Number worksheet — GCSE Higher

1.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

2.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

3.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.

4.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

5.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

6.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

7.Work out 6² − 4².

8.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

9.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

10.Write 90 as a product of its prime factors.

11.Work out (−36) ÷ (−6) × 2

12.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

13.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

14.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

15.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.