Understanding Engineering Mathematics

or, with 6 the LCM of 2 and 3

=

3

6

+

12

6

+

4

6

=

19

6

(−^1 )

and so the equivalent resistance is

R=

6

19



Finally, on fractions, recall the ideas ofratioandproportion. These are met early in
our mathematical education, yet often continue to confuse us later in life. Specifically, it
is not uncommon to see someone make errors such as:

‘a

b

=

1

3

meansa=1andb= 3 ’

so it is worth having a quick review of this topic.
The notationa:bis used to indicate that the numbersaandbare in a certain ratio or
proportionality to each other.

a:b=1:3

simply means that

a

b

=

1

3

and this most certainly does not meana=1andb=3. For example

3:9=2:6=7:21=1:3

Alla:b=1:3meansisthat

a=

b

3

i.e.aisathird ofb. If we are givena(orb) then we can findb(ora). The review
question illustrates this.
In general, if we can writea=kbwherekis some given constant then we say ‘ais
proportional tob’ and write this asa∝b.aandbare then in the ratioa:b=1:k.On
the other hand if we can writea=k/bthen we say ‘a is inversely proportional tob’and
writea∝ 1 /b.

Solution to review question 1.1.5

A. (i)

4

6

=

2 × 2

2 × 3

=

2

3

(ii)

18

9

=

9 × 2

9

= 2