5.1 : Ratio of Two Quantities
 Use
ratios
 To determine if given ratios are equivalent
 Write ratios in their simplest form
Ratio is a comparison between two quantities
of the same kind
Ratio of two quantities, a and b, is written as
a:b
a
b
Read as ‘a is to b’
What is the ratio of women to men?
3:2
What is the ratio of men to women?
2:3
What is the ratio of blue balls to pink?
9:3
or 3 : 1
What is the ratio of pink balls to blue?
9:6
or 3 : 2
An equivalent ratio can be obtained when we
multiply or divide both quantities in a ratio
by the same number
2
1
x3
x3
6
=
3
8 ÷4 2
÷4 =
12
3
2:3
6:9
A proportion is an equation that states
that two ratios are equal, such as:
In simple proportions, all you need to do is
examine the fractions.
If the fractions both reduce to the same
value, the proportion is true.
Are these
proportional?
5
2
and
15 6
55 1

15  5 3
22 1

62 3
This is a true proportion, since both
fractions reduce to 1/3.
In simple proportions, you can use this same
approach when solving for a missing part of
a proportion.
Remember that
both fractions must
reduce to the same
value.
To determine the
unknown value, you
must cross multiply.
(3)(x) = (2)(9)
3x = 18
x=6
Check your
proportion
(3)(x) = (2)(9)
(3)(6) = (2)(9)
18 = 18
True!
2 10

3 5
4 x

6 12
No
x=8
25 5

x 2
x=10
a) If 4 tickets to a b) A house which is
appraised for $10,000
show cost $9.00,
pays $300 in taxes.
find the cost of 14
What should the tax be
tickets.
on a house appraised at
$15,000.
=$31.50
=$450
A house painter mixes yellow paint
with blue paint to get green paint.
The ratio of the volume of the yellow
paint to the volume of the blue paint is
5:3. if the difference in volumes of the
two paints is 500ml, find the volume of
the green paint.
5
:
3
+
=
 4
500
5
3 ml
Difference in volumes
between yellow and blue
5  3ml
 2000
= 500ml
Volume of green paint
Difference in volumes
between yellow and blue
Volume of green paint
500 ml
Volume of green paint
53
=
53
8
=
2
 4  500ml
 2000ml
Ratio of three quantities is a comparison of
three quantities having the same unit of
measurement
Eg: The ages of three children are 10 years, 11
years and 13 years.
Ratio of their ages is 10:11:13
REMEMBER?
Unit is not shown in
the ratio
Are these
equivalent?
1:5:7 and 4:20:28
yes
1 : 5 : 7
x4 : x4 : x4
4 : 20 : 28 =
4 : 20 : 28
Are these
equivalent?
No
2:3:5 and 10:14:20
2 : 3 : 5
x5 : x5 : x5
10 : 14 : 20
≠
10 : 15 : 25
Whole
Number
Divide each
by HCF
Fractions
or mixed
number
Multiply each
by LCM
REMEMBER!
Ratio in lowest terms must
be in whole number
Decimals
Multiply
each term
by 10,
100, 1000
..
Whole
Number
Divide each
by HCF
4 : 20 : 28
÷4 : ÷4 : ÷4
1 : 5 : 7
Simplify
6 : 72 : 42
Fractions or
mixed number
Multiply each by
LCM
1 1
:
:3
2 4
x4
:
1
4
2
2
x4
:
x4
Simplify
2 1 1
: :
3 2 6
1
 4 3 4
4
:
1
:
12
Answer!
Multiply each term by 10,
100, 1000 ..
Decimals
0.1 :
2
: 0.036
x1000 : x1000 : x1000
100 : 2000 : 36
Simplify
0.3: 0.0045: 0.24
Snakes : cats
2 : 3
Cats : Tigers
3 : 5
Snakes : Cats : Tigers
2 : 3 : 5
Adam’s
pet
Red : Blue
1 : 2
x2
:
x2
Blue : Yellow
4 : 7
Red : Blue : Yellow
2 : 4 : 7
Faiz’s
marbles
Given the ratio of a bungalow to a semi-detached house
to a terrace house is 5 : 3 : 2.
If the price of bungalow is RM 1 200 000, what is the
price for a semi-detached house?
Unitary
method
Proportional
method
Bungalow : Semi-D : Terrace
5
:
3
:
2
5 parts represent RM 1 200 000
1 part represents = RM 1 200 000
5
= RM 240 000
Semi-D
3 parts represent = RM 240 000 x 3
= RM 720 000
Terrace
2 parts represent = RM 240 000 x 2
= RM480 000
Bungalow : Semi-D : Terrace
5
:
3
:
2
Let the price of a semi-detached house be x :
Semi-D
Terrace
x
2
x
3


1200000 5
1200000 5
2
3
x   1200000
x  1200000
5
5
 720000
 480000
A curtain of length 810m has three parts with different
materials. The ratio of the lengths of PQ to QR to RS is
4 : 2 : 3. What is the length of PQ?
4
P
2
Q
810m
3
R
S
4
2
P
Q
810m
PQ + QR + RS = 4 + 2 + 3 = 9 parts
9 parts = 810 m
PQ
1 part represents = 810 m
9
= 90 m
4 parts represent = 90 x 4
= 360 m
3
R
S
4
P
2
Q
810m
PQ : QR : RS
4 : 3 : 2
PQ
4

810 4  2  3
4
PQ   810
9
PQ  360m
3
R
S
The ratio of the sides AB, BC and AC of triangle ABC are in
the ratio 7 : 5 : 6. Find the length of side AB if the difference
of the sides AB and BC is 4 cm
C
5
6
A
7
B
C
5
6
A
AB-BC = 4 cm
AB ─ BC = 7 ─ 5 = 2
2 parts represent = 4 cm
1 part = 2 cm
AB = 7 parts × 2cm
= 14 cm
7
B
The ratio of the sides DE, EF and FD of triangle DEF are in
the ratio 11 : 9 : 5. Find the sum of the three sides if the
difference of the sides DE and DF is 18 cm
F
9
5
D
11
E
F
9
5
D
11
DE ─ DF = 18 cm
DE ─ DF = 11 ─ 5 = 6
6 parts represent = 18 cm
1 part = 3 cm
Sum of all sides = 11 + 9 + 5 =25 parts
= 25 parts × 3cm
= 75 cm
E