The four operations

Samina works in a shop that sells pens. The table shows the number of blue pens and the number of red pens Samina sold in each of three months.

Work out the total number of blue pens and red pens Samina sold in June.

Samina says, “In these three months, in total, I sold more than twice as many blue pens as red pens.”

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

Here is a number machine.

Find the output when the input is 6

Find the input when the output is –11

15Work out 1.35 × 48

Four numbers add up to 76 One of the numbers is 13 The other three numbers are each the same number. Work out the value of each of the other three numbers.

Write down the value of the 7 in the number 49.715

Abi has some £10 notes and some £20 notes. The notes have a total value of £400 Abi has six £20 notes. Work out the number of £10 notes Abi has.

Use your calculator to work out the value of

Give your answer as a decimal. Write down all the figures on your calculator display.

Write your answer to part (a) correct to 2 significant figures.

Give your answer correct to 3 significant figures.

Work out 500 + 145

Javid hires a car for 10 days. He pays £45 for each day. He also pays £30 for insurance. Javid pays with ten £50 notes. Work out how much change he should get.

12Olly was asked to work out 5 – 3×4 Olly wrote 5 – 3 = 2 He then worked out 2×4 Explain what is wrong with Olly’s method.

Here is a number machine.

Find the output when the input is 11

Here is a different number machine.

When the input is 10, the output is 28

Complete this number machine.

18Work out 818.4 1.2

Give your answer as a mixed number.

Work out 818.4 1.2

Give your answer as a mixed number.

Find the number that is exactly halfway between –2 and 8

Jo uses beads to make bracelets. For each bracelet she uses 5 red beads and 7 white beads. Jo has 52 red beads and 80 white beads. Work out the greatest number of bracelets Jo can make. You must show all your working.

Junaid says that 20 is a square number because 10² = 20

Is Junaid correct? Give a reason for your answer.

Chloe says, “ When you divide an even number by an even number the answer is always an even number.”

Write down an example to show that Chloe is wrong.

20Use your calculator to work out the value of

Write down all the digits on your calculator display.

Use your calculator to work out the value of

Write down all the digits on your calculator display.

Write down the value of the 7 in the number 3721

Nina orders some items from a DIY shop. Here is her bill.

Complete all the missing information in the bill.

At the beginning of January, Jeff had £892.48 in his bank account. During January, Jeff had £4.47 interest added to his account paid £240 into his account spent £365.50 from his account.

How much money did Jeff have in his account at the end of January?

Harry works in a shop. From Monday to Friday his basic rate of pay is £8 per hour. On Saturday and Sunday, Harry’s rate of pay is 1 times his basic rate of pay. The table shows the number of hours Harry worked each day last week.

Work out Harry’s total pay last week.

Ryan buys 4 cakes at £1.30 each 2 identical tins of soup. Ryan pays with a £10 note. He gets £1.80 change. How much does Ryan pay for each tin of soup?

Here is a number machine.

Work out the output when the input is 13

Work out the input when the output is 28

Show that there is a number for which the output is the same as the input.

Work out –12 ÷ –4

Find the value of 2⁵

Write one pair of brackets in this calculation so that the answer is correct. 30 ÷ 3 + 2 − 4 = 2

14Work out 273 54

Kevin was asked to work out 2 × Here is his working and his answer.

Kevin’s answer is wrong.

What mistake has Kevin made?

Kevin was asked to work out 2 × Here is his working and his answer.

Kevin’s answer is wrong.

What mistake has Kevin made?

Anil has a job as a driver. He is paid for each mile he drives. He is also paid expenses. One week Anil writes down the distance readings from his car. Start of week: 4 7 2 4 1 miles End of week: 4 7 8 7 9 miles For this week, Anil is paid 47p for each mile he drives. He is also paid expenses of £80 Work out the total amount that Anil is paid. Give your answer in pounds.

Write down all the numbers on your calculator display.

