Number worksheet — GCSE Foundation

1.£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.

2.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

3.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

4.Work out the value of 2⁻²

5.Work out 5 + 3 × (9 − 6)

6.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

7.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

8.In the number 3.472, work out the value of the digit 7.

9.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

10.Write down the reciprocal of 0.2

11.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

12.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

13.Estimate the value of √45, giving your answer to the nearest whole number.

14.Which one of these statements about negative numbers is true?

15.Amelia eats 5/8 of a bar of chocolate and Oliver eats 3/4 of an identical bar. Write both amounts as eighths and write down the greater of the two fractions.