Understanding Engineering Mathematics

Brackets can be used if we want to override such rules. For example:

2 ×( 3 + 5 )= 2 × 8 = 16

In general, an arithmetic expression, containing numbers, ( ),x,÷,+,−,mustbe
evaluated according to the following priorities:

BODMAS

Brackets ( ) first

Of (as in ‘fraction of’−rarely used these days)

Division÷

}

second

Multiplication×

Addition+

}

third

Subtraction−

If an expression contains only multiplication and division we work from left to right. If
it contains only addition and subtraction we again work from left to right. If an expression
contains powers orindices(Section 1.2.7) then these are evaluated after any brackets.
Products and quotients of negative numbers can be obtained using the following rules:

(+ 1 )(+ 1 )=+ 1 (+ 1 )(− 1 )=− 1

(− 1 )(+ 1 )=− 1 (− 1 )(− 1 )=+ 1

1

(− 1 )

=− 1

For example (− 2 )(− 3 )=(− 1 )(− 1 ) 6 = 6

Note that if you evaluate expressions on your calculator, it may not follow the BODMAS
order, simply because of the way your calculator operates. However, BODMAS is the
universal convention in Western mathematics and applies equally well to algebra, as we
will see in Chapter 2.

Solution to review question 1.1.4

Following the BODMAS rule

(i) 2+ 3 − 7 = 5 − 7 =− 2

(ii) 4× 3 ÷ 2 = 12 ÷ 2 = 6

(iii) 3+ 2 × 5 = 3 + 10 = 13

(iv)( 3 + 2 )× 5 = 5 × 5 = 25

(v) 3+( 2 × 5 )= 3 + 10 =13. In this case the brackets are actually

unnecessary, since the BODMAS rules tell us to evaluate the multi-

plication first.

(vi) 18÷ 2 × 3 = 9 × 3 =27 following the convention of working from

left to right.

(vii) 18÷( 2 × 3 )= 18 ÷ 6 =3 because the brackets override the left to

right rule.