Write your answer to part (a) correct to 2 significant figures.

Write down the value of the 3 in the number 62 837

Aisha was born in 1993 There was an election in the year of Aisha’s 18th birthday. There is an election every 5 years. Will there be an election in 2030? You must show how you get your answer.

Lucia is going on a skiing holiday. The cost of ski hire is £26 per day. The cost of a lift pass is £45 per day. The cost of ski lessons is £23.50 per hour. Lucia will pay for ski hire for 5 days a lift pass for 4 days ski lessons for 8 hours. Lucia has £500 Show that Lucia has enough money to pay for the total cost of ski hire, the lift pass and the ski lessons.

At the start of 2022 Kim invested some money in a savings account. The account paid 3.5% compound interest each year. At the end of 2022 interest was added to the account then Kim took £750 from the account. At the end of 2023 interest was added to the account then Kim took £1000 from the account. There was then £2937.14 in the account. Work out how much money Kim invested at the start of 2022 You must show all your working.

Work out 120 – 89

Chloe is making scrunchies. Chloe has a large number of hair bands. Each hair band costs 8p. She buys 100 g of wool for £3 Chloe uses 1 hair band and 5 g of wool to make each scrunchy. She makes as many scrunchies as she can. Work out the total cost of each scrunchy that she makes. Give your answer in pence.

Steve is buying a car. The car costs £12 000 Steve pays 25% of the cost as a deposit. He pays the rest of the cost in 20 equal monthly payments. How much is each monthly payment?

Give your answer as a mixed number.

18Work out 6.3×2.4

Work out 6.32.4

Curtis needs to buy some items for his sports club. Here are the prices.

Curtis needs to buy 5 footballs 6 hockey sticks 2 cricket bats 4 tennis balls. Curtis has £200 to spend. Show that Curtis can buy all the items he needs.

3 kg of flour costs £4.05 5 kg of flour and 6 kg of sugar cost £11.85 Work out the cost of 2 kg of flour and 5 kg of sugar.

Give your answer as a decimal. Write down all the figures on your calculator display.

Write your answer to part (a) correct to 2 decimal places.

Write down the value of the 9 in the number 27.963

Miklos is swimming lengths of a swimming pool. Each length of the pool is 25 m. Miklos has swum 178 lengths of the pool. He wants to swim a total distance of 8050 m. Calculate how many more lengths Miklos needs to swim.

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.

Work out – 9 + 5

Max sees this special offer in a shop. Buy one large plate and get one small plate for half the normal price.

The normal price of a large plate is £2 The normal price of a small plate is 80p Max wants to buy 6 large plates and 6 small plates using this offer. He has £15 Has Max got enough money? You must show how you get your answer.

A total of 700 tickets were on sale for a football match. 452 of the tickets were sold.

How many tickets were not sold?

For a different football match, 297 tickets were sold for £9.50 each. 399 tickets were sold for £19.50 each.

Work out an estimate for the total amount of money paid for these tickets. You must show all your working.

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

Give your answer as a fraction in its simplest form.

20Work out 8.46 0.15

Give your answer as a mixed number.

Work out 8.46 0.15

Give your answer as a mixed number.

The table shows information about the weights of the people in a hotel lift.

Show that the total weight of the people in the lift is less than 1200 kg.

Asha buys 180 cans of cola. The cans are sold in packs. There are 12 cans in each pack. Each pack costs £3

Work out the total cost of the cola Asha buys.

Ethan buys a box of 24 cans of lemonade for £7 There are 330 ml of lemonade in each can.

Work out the cost of 100 ml of lemonade. Give your answer correct to the nearest penny.

Write down all the figures on your calculator display.

Work out the value of the reciprocal of 0.625

Write down all the figures on your calculator display.

Work out the value of the reciprocal of 0.625

Write the number three thousand one hundred and seven in figures.

Gabriel thinks of a number. He multiplies his number by 5 and then adds 7 His answer is 72 What number did Gabriel think of?

