Number worksheet — GCSE Foundation

1.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

2.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

3.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

4.On one night in Manchester the temperature at 3 am was 8 °C below zero and at 9 am it was 3 °C below zero. Write down the warmer of the two readings.

5.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

6.A student always writes the digits after the decimal point over a denominator of 100, whatever the number of decimal places. Using this wrong rule, they convert 0.9 to a fraction. Work out the correct fraction that 0.9 is equal to, giving your answer in its simplest form.

7.A concert hall has 300 seats. 20% of the seats are in the balcony. Work out how many of the seats are in the balcony.

8.The mass of a parcel is 3 kg, correct to the nearest kilogram. Which of these masses is not possible for the parcel?

9.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

10.During one night on a mountain, four hikers each recorded the temperature they felt: Ben −6 °C, Priya −2 °C, Sam −9 °C, Alex 1 °C. Work out the difference between the coldest and the warmest of these four temperatures.

11.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

12.Work out √49

13.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

14.A tin of soup has a mass of 450 g. A bag of potatoes has a mass of 2.6 kg. Work out the total mass, in kilograms.

15.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.