Ratio and Proportion
Ratio
A comparison of the relative
values of number/quantities.
Expressed as the quotient
x divided by y such that y ≠ 0.
Ratio
May be written in the ff. ways:
“5 is to 2”
“5 : 2”
“5”
2
“2.50”
Ratio in Simplest Form
To express a ratio
in simplest form,
divide out the
common factors
Write each ratio in simplest form.
1.
3x
1

2
6x
2x
Write each ratio in simplest form.
2.
x  7   x  7 
2
2
2 x
 98
 2x

 49

x1 7 

=
 x +
22(𝑥
7 7)
x  7
Allocated based on Ratio
Dividing a whole into a number
of parts based on ratio
Example:
Allocate P48,000 in the ratio 5:3.
Divide the net income Php72,000
in the ratio 4:3:2.
Rate
A comparison of two
quantities that have
different units.
“m/s”
“miles per hour”
Rate
Recently an automobile
manufacturer spent Php946,000
for a 48-second television
commercial shown on a national
network. What is the rate of
pesos spent to seconds of
commercial time?
Proportion
1 25

4 100
5 30

3 18
Proportion
the equality of
two ratios
a c

b d
where b≠0, d≠0
Proportion
Each number in a
proportion is called a
term.
Terms:
st
1
nd
2
rd
3
th
4
a:b=c:d
Proportion
Terms:
st
1
nd
2
rd
3
th
4
a:b=c:d
means
extremes
Properties of Proportions
1. Means-Extremes Product Law
the product of the means equals
product of the extremes
a c
If
 , then ad  bc,
b d
where b  0, d  0.
Properties of Proportions
2. Reciprocal Law
reciprocals of the ratios of a proportion
a c
b d
If
 , then
 ,
b d
a c
where a, b, c, and d are nonzero real
numbers.
Example 1
Find the value of x in the proportion
4 2
=
𝑥 6
2: 5 = 8: 𝑥
Example 2
If the property tax on a
Php3,750,000 house is
Php19,100, what is the
tax on a Php4,500,000
house?
Example 3
Two contractors agreed to share
revenue from a job in the ratio 2:3.
Contractor A, who received the
smaller amount, made a profit of
Php480,000 on the job. If
contractor A’s profit compared to
revenue is in the ratio 3:8,
determine contractor A’s revenue.