Work out 20 ÷ (3 + 2)

Fay is planning a trip to a theme park for 1 adult and 2 children. These are the costs for the trip. Total cost of petrol £23 Tickets to theme park £33 each adult £24.50 each child Meals £15 each adult £10 each child Fay has £200 to spend. She pays all the costs. How much money does she have left?

A shop sells jars of coffee. Each jar of coffee costs £4 Michael has £23

Work out the greatest number of jars of coffee Michael can buy.

In a sale on Wednesday, jars of coffee are sold at half price. Michael thinks that he can now buy exactly twice the number of jars of coffee for £23

Is Michael correct? You must give a reason for your answer.

Give your answer as a mixed number.

22Work out 0.004 0.32

Give your answer as a mixed number.

Work out 0.004 0.32

Here are four cards. There is a number on each card.

Write down the smallest 4-digit even number that can be made using each card only once.

Myles writes down the distance readings from his car at the start and end of a journey. Start of journey 1 2 4 6 8 miles

End of journey 1 2 8 4 5 miles Myles knows that the cost of petrol for this journey is 13p per mile. Work out the total cost of the petrol used for this journey. Give your answer in pounds.

Find the value of the reciprocal of 0.8

x = 4700 correct to 2 significant figures.

Complete the error interval for x.

Write down the value of the 2 in the number 12 345

Four students play a game. The table shows the number of points each student has.

Barbara has more points than Danesh.

How many more?

Work out the mean number of points.

Write 87 569 correct to 3 significant figures.

Give your answer as a decimal.

Write down the value of the 6 in the number 16 007

Simon buys some candles. Each candle costs £2 Simon pays with a £20 note. He gets £6 change. Work out the number of candles Simon buys.

In Norway last year, the lowest temperature was −15°C. In Norway last year, the highest temperature was 42°C greater than the lowest temperature. Work out the highest temperature in Norway last year.

At the end of October, Fiona’s electricity meter reads 88 738 kWh. At the end of November, her electricity meter reads 89 198 kWh. Each kWh of electricity Fiona uses costs 16p Work out how much Fiona had to pay for the electricity she used in November.

Give your answer as a fraction in its simplest form.

Work out an estimate for the value of 92 × 1.63 You must show all your working.

Given that 2.96 × 3.2 = 9.472

find the value of 29.6 32

The diagram shows three identical rectangles A, B and C.

Work out the fraction of rectangle B that is shaded.

Write a fraction in the box to make the calculation correct.

Sonia wants to book a holiday. The holiday will cost £1428 Sonia will pay a deposit of £150 She will then pay the rest of the cost in 6 equal monthly payments. How much is each monthly payment?

Here is a number machine.

Work out the output when the input is 28

Here is a different number machine. The number machine is not complete.

When the input is 8, the output is 154

Complete the number machine.

The box below contains three mathematical symbols.

From the box, choose a symbol to make each of the following statements correct.

−2 × −3_........ −3 + 9

Nimra buys a 3 kg box of sweets for £17.60 She puts the sweets into bags to sell. Each bag contains 150 g of sweets. Nimra fills as many bags as possible. She will sell each bag for the same price. Nimra wants to make a profit of at least 35% Assuming she sells all the bags, what is the lowest price Nimra should charge for each bag?

The table shows the total number of apples sold and the total number of oranges sold in a shop in each of three weeks.

In total for the three weeks, more apples than oranges were sold. How many more?

Sinita wants to make 35 picture frames. She needs 4 nails for each frame. Sinita has 3 boxes of nails. There are 48 nails in each box. Has Sinita got enough nails to make all 35 frames? Show how you get your answer.

7 £42 is shared equally between 3 friends. How much does each friend get?

Danny buys, 1 loaf of bread for £1.20 1 bottle of milk for 70p 2 packets of cheese for £2.30 each packet Danny pays with a £10 note. He says, “I should get £3.30 change.” Is Danny correct? You must show how you get your answer.

