Form 2: Ratio, Rate & Proportion

Definition of ratio: The ratio of two quantities is

the comparison between

two quantities which have

the same unit.

Example:

Write the ratio of 3000m to 1500m in the form

of a:b.

Answer: 3000

15002

12 :1

=

=

=Read as, two is to one.

How does ratio relate to vector?

Look at the next example

so that you can see why

ratio is related to vector.

Example:

In the diagram, PQR is a triangle. T is point on

such that 4PS=SQ. Given that and

, determine each of the following vectors in term of

a and b.

a)

b)

PS

R

T

Q

5PQ a=uuur

4PR b=uuur

QTuuurRQuuur

The solution:

a)

b) Given that,

RQ RP PQ= +uuur uuur uuur

4 5

5 4

PR PQ

b a

a b

= − += − += −

uuur uuur

2 3RT TQ=

3

2RT TQ=uuur uuur

RATIO CONCEPT IS

APPLIED

Continue…RQ RT TQ= +uuur uuur uuur

3

25

2

TQ TQ

TQ

= +

=

uuur uuur

uuur

2

5TQ RQ=uuur uuur

2(5 4 )5a b= −

2(5 4 )5

QT a b= − −uuur

2(4 5 )5b a= −

Point To Be Noted

• As we can see, the concept of ratio is also used in vector. So, it is very helpful for students if they can master the ratio concept well first so that they do not have much problem later on when dealing with vector.