutes.

Show that Jamie drives for less than 4 hours in total.

A car travels for 2 hours at a steady speed of 65 mph.

Work out the distance the car travels.

27Metal rods are made from steel with density 8 g/cm³ Each metal rod has a volume of 1500 cm³ The maximum mass of metal rods that can be put on a trolley is 300 kg. Work out the greatest number of metal rods that can be put on the trolley.

Metal rods are made from steel with density 8 g/cm³ Each metal rod has a volume of 1500 cm³ The maximum mass of metal rods that can be put on a trolley is 300 kg. Work out the greatest number of metal rods that can be put on the trolley.

Elena’s height is 136 centimetres. George’s height is 1.2 metres. Elena’s height is greater than George’s height. How many centimetres greater?

In London, 2 kg of carrots cost £3.75 In New York, 5 lbs of carrots cost 4.90 US dollars. £1 = 1.20 US dollars 1 kg = 2.2 lbs In which city are carrots better value for money, London or New York? You must show how you get your answer.

A plane takes 2 hours 24 minutes to fly from Luton to Alicante. The plane flies a distance of 1512 kilometres. Work out the average speed of the plane. Give your answer in kilometres per hour.

_........ kilometres per hour

In London, 2 kg of carrots cost £3.75 In New York, 5 lbs of carrots cost 4.90 US dollars. £1 = 1.20 US dollars 1 kg = 2.2 lbs In which city are carrots better value for money, London or New York? You must show how you get your answer.

A plane takes 2 hours 24 minutes to fly from Luton to Alicante. The plane flies a distance of 1512 kilometres. Work out the average speed of the plane. Give your answer in kilometres per hour.

_........ kilometres per hour

Change 15 centimetres into millimetres.

Write 140 minutes in hours and minutes.

A map has a scale of 1: 25 000 On the map, a road has a length of 14 cm. Work out the real length of the road. Give your answer in kilometres.

You can use this graph to change between miles and kilometres.

kilometres

Change 10 miles into kilometres.

Rob drives 17 miles from Bridlington to Scarborough. He then drives 50 kilometres from Scarborough to Staithes.

What is the total distance Rob drives? Give your answer in miles.

The diagram shows a crate and a box.

The crate is 3 m by 1 m by 1.5 m. The crate is completely filled with boxes. Each box is 20 cm by 10 cm by 75 cm. Work out the number of boxes in the crate.

Change 5000 millilitres to litres.

On Monday, Lizzie cycled 36 kilometres in 3 hours.

Work out Lizzie’s average speed.

_........ kilometres per hour On Tuesday, Lizzie cycled 36 kilometres at an average speed of 16 kilometres per hour. Lizzie says that the total time she cycled on Monday and Tuesday was less than 5 hours 20 minutes.

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

You can use this graph to change between ounces and grams.

Change 6 ounces to grams.

Change 1 kg to ounces.

Change 800 centimetres to metres.

There are 8 episodes in a TV series. Each episode lasts 45 minutes. Work out the total time that the 8 episodes last. Give your answer in hours.

A paddling pool is in the shape of a cylinder.

The pool has radius 100 cm. The pool has depth 30 cm. The pool is empty. It is then filled with water at a rate of 250 cm³ per second. Work out the number of minutes it takes to fill the pool completely. Give your answer correct to the nearest minute. You must show all your working.

A paddling pool is in the shape of a cylinder.

The pool has radius 100 cm. The pool has depth 30 cm. The pool is empty. It is then filled with water at a rate of 250 cm³ per second. Work out the number of minutes it takes to fill the pool completely. Give your answer correct to the nearest minute. You must show all your working.

There are 3 litres of oil in a can. Jermaine uses 700 millilitres of the oil. Work out the amount of oil left in the can. Give your answer in millilitres.

Change 7 metres to centimetres.

The diagram shows an empty tank in the shape of a cylinder.

The cylinder has radius 15 cm and height 43 cm. Water flows into the tank at a rate of 0.47 litres per minute. Calculate the number of minutes it will take to completely fill the tank. Give your answer correct to the nearest minute.

The diagram shows an empty tank in the shape of a cylinder.

