Number worksheet — GCSE Higher

1.Work out (−36) ÷ (−6) × 2

2.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

3.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

4.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

5.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

6.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

7.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

8.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.

9.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

10.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

11.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

12.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

13.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

14.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

15.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.