Number

Work out \(2\frac{3}{4} - 1\frac{5}{6}\).

Work out \(\frac{3}{5} \div \frac{9}{10}\).

In a sale, the price of the jacket is reduced by 15%. Work out the sale price.

The shop bought the jacket for $40 and sells it at the normal price of $64. Work out the percentage profit.

Write 0.35 as a fraction in its simplest form.

Write \(\frac{3}{8}\) as a percentage.

Write these numbers in order of size, starting with the smallest.
0.38    \(\frac{3}{8}\)    37%    \(\frac{7}{20}\)

45% of the students walk to school. Work out how many students walk to school.

126 students cycle to school. Work out the percentage of students who cycle to school.

All the other students travel by bus. Write the fraction of students who travel by bus in its simplest form.

Work out the interest Kofi earns in 4 years.

Work out the total amount in the account after 4 years.

Write 0.0047386 correct to 3 significant figures.

By rounding each number to 1 significant figure, estimate the value of \(\frac{48.7 \times 3.12}{0.198}\).
Show all your working.

Work out how much Chen receives.

Chen then gives one quarter of his share to Amira.
Find the new ratio Amira : Ben : Chen in its simplest form.

Write down the lower bound and the upper bound of the side length.

Calculate the upper bound of the perimeter of the tile.

Change €250 into dollars.

Change $500 into euros. Give your answer correct to the nearest cent.

A jacket costs €85 in Paris and $95 in New York.
Find which city sells the jacket more cheaply and by how many dollars.

Work out the mass of flour needed for 15 muffins.

Lina has 7 eggs and plenty of every other ingredient.
Find the greatest number of muffins she can make.

all the prime numbers,

all the square numbers,

a cube number,

a multiple of 13.

Write 360 as a product of its prime factors. Give your answer in index form.

Find the smallest positive integer k such that 360k is a square number.

List all the factors of 18.

Find the highest common factor (HCF) of 18 and 24.

Find the lowest common multiple (LCM) of 18 and 24.

Find the next time both buses leave together.

Find how many times the two buses leave together from 08 00 to 13 00, including both of these times.

From this list, write down the irrational numbers.

√5    0.25    2π    √49    \(\frac{7}{9}\)    ∛27

Write down an integer between √50 and √70.

Write down the prime number between 40 and 50 that is 1 more than a multiple of 6.

\(x^5 \times x^3\)

\(\frac{y^{12}}{y^4}\)

\((2p^3)^4\)

Write 0.000 407 in standard form.

Write 6.3 ×10⁵ as an ordinary number.

Work out (4 ×10⁶) × (7 ×10⁻²). Give your answer in standard form.

Write down the value of \(7^0\).

Find the value of \(3^{-2}\) as a fraction.

Find the value of \(n\) when \(2^n = \frac{1}{32}\).

Write 12 and 18 each as a product of prime factors.

Find how many seconds pass before the lamps next flash together.

Calculate the sale price.

A sales tax of 23% is then added to the sale price. Calculate the price the customer pays.

What fraction of the trail is still to be run after two hours?

The distance still to be run is 15 km. Work out the total length of the trail.

Write 1.2 × 10⁻⁷ as an ordinary number.

Particles are placed side by side in a straight line to make a length of 3 mm. Calculate how many particles are needed.

A batch of the mix has a total mass of 56 kg. Calculate the mass of sand in the batch.

A different batch contains 90 kg of gravel. Calculate the mass of cement in this batch.

Write down the two prime numbers.

Write down the two square numbers.

Write down the cube number.

Write 36 as a product of prime factors.

A jacket costs €85. In the sale its price is reduced by 15%. Calculate the sale price.

A pair of boots has a sale price of €36 after a reduction of 20%. Calculate the original price.

Calculate the smallest share.

The exchange rate is €1 = £0.86. Convert €126 to pounds.

Show how this value can be estimated by rounding each number to 1 significant figure.

Calculate the value, giving your answer to 3 significant figures.

Write down the two prime numbers in the list.

Write 84 as a product of its prime factors.

Calculate the fraction of the route ridden in the first two days. Give your answer as a fraction in its simplest form.

Calculate the distance still to ride on the third day.

Calculate the percentage increase in power drawn.

A new design reduces the 736 kW by 8%. Calculate the new power drawn. Give your answer correct to 3 significant figures.

Write 0.0000472 in standard form.

Calculate the total mass of all the shards. Give your answer in standard form.

Write 18 and 30 as products of prime factors.

Find the lowest common multiple of 18 and 30.

Find how many seconds after 08:00:00 the lamps flash together for the third time.

Calculate the mass of fat in the sample.

Find the fraction of the sample that is neither fat nor protein.

Write the fraction of protein as a percentage.