The cylinder has radius 15 cm and height 43 cm. Water flows into the tank at a rate of 0.47 litres per minute. Calculate the number of minutes it will take to completely fill the tank. Give your answer correct to the nearest minute.

Mandy buys a 12 kilogram bag of dog food. Mandy’s dog has 3 meals a day. She gives her dog 105 grams of dog food for each of these meals. How many complete weeks will the bag of dog food last? You must show all your working.

Riley travelled by car and by aeroplane. He travelled 143 miles by car at an average speed of 55 miles per hour. Riley then travelled for 5 hours and 20 minutes by aeroplane. Work out, in hours and minutes, Riley’s total travelling time.

Riley travelled by car and by aeroplane. He travelled 143 miles by car at an average speed of 55 miles per hour. Riley then travelled for 5 hours and 20 minutes by aeroplane. Work out, in hours and minutes, Riley’s total travelling time.

The floor plan of a house is drawn using a scale of 1: 50 On the plan, a room in the house has a floor area of 48 cm² Work out the real area of the floor of this room. Give your answer in m²

Change 9 metres into centimetres.

Packets of sweets are put into boxes.

Packet Box Each packet is a cuboid, 80 mm by 60 mm by 20 mm. Each box is a cuboid, 72 cm by 48 cm by 24 cm. Work out the greatest number of packets that can be put into each box.

Paulo drives at an average speed of 56 km / h for 1 hour 45 minutes. Work out the distance Paulo drives.

Change 4000 grams into kilograms.

25Lava flows from a volcano at a constant rate of 11.9 m³/s How many days does it take for 67 205 600 m³ of lava to flow from the volcano? Give your answer correct to the nearest day.

Lava flows from a volcano at a constant rate of 11.9 m³/s How many days does it take for 67 205 600 m³ of lava to flow from the volcano? Give your answer correct to the nearest day.

14Jenny drives from London to Swindon at an average speed of 54 miles per hour. She drives for 1 hours.

Work out the distance from London to Swindon.

Aleksy is using a map. The map has a scale of 1: 25 000 On the map a road has a length of 6 cm.

Work out the length, in kilometres, of the real road.

Change 53 centimetres to millimetres.

A race is measured to have a distance of 10.6 km, correct to the nearest 0.1 km. Sam runs the race in a time of 31 minutes 48 seconds, correct to the nearest second. Sam’s average speed in this race is Vkm/hour. By considering bounds, calculate the value of V to a suitable degree of accuracy. You must show all your working and give a reason for your answer.

Karina has 4 tanks on her tractor. Each tank is a cylinder with diameter 80 cm and height 160 cm.

The 4 tanks are to be filled completely with a mixture of fertiliser and water. The fertiliser has to be mixed with water in the ratio 1: 100 by volume. Karina has 32 litres of fertiliser. 1 litre = 1000 cm³ Has Karina enough fertiliser for the 4 tanks? You must show how you get your answer.

Change 8000 cm³ to m³

Change a speed of 180 km per hour to metres per second.

_........ metres per second

Karina has 4 tanks on her tractor. Each tank is a cylinder with diameter 80 cm and height 160 cm.

The 4 tanks are to be filled completely with a mixture of fertiliser and water. The fertiliser has to be mixed with water in the ratio 1: 100 by volume. Karina has 32 litres of fertiliser. 1 litre = 1000 cm³ Has Karina enough fertiliser for the 4 tanks? You must show how you get your answer.

Change 8000 cm³ to m³

Change a speed of 180 km per hour to metres per second.

_........ metres per second

Change 40 centimetres into millimetres.

This sign was in a doctor’s waiting room.

Work out the mean length of time for each missed appointment. Give your answer in minutes.

24Festival A will be in a rectangular field with an area of 80 000 m² The greatest number of people allowed to attend Festival A is 425 Festival B will be in a rectangular field 700 m by 2000 m. The greatest number of people allowed to attend Festival B is 6750 The area per person allowed for Festival B is greater than the area per person allowed for Festival A.

How much greater? Give your answer correct to the nearest whole number.

Callum says, “300 cm² is the same as 3 m² because there are 100 cm in 1 m so you divide by 100” Callum’s method is wrong.

Explain why.