Rachel records the temperature in her garden at noon each day. On Monday, the temperature was 5C. On Tuesday, the temperature was 10 less than the temperature on Monday. On Wednesday, the temperature was 3 greater than the temperature on Tuesday. Find the difference between the temperature on Monday and the temperature on Wednesday. You must show all your working.

3 kg of carrots cost £1.80 2 kg of carrots and 5 kg of potatoes cost a total of £3.45 Work out the total cost of 4 kg of carrots and 2 kg of potatoes. You must show all your working.

Work out 3.674.2

Work out 59.84 ÷ 1.6

Give your answer as a mixed number.

Work out 3.674.2

Work out 59.84 ÷ 1.6

Give your answer as a mixed number.

A baker has three bags of flour, A, B and C. Bag A and bag B contain the same amount of flour. Bag C contains 940 g of flour. In the three bags, there is a total of 2500 g of flour. Work out the amount of flour in bag A.

Alec needs to work out the value of 2 + 34 He writes

Alec is wrong. Explain why.

The incomplete table gives some information about the lengths of the planks of wood in Ben’s workshop.

The total length of these planks is 92 metres. Work out the number of planks of length 2 metres in Ben’s workshop.

On Monday, Sandy pays for 2 plane tickets, 7 nights in a hotel and 2 theme park tickets.

Show that Sandy pays more than 2500 dollars on Monday.

Corina has £300 to spend on books. Each book costs £4.85 Work out the greatest number of books Corina can buy.

Write down the value of the 7 in the number 8765

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.

12The diagram shows a number machine.

Find the output when the input is 7

Find the input when the output is 41

A machine fills bags with sweets. There are 4275 sweets. There are 28 sweets in each full bag. The machine fills as many bags as possible. How many sweets are left?

Karim buys 200 tiles. The tiles are sold in boxes. There are 25 tiles in each box. Each box of tiles costs £9.75 Work out the total cost of the boxes of tiles Karim buys.

Work out the value of

Work out the value of (6 − 2.5)(8 + 4)

Write down the reciprocal of 20

Write down the value of the 7 in the number 1074

Prasha has five blocks of wood.

The total weight of all five blocks of wood is 3 kilograms. 4 of the blocks of wood each have a weight of 650 grams.

Work out the weight, in grams, of the other block of wood.

Rehan is on holiday in the USA.

He has $200 to spend on clothes.

Rehan buys 1 pair of trainers costing $60 3 T-shirts costing $25 each.

He also wants to buy a jacket costing $80

Has Rehan got enough money to buy the jacket? You must show how you get your answer.

The trainers cost $60 The exchange rate is $1 = £0.749

Rehan says, “The trainers cost less than £40”

Rehan is wrong.

Using a suitable approximation, show working to explain why.

Give your answer as a mixed number.

Give your answer as a mixed number.

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.

Cornflakes are sold in two sizes of box.

Rae buys 3 small boxes of cornflakes and some large boxes of cornflakes. In total she buys 5850 g of cornflakes.

Work out the number of large boxes of cornflakes Rae buys.

Write down all the figures on your calculator display.

Write your answer to part (a) correct to 4 significant figures.

Write down all the figures on your calculator display.

Write your answer to part (a) correct to 4 significant figures.

Work out 10 (3 + 5)

Find the number that is exactly halfway between 7 and 15

Harry is planning a holiday for 4 people for 7 days. Here are the costs for the holiday for each person. Travel £150 Hotel £50 for each day Spending money £250 Work out the total cost of the holiday for 4 people for 7 days.

Work out 74 58

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.

The diagram shows a rectangular garden path.

120 cm

600 cm Wasim is going to cover the path with paving stones. Each paving stone is a square of side 30 cm. Each paving stone costs £2.50 Wasim has £220 to spend on paving stones. Show that he has enough money to buy all the paving stones he needs.