A jacket costs €240. In a sale the price is reduced by 15%. Calculate the sale price.

Boots have a sale price of €144, which is 20% less than the original price. Calculate the original price.

Calculate the time taken for a signal to travel from the satellite to the ground station. Give your answer in standard form.

A file of \(4.8 \times 10^{9}\) bytes downloads at a steady rate of \(6.0 \times 10^{6}\) bytes per second. Calculate the time taken. Give your answer in standard form.

Write 18 as a product of its prime factors.

Find the lowest common multiple of 12, 18 and 30.

After 08:00, the three instruments send bursts together again several times up to and including 20:00 on the same day. Work out how many times this happens.

Calculate the toll before the increase.

Write down the increase in the toll, in euros.

On one day 3250 cars pay the new toll. Calculate the total toll collected from these cars.

Calculate the time taken for a signal to reach Earth from the probe. Give your answer in seconds in standard form.

Write this time in minutes, correct to 3 significant figures.

Write down the prime number in the list.

Write down the number in the list that is both a square number and a cube number.

Find the sum of the identification numbers that are multiples of 3.

From the list, write down the prime number.

From the list, write down the number that is both a square number and a cube number.

Write 36 as a product of its prime factors.

Write 18 and 24 each as a product of prime factors.

Find the lowest common multiple of 18 and 24.

At what time do the roasters next finish a batch together?

How many batches does roaster A finish between 08:00 and that time, counting the batch at the later time but not the one at 08:00?

Work out the fraction of the cables inspected over the two days.

Write down the fraction of the cables not yet inspected.

The bridge has 240 cables. Work out how many have not been inspected.

Calculate the new price per kilogram.

Roasting makes the beans lose 18% of their mass. Calculate the mass of roasted coffee obtained from 25 kg of green beans.

The roasted coffee is packed into bags that each hold 250 g. How many bags can be filled completely?

Find the fraction of the job completed in the first two hours.

Find the fraction of the job still to be done.

Write your answer to part (b) as a decimal.

Calculate the sale price.

Calculate the shop's percentage profit on the cost price when the dress is sold at the sale price.

Write down all the prime numbers in the list.

Write 36 as a product of its prime factors.

Find the highest common factor (HCF) of 36 and 90.

Write 84 as a product of its prime factors.

Find the highest common factor (HCF) of 84 and 126.

Find the smallest number of boxes needed.

Find the lowest common multiple (LCM) of 40 and 50.

They are next together at the starting end after a whole number of laps for each swimmer. Work out how many laps Ben has swum by then.

Work out the number of offshore turbines.

20% of the onshore turbines are shut down for maintenance. Work out how many onshore turbines are shut down.

Write the number of turbines shut down as a percentage of all 48 turbines.

Write 4 500 000 in standard form.

Calculate the electricity generated in 30 days. Give your answer in standard form.

Work out how many days the wind farm takes to generate 1.8 × 10⁷ kWh.

Write down the prime number in the list.

Write down the square number in the list.

Find the highest common factor (HCF) of 12 and 18.

Work out the distance she rides in the morning.

Work out the fraction of the route that she has still to ride. Give your answer as a fraction in its simplest form.

Write your answer to part (b) as a percentage. Give your answer correct to 1 decimal place.

Write 48 000 000 000 in standard form.

Calculate the total number of bytes the drives can store. Give your answer in standard form.

A different data centre must store 1.8 × 10¹⁵ bytes using the same type of drive. Work out the smallest number of drives needed.

The thickness of the shard is 0.004 862 m. Write this correct to 2 significant figures.

A density index is S = (19.8 × 4.07) ÷ 0.52. Estimate the value of S by rounding each number to 1 significant figure. Show your working.

Calculate the exact value of S. Give your answer correct to 3 significant figures.

Write down the cube number in the list.

Write 24 as a product of prime factors.

Write down the odd multiple of 7 in the list.

Work out the mass of cod.

Write the mass of haddock as a fraction of the whole catch. Give your answer in its simplest form.

Work out the speed of the robot in metres per second.

Work out the distance the robot travels in 1 minute 30 seconds at this speed.

The diameter of the thread is 0.000 045 m. Write this in standard form.

One spool holds 2.5 × 10³ m of thread. The factory uses 6 × 10² spools. Work out the total length of thread. Give your answer in standard form.

Write your answer to part (b) in kilometres, in standard form.

Write down the two prime numbers in the list.

Write down the cube number in the list.

Write 36 as a product of prime factors.

Work out the mass lost during roasting.

Write down the mass of roasted coffee.

The roasted coffee is packed into bags that each hold 0.3 kg. Work out the number of bags that can be filled completely.

Write 5 600 000 000 in standard form.

Work out the time, in seconds, for a signal to travel from the probe to Earth. Give your answer in standard form.