In Spain, Sam pays 27 euros for 18 litres of petrol. In Wales, Leo pays £40.80 for 8 gallons of the same type of petrol. 1 euro = £0.85 4.5 litres = 1 gallon Sam thinks that petrol is cheaper in Spain than in Wales. Is Sam correct? You must show how you get your answer.

Festival A will be in a rectangular field with an area of 80 000 m² The greatest number of people allowed to attend Festival A is 425 Festival B will be in a rectangular field 700 m by 2000 m. The greatest number of people allowed to attend Festival B is 6750 The area per person allowed for Festival B is greater than the area per person allowed for Festival A.

How much greater? Give your answer correct to the nearest whole number.

Callum says, “300 cm² is the same as 3 m² because there are 100 cm in 1 m so you divide by 100” Callum’s method is wrong.

Explain why.

In Spain, Sam pays 27 euros for 18 litres of petrol. In Wales, Leo pays £40.80 for 8 gallons of the same type of petrol. 1 euro = £0.85 4.5 litres = 1 gallon Sam thinks that petrol is cheaper in Spain than in Wales. Is Sam correct? You must show how you get your answer.

Jessica runs for 15 minutes at an average speed of 6 miles per hour. She then runs for 40 minutes at an average speed of 9 miles per hour. It takes Amy 45 minutes to run the same total distance that Jessica runs. Work out Amy’s average speed. Give your answer in miles per hour.

Change 30 metres per second to kilometres per hour.

_........ kilometres per hour

Change 3 metres into centimetres.

Write 196 minutes in hours and minutes.

A train travels x miles in 2 hours.

Write down an expression, in terms of x, for the average speed of the train.

18Change 1 m² into cm²

A water tank is empty. Anil needs to fill the tank with 2400 litres of water. Company A supplies water at a rate of 8 litres in 1 minute 40 seconds. Company B supplies water at a rate of 2.2 gallons per minute. 1 gallon = 4.54 litres Company A would take more time to fill the tank than Company B would take to fill the tank. How much more time? Give your answer in minutes correct to the nearest minute.

A water tank is empty. Anil needs to fill the tank with 2400 litres of water. Company A supplies water at a rate of 8 litres in 1 minute 40 seconds. Company B supplies water at a rate of 2.2 gallons per minute. 1 gallon = 4.54 litres Company A would take more time to fill the tank than Company B would take to fill the tank. How much more time? Give your answer in minutes correct to the nearest minute.

The diagram shows two points, A and B, on a map.

Scale: 1 to 25 000

Find the bearing of B from A.

Work out the real distance between A and B. Give your answer in kilometres.

Jamil makes a drink by mixing 1 part of orange squash with 9 parts of water. He uses 750 millilitres of orange squash. Jamil is going to put the drink he has mixed into 1 litre bottles. Work out the greatest number of 1 litre bottles that Jamil can completely fill.

This scale can be used to change between kilometres and miles.

Use the scale to change 40 kilometres to miles.

Here is an approximate rule to change from kilometres to miles.

Use this approximate rule to change 40 kilometres to miles.

Compare your answer to part (b) with your answer to part (a).

Change 300 centimetres into metres.

Andy cycles a distance of 30 km at an average speed of 24 km/h. He then runs a distance of 12 km at an average speed of 8 km/h. Work out the total time Andy takes. Give your answer in hours and minutes.

Andy cycles a distance of 30 km at an average speed of 24 km/h. He then runs a distance of 12 km at an average speed of 8 km/h. Work out the total time Andy takes. Give your answer in hours and minutes.

Change 4 kilometres into metres.

Write 37 cm³ in mm³

Nimer was driving to a hotel. He looked at his Sat Nav at 13 30

Nimer arrived at the hotel at 14 48

Work out the average speed of the car from 13 30 to 14 48 You must show all your working.

Write 37 cm³ in mm³

Nimer was driving to a hotel. He looked at his Sat Nav at 13 30

Nimer arrived at the hotel at 14 48

Work out the average speed of the car from 13 30 to 14 48 You must show all your working.

Write 180 minutes in hours.

The length of a line is x centimetres. Write down an expression, in terms of x, for the length of the line in millimetres.

Change 1756 grams to kilograms.

