Operations on Numbers - SS1 Mathematics Lesson Note

The main operations we carry out in mathematics are multiplication, division, addition, and subtraction (\(\times , \div , + , -\)), with the inclusion of brackets and ‘of’. The Order of operations by which these operations are carried out in the acronym ‘BODMAS’ which stands for the operations of Brackets, of, division, multiplication, addition, and subtraction being carried out is this order. Note, after brackets and ‘of’ either multiplication or division can be done first; then addition or subtraction.

Example 1 Simplify \(6\frac{3}{4} \div \lbrack\left( 21\frac{1}{3}\ of\ 2\frac{1}{4} \right) - 21\rbrack\)

Solution \(6\frac{3}{4} \div \lbrack\left( 21\frac{1}{3}\ of\ 2\frac{1}{4} \right) - 21\rbrack\) = \(6\frac{3}{4} \div \lbrack\left( \frac{64}{3}\ of\ \frac{9}{4} \right) - 21\rbrack\) solve the content within the innermost brackets first; ‘of’ functions much the same way as multiplication

= \(6\frac{3}{4} \div \lbrack 48 - 21\rbrack\) the outer square brackets are then evaluated

= \(6\frac{3}{4} \div 27\)

= \(\frac{27}{4} \div 27\)

= \(\frac{27}{4} \times \frac{1}{27}\)

= \(\frac{1}{4}\)