RATIO AND
PROPORTION
LESSON OBJECTIVE
At the end of the lesson, at least 80% of the students
will be able to:
Express the ratio in simplest form
Defines a proportion.
Believe that they can form ration and
proportion for group of objects or numbers.
RATIO
Ratio
•
•
•
A ratio is the comparison between two numbers/ quantities of the
same units. It is the result of comparing them by division.
The ratio of squares to triangles.
Ratio can be expressed in four ways and can be written as:
a:b (colon form)
a to b (phrase form)
𝑎
(fraction form) where 𝑏 ≠ 0
𝑏
Ratio must be written in its simplest form.
EXAMPLES
1) Find the ratio of a to b if a = 6 cm and b = 8 cm.
6:8 or 3:4
2) 1 hour to 40 minutes 8 ÷ 2 = 4 𝑜𝑟 4: 11
22 2 11
3) Eight out of 30 passengers are tourists. Find the
ratio of the number of tourists to the number of other
passengers. 60 ÷ 20 = 3 or 3:2
40
20
2
PRACTICE
Direction: Express each of the following as ratios in
simplest forms.
1
1. Php 6 to Php 72 12 𝑜𝑟 1: 2
7
2. 2 weeks to 4 days 2 𝑜𝑟 7: 2
3. In a certain room, there are 28 women and 21 men.
a. What is the ratio of the number of men to the
3
number of women? 4 𝑜𝑟 3: 4
b. What is the ratio of the number of women to the
4
total number of people? 7 𝑜𝑟 4: 7
Johnny, Jay, and Jun buy calamansi from
the same wholesale dealer and sell them at
retail as follows: Johnny: Php24 for every 10
pieces
Jay: Php27 for every 12 pieces
Jun: Php36 for every 15 pieces
Which one is a better buy?
PROPORTION
Proportion
•
•
A proportion is the equality between two ratios.
It can be written in two ways:
𝑎: 𝑏 = 𝑐: 𝑑 𝑜𝑟 𝑎𝑏 = 𝑐𝑑 , where 𝑏 ≠ 0, 𝑑 ≠ 0
𝑎, 𝑏, 𝑐, 𝑎𝑛𝑑 𝑑 ⇒ 𝑡𝑒𝑟𝑚𝑠
𝑏 𝑎𝑛𝑑 𝑐 ⇒ 𝑚𝑒𝑎𝑛𝑠
𝑎 𝑎𝑛𝑑 𝑑 ⇒ 𝑒𝑥𝑡𝑟𝑒𝑚𝑒𝑠
• Two ratios are proportional if the product of the means is
equal to the product of the extremes.
• If two ratios can be simplified into the same ratio, then
the two ratios form a proportion.
EXAMPLE
4
9
1. Determine if = is a proportion or
12
27
27 = 9 27
not. (4) 108
= 108 PROPORTION
2. Is 4:6=8:12 a proportion?
(4) 12 = 6 8
48 = 48 PROPORTION
LET’S TRY!
Direction: Identify the means and extremes of a given pair of
ratios and tell whether it form a proportion or not.
Ratios
Means
Extremes
Proportion or
not
1) 4:5, 24:30
5 and 24
4 and 30
Proportion
2) 5:6 20:24
6 and 20
5 and 24
Proportion
3) 2:7, 20:56
7and 20
2 and 56
NOT
10 and 35
7 and 70
NOT
8 and 30
6 and 40
4)
7 35
,
10 70
6 30
5) 8 , 40
Proportion
Activity: Is this Fair?
Direction: Write ratios for the quantities mentioned in each
situation then compare the ratios. If those ratios are equal, write
FAIR and if not, write UNFAIR. Explain your answer.
1) Ron and Mark are card collectors. Ron traded 24 basketball
cards for 15 boxing cards and Mark traded 20 basketball cards
for 32 boxing cards. Is this fair? UNFAIR
2) On a math exam, Lily scored 85 points for answering 17
questions correctly and Tom scored 80 points for answering 16
questions correctly. Is this fair? FAIR
SOLVING
PROPORTIONS
Solving Proportions
We can solve for the missing values in a
proportion using the Cross Multiplication Property or
by Means-Extremes Property.
Example 1: Solve for the value of x in
Solution:
5(𝑥) = (2)(30)
5𝑥
60
=
5
5
𝑥 = 12
2
5
=
𝑥
30
Solving Proportions
We can solve for the missing values in a
proportion using the Cross Multiplication Property or
by Means-Extremes Property.
Example 2:
Solve for the value of 𝑏 in 5:25 = 𝑏:150
Solution:
(5)(150) = 25𝑏
25𝑏=750
𝑏= 30
Solving Proportions
We can solve for the missing values in a
proportion using the Cross Multiplication Property or
by Means-Extremes Property.
Example 3:
Solve for the value of a in
4𝑎−1
3
Solution:
5(4a −1) = 3(6a+1)
20a − 5 = 18a +3
20a − 18a = 5+3
2a = 8
a=4
=
6𝑎+1
5
TRY THIS!
Solve for the value of x in each of the following
proportions.
2
3
1) =
𝑥
9
𝑥+4
4
2) 6: 10 = 𝑥: 25 3) 2𝑥+13 = 9
Solving World Problems
Ms. Peters wants to prepare a party for 80 people.
She has a chocolate cake recipe that makes 3 small cakes
that can serve 16 people. How many cakes does she need
to bake for her party?
Solution: Let 𝑥 be the number of cakes to be baked for the party.
3 𝑐𝑎𝑘𝑒𝑠
𝑥
=
16 𝑝𝑒𝑜𝑝𝑙𝑒
80 𝑝𝑒𝑜𝑝𝑙𝑒
(3)(80) = 15𝑥
240 = 16𝑥
𝑥 = 15
She needs to make 15 cakes for her party.
Solving World Problems
In a photograph, Jane is 9 cm tall and her brother
John is 10 cm tall. Jane’s actual height is 153 cm. What is
John’s actual height?
Solution: Let 𝑥 be the actual height of John in cm.
9
153
=
10
𝑥
9x = 153(10)
9x = 1,530
𝑥 = 170 𝑐𝑚
John’s actual height is 170 𝑐𝑚
TASK 2
A. Find the missing value in each given
proportion.
1)
3: 45 = 4:k
TASK 2
A. Find the missing value in each given
proportion.
2)
5
7
=
15
𝑛
TASK 2
A. Find the missing value in each given
proportion.
3)