Machine A and machine B both make car parts. Machine A makes 6 parts every 10 minutes. Machine B makes 13 parts every 15 minutes. On Monday machine A makes parts for 12 hours machine B makes parts for 10 hours Work out the total number of parts made by the two machines on Monday.

A container is in the shape of a cuboid.

The container is full of water. A cup holds 275 ml of water. What is the greatest number of cups that can be completely filled with water from the container?

A container is in the shape of a cuboid.

The container is full of water. A cup holds 275 ml of water. What is the greatest number of cups that can be completely filled with water from the container?

Change 1.5 kilometres to metres.

In October Sally drove 560 miles in her car. The car travelled 34.5 miles for each gallon of petrol used. Petrol cost £1.08 per litre. 1 gallon 4.55 litres. Work out the cost of the petrol the car used in October.

The density of ethanol is 1.09 g/cm³ The density of propylene is 0.97 g/cm³ 60 litres of ethanol are mixed with 128 litres of propylene to make 188 litres of antifreeze. Work out the density of the antifreeze. Give your answer correct to 2 decimal places.

A plane travels at a speed of 213 miles per hour.

Work out an estimate for the number of seconds the plane takes to travel 1 mile.

Is your answer to part (a) an underestimate or an overestimate? Give a reason for your answer.

Change 4560 g into kg.

Change 7.3 m into mm.

Shaun is 1.88 m tall.

David is 6 cm taller than Shaun.

How tall is David?

Lara is a skier.

She completed a ski race in 1 minute 54 seconds. The race was 475 m in length.

Lara assumes that her average speed is the same for each race.

Using this assumption, work out how long Lara should take to complete a 700 m race. Give your answer in minutes and seconds.

Lara’s average speed actually increases the further she goes.

How does this affect your answer to part (a)?

Change 35 cm to mm.

Change 7700 millilitres to litres.

Change 0.32 kilograms to grams.

This is part of a bus timetable between Bury and Manchester.

How many minutes should the 08 25 bus take to go from Bury to Manchester?

Daniel goes from Whitefield to Manchester by bus.

Daniel takes 17 minutes to get from his house to the bus stop in Whitefield. He takes 15 minutes to get from the bus stop in Manchester to work.

Daniel has to get to work by 10 am. He leaves his house at 8.45 am.

Does Daniel get to work by 10 am? You must show all your working.

Change 365 cm into metres.

Change 2.7 kg into grams.

James and Peter cycled along the same 50 km route.

Peter started to cycle 5 minutes after James started to cycle. Peter caught up with James when they had both cycled 15 km.

James and Peter both cycled at constant speeds.

Work out Peter’s speed.

Thais has a large bottle of shampoo. There are 2 litres of shampoo in the large bottle.

Thais also has some empty small bottles. Each small bottle can be completely filled with 150 m l of shampoo.

How many small bottles can be completely filled with shampoo from the large bottle?

Chloe has a van.

She is going to use the van to deliver boxes. Each box is a cuboid, 40 cm by 30 cm by 35 cm.

The space for boxes in the van has maximum length 2.4 m maximum width 1.5 m maximum height 1.4 m

The space for boxes is empty. Chloe wants to put as many boxes as possible into the van.

She can put 3 boxes into the van in one minute. Assume that the space for boxes is in the shape of a cuboid.

Work out how many minutes it should take Chloe to put as many boxes as possible into the van.

The space for boxes might not be in the shape of a cuboid.

Explain how this could affect the time it would take Chloe to put as many boxes as possible into the van.

In London, 1 litre of petrol costs 108.9p In New York, 1 US gallon of petrol costs $2.83

1 US gallon = 3.785 litres £1 = $1.46

In which city is petrol better value for money, London or New York? You must show your working.

A gold bar has a mass of 12.5 kg.

The density of gold is 19.3 g/cm³

Work out the volume of the gold bar. Give your answer correct to 3 significant figures.

There are only blue counters, yellow counters, green counters and red counters in a bag. A counter is taken at random from the bag.

The table shows the probabilities of getting a blue counter or a yellow counter or a green counter.

Work out the probability of getting a red counter.

What is the least possible number of counters in the bag? You must give a reason for your answer.