Give your answer as a fraction in its simplest form.

(2.3)⁶ = 148 correct to 3 significant figures.

Find the value of (0.23)⁶ correct to 3 significant figures.

Find the value of 5^–2

Write the number two million in figures.

Dave goes into a cafe and buys 2 cups of coffee and a piece of cake. Each cup of coffee costs £2.75 The cake costs £2.90 Dave pays with a £10 note. He thinks he will get more than £1.50 in change. Is Dave correct? You must show how you get your answer.

There are four types of counter in a bag. The table shows the number of each type of counter in the bag.

There are more green counters than red counters. How many more?

The table shows the costs of sending a parcel by the Express service and by the Rapid service.

Brendan has to send 12 parcels. It will be cheaper to send the parcels by the Express service than by the Rapid service.

How much cheaper?

Luke wants to send 21 parcels by the Express service. He does the calculation 20 £15 £300 to estimate the cost.

Explain why Luke’s calculation shows the actual cost will be more than £300

Give your answer as a decimal. Write down all the figures on your calculator display.

Give your answer correct to 3 significant figures.

Work out 3 5 + 7

Work out 2³

Write brackets () in this statement to make it correct.

Sue has 2 cats. Each cat eats of a tin of cat food each day.

Sue buys 8 tins of cat food.

Has Sue bought enough cat food to feed her 2 cats for 14 days? You must show how you get your answer.

Here are some fractions.

One of these fractions is not equivalent to

Which fraction?

(b) Work out

Write down the value of the 4 in the number 542.3

Here is a number machine.

Work out the output when the input is 8

Work out the input when the output is 28

Adrian is going to make concrete. He is going to use

180 kg of cement 375 kg of sand 1080 kg of stone

Cement, sand and stone are sold in bags.

Adrian already has

10 bags of cement 20 bags of sand 20 bags of stone

Work out what bags he needs to buy to make the concrete.

The diagram shows a floor in the shape of a trapezium.

John is going to paint the floor.

Each 5 litre tin of paint costs £16.99 1 litre of paint covers an area of 2 m²

John has £160 to spend on paint.

Has John got enough money to buy all the paint he needs? You must show how you get your answer.

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

56.3 +_........ = 100

8 2 pens cost £2.38 5 folders cost £5.60

Ben wants to buy 20 pens and 20 folders. He only has £50

Does Ben have enough money to buy 20 pens and 20 folders? You must show how you get your answer.

Annie sold

45 books at £1.20 each 34 candles at £1.50 each some calendars at 90p each

She got a total of £150

Work out how many calendars Annie sold.

Trevor buys a boat. The cost of the boat is £14 200 plus VAT at 20%

Trevor pays a deposit of £5000 He pays the rest of the cost in 10 equal payments.

Work out the amount of each of the 10 payments.

Write 7357 correct to 3 significant figures.

Write down all the figures on your calculator display.

8 3 kg of meat costs 54 Nina buys 2 kg of the meat.

Work out how much Nina pays.

Tim and three friends go on holiday together for a week.

The 4 friends will share the costs of the holiday equally.

Here are the costs of the holiday.

1280 for 4 return plane tickets 640 for the villa 220 for hire of a car for the week

Work out how much Tim has to pay for his share of the costs.

A piece of wire is 240 cm long.

Peter cuts two 45 cm lengths off the wire. He then cuts the rest of the wire into as many 40 cm lengths as possible.

Work out how many 40 cm lengths of wire Peter cuts.

Give your answer as a mixed number in its simplest form.

Give your answer as a mixed number in its simplest form.

Write down a 6 digit number that has 4 as its thousands digit. You can only use the digit 4 once.

Neil buys 30 pens, 30 pencils, 30 rulers and 30 pencil cases.

What is the total amount of money Neil spends?

David has twice as many cousins as Becky. Becky has twice as many cousins as Nishat.

Nishat has 6 cousins.

How many cousins does David have?