Change your answer to part (b) into hours. Give your answer correct to 3 significant figures.

Write 18 as a product of prime factors.

Find the highest common factor (HCF) of 12 and 18.

Both crews visit on the same day. Find the number of days until they next visit on the same day.

Write 12 and 18 each as a product of prime factors.

Find the highest common factor (HCF) of 12 and 18.

Find the next time after 06:00 when both services depart together.

Find the fraction of the field planted with oats.

Write the fraction of the field planted with wheat as a percentage.

Work out the area planted with oats.

Find the guitarist's share.

Write the drummer's share as a percentage of the total.

Write 8.0 × 10² as an ordinary number.

Calculate the time for the flight in hours.

Write this time in seconds, in standard form.

Write down the prime number from the list.

Write down the cube number from the list.

Write 36 as a product of its prime factors.

Find the highest common factor (HCF) of 36 and 45.

Write down the lower bound and the upper bound of the length of the pier.

Write down the upper bound of the length of the rope.

Estimate how many ropes of length 4.6 m fit along the pier by rounding each length to 1 significant figure.

Work out the total cost of 3 dives on one day, including one day of equipment hire.

The exchange rate is £1 = €1.16. Convert your answer to part (a) into pounds. Give your answer to the nearest penny.

Write down the prime numbers in the list.

Write down the square number in the list that is also a multiple of 6.

Write 84 as a product of its prime factors.

Calculate the distance she runs on Monday.

Calculate the distance she runs on Tuesday.

Find the fraction of the weekly distance still to be run after Tuesday. Give your answer in its simplest form.

Write 2⁻³ as a fraction.

Find the value of n in 5ⁿ ÷ 5² = 5⁴.

Work out 4⁻² × 4³.

Estimate the value of the expression by rounding each number to 1 significant figure.

Work out the value of the expression. Give your answer correct to 3 significant figures.

State whether your estimate in (a) is greater or less than the value in (b).

Work out the monthly rent before the increase.

The following year, the monthly rent of $1008 decreased by 12%. Work out the new monthly rent.

Work out the overall percentage change from the original rent to the rent in part (b). State whether it is an increase or a decrease.

Show that the fraction of her pay that she spends on food is \(\frac{3}{20}\).

Work out the fraction of her pay that is left after rent and food.

Amira has $360 left after paying for rent and food. Work out her monthly pay.

Work out the value of the car after 3 years.

Work out the total percentage of the original value that the car has lost after 3 years.

Work out the deposit.

Work out the total cost of buying the television on hire purchase.

Work out how much more the hire purchase cost is than the cash price, as a percentage of the cash price.

Work out how many days 12 workers would take to build the same wall.

The wall must be built in 6 days.
Find how many workers are needed in addition to the original 8.

Calculate the value of her investment at the end of 5 years. Give your answer correct to the nearest cent.

Sam also invests $4500 for 5 years, but at r% per year simple interest.
At the end of 5 years Sam's investment has the same value as Priya's.
Find r.

Find the number of red counters in the bag.

Some red counters are now removed from the bag. The ratio red : blue becomes 1 : 2.
Find how many red counters are removed.

Without using your calculator, estimate the value of E by rounding each number to 1 significant figure. Show your working.

Use your calculator to find the value of E. Give your answer correct to 3 significant figures.

Calculate the percentage error in your estimate, using the unrounded value of E.

Find the highest common factor (HCF) of A and B. Give your answer as an ordinary number.

Find the lowest common multiple (LCM) of A and B. Give your answer as an ordinary number.

Find the smallest positive integer n such that An is a cube number.

Find the largest possible side length of a tile.

Find the number of tiles needed when this largest tile is used.

Find the greatest number of bags that can be made.

Find the total number of sweets in each bag.

"The sum of any two prime numbers is always even."

"For every positive integer n, the number n² + n + 1 is prime."

"For every positive integer n, the number n² + n is even."

Find the lowest common multiple of 6, 8 and 15.

Find the smallest square number that is a multiple of 6, 8 and 15.

Find the smallest integer greater than 1000 that leaves a remainder of 1 when divided by 6, by 8 and by 15.

Write these numbers in order of size, starting with the smallest.
4.1 ×10⁻³    0.0039    3.9 ×10⁻⁴    0.04

Work out (8.4 ×10⁷) ÷ (2.1 ×10⁻³). Give your answer in standard form.

Work out 3.2 ×10⁴ + 5 ×10³. Give your answer in standard form.

Calculate the average number of people per km² of land.

On average, each person produces 0.74 kg of waste per day.
Calculate the total waste produced by the world's population in one year of 365 days. Give your answer in kilograms, in standard form.

1 tonne = 1000 kg. Write your answer to part (b) in tonnes, in standard form.