Find the value of (3.54 – 0.96)² – 4.096

Jenny is asked to find the value of 12 – 2 4

Here is her working.

Jenny’s answer is wrong.

Explain what Jenny has done wrong.

Rehan is asked to find the range of the numbers 3 1 8 7 5

Here is his working. Range = 5 – 3 = 2

This is wrong.

Explain why.

Work out 2 + 7 10

Here are four numbers.

–9 –2 2 9

Write one of these numbers in each box to make a correct calculation.

Jacqui wants to work out 3480 ÷ 5

She knows that 3480 ÷ 10 = 348

Jacqui writes 3480 ÷ 5 = 174

because 10 ÷ 5 = 2

and
348 ÷ 2 = 174

What mistake did Jacqui make in her method?

There are 30 children in a nursery school. At least 1 adult is needed for every 8 children in the nursery.

Work out the least number of adults needed in the nursery.

2 more children join the nursery.

Does this mean that more adults are needed in the nursery? You must give a reason for your answer.

Here are two fractions.

Work out which of the fractions is closer to 1 You must show all your working.

Berenika wants to buy 35 T-shirts.

Each T-shirt costs £5.80 Berenika does the calculation 40 6 = 240 to estimate the cost of 35 T-shirts.

Explain how Berenika’s calculation shows the actual cost will be less than £240

There is a special offer.

Work out the actual cost of buying 35 T-shirts using the special offer.

Give your answer in standard form.

Write down the value of 2^–3

Ken buys some fruit.

He buys apples, bananas, peaches and oranges. Ken buys

4 apples weighing 125 g each 2 bananas weighing 170 g each 3 peaches weighing 135 g each

Each orange has a weight of 90 g.

The fruit has a total weight of 1.785 kg.

Work out how many oranges Ken buys.

Jane wants to buy 15 tomatoes. She asks for 1 kg of tomatoes at a shop. Jane assumes that each tomato has a weight of 75 g.

If Jane’s assumption is correct, will she get 15 tomatoes? You must show how you get your answer.

If Jane’s assumption is not correct, could she get 15 tomatoes? Justify your answer.

Write down all the figures on your calculator display.

Write your answer to part (a) correct to 2 decimal places.

The table gives information about the prices of cinema tickets.

Mr Edwards and his 3 children go to the cinema.

It is cheaper for Mr Edwards to buy 1 family ticket rather than 4 separate tickets.

How much cheaper?

The film starts at 6.45 pm. The film lasts 102 minutes.

What time does the film finish?

Find the value of the reciprocal of 1.6 Give your answer as a decimal.

Jess rounds a number, x, to one decimal place. The result is 9.8

Write down the error interval for x.

Find the value of the reciprocal of 1.6 Give your answer as a decimal.

Jess rounds a number, x, to one decimal place. The result is 9.8

Write down the error interval for x.

Fahima buys

2 packets of bread rolls costing £1.50 for each packet 1 bottle of ketchup costing £1.60 3 packets of sausages

Fahima pays with a £10 note. She gets 30p change.

Fahima works out that one packet of sausages costs £2.30

Is Fahima right? You must show how you get your answer.

5 tins of soup have a total weight of 1750 grams. 4 tins of soup and 3 packets of soup have a total weight of 1490 grams.

Work out the total weight of 3 tins of soup and 2 packets of soup.

Work out 54.6 × 4.3

The table shows the lengths of five rivers.

Write down the rivers in order of length.

Start with the shortest river.

Ami says,

“The River Thames is more than three times as long as the River Don.”

Show that Ami is correct.

Here are four digits.

5 6 1 9

Write down the smallest possible two digit number that can be made with two of the digits.

Write down the three digit number closest to 200 that can be made with three of the digits.

Joanne wants to buy a dishwasher.

The dishwasher costs £372

Joanne will pay a deposit of £36 She will then pay the rest of the cost in 4 equal monthly payments.

How much is each monthly payment?