Calculate the percentage increase in appointments.

In the third year the number of appointments falls by 15% from the second year. Calculate the number of appointments in the third year.

Write 7 462 correct to 2 significant figures.

Estimate the value of N by rounding each number in the calculation to 1 significant figure.

Calculate the exact value of N.

Calculate the mass of filament needed to print 10 of these parts.

A spool holds 1.2 kg of filament. Calculate the greatest number of whole parts that can be printed from one spool.

Write 12 and 20 as products of prime factors.

Find the highest common factor of 12 and 20.

Find the number of seconds after 06:00:00 at which the two lights next flash together.

Find the fraction of the whole farm used for access roads.

Find the fraction of the whole farm that is grassland.

Calculate the area of grassland.

A virus particle has diameter 1.25 × 10⁻⁷ m. Calculate how many such particles placed side by side in a straight line would span 5 × 10⁻⁵ m.

In a city of 8.4 × 10⁶ people, 0.35% are infected. Calculate the number infected. Give your answer in standard form.

Find the number of seconds until they are next level on the line together.

After the ride, the club packs 72 bottles and 90 energy bars into identical boxes. Every box has the same number of bottles and the same number of bars, with none left over. Find the greatest possible number of boxes.

Write down the lower bound and the upper bound of the length.

A bracelet has a mass of 85 g, correct to the nearest 5 g. Write down the error interval for its mass, m.

Three bones, each recorded as 24.6 cm correct to the nearest 0.1 cm, are laid end to end. Calculate the lower bound of their total length.

Calculate the total prize fund.

The rider with the largest share spends 35% of it on equipment. Calculate the amount spent.

Calculate the number of drives. Give your answer in standard form.

Each drive costs €1.2 × 10³. Calculate the total cost of the drives. Give your answer in standard form.

The data can be read at 2.5 × 10⁹ bytes per second. Calculate the number of days needed to read all 4.8 × 10¹⁵ bytes. There are 86400 seconds in a day. Give your answer correct to 1 decimal place.

Calculate the largest share.

The other two shares are €378 and €252. Write the ratio 378 : 252 in its simplest form.

Write the smallest share as a percentage of the total cost.

Estimate the time taken in seconds by rounding each value to 1 significant figure.

Calculate the time taken. Give your answer in seconds correct to 3 significant figures.

Is the estimate in part (a) smaller or larger than the calculated time?

Write down the prime numbers in the list.

Write down the number in the list that is both a square number and a cube number.

Write 91 as a product of two prime numbers.

Write down the multiple of 19 in the list.

A buffer has \(2^{14}\) bytes of memory. Find how many packets fit in the buffer. Give your answer as a number.

Write \(5^{-2}\) as a fraction.

Find the value of \(n\) when \(3^{n} = \frac{1}{81}\).

Calculate the mass of the roasted beans, in kg.

Work out how many full bags can be filled with the roasted beans.

Calculate the income from selling all of these bags.

Calculate the mass of Colombian beans in the blend.

Calculate the total cost of the beans in the blend.

Work out the cost of the blend per kg.

Estimate the number of litres of paint needed by rounding each number to 1 significant figure. Show your working.

Calculate the number of litres needed, correct to 3 significant figures.

Work out the percentage by which the estimate in part (a) is greater than the unrounded value 191.05 litres. Give your answer correct to 3 significant figures.

Calculate the total interest earned after 4 years.

The company needs the account to reach €15000 in total. Calculate how many years this takes.

Write 126 as a product of its prime factors.

Find the highest common factor of 126 and 210, given that 210 = 2 × 3 × 5 × 7.

Find the total number of pieces.

Calculate the time taken for the signal to reach Earth. Give your answer in seconds, in standard form.

Change your answer to hours. Give your answer correct to 3 significant figures. Use the exact value 1.5 × 10⁴ s.

Show that the batch contains 4.8 kg of Robusta beans.

Arabica beans cost €14.50 per kilogram and Robusta beans cost €9.00 per kilogram. Calculate the cost of the beans in the batch.

The blend is sold at €17.25 per kilogram. Calculate the percentage profit on the cost of the batch, correct to 3 significant figures. Use €159.20 as the cost.

Estimate the total mass of the sections by rounding each number to 1 significant figure.

Calculate the exact total mass.

Work out the percentage error in the estimate, correct to 3 significant figures. Use the exact total mass as the true value.

Write 84 and 60 each as a product of prime factors.

Find the side length of the largest square slab that can be used.

Work out how many of these slabs are needed.

The workshop uses 450 ml of oil. Calculate the volume of solvent needed.

Find the percentage of the mixture that is oil.

Each robot joint needs 30 ml of the mixture from part (a). How many joints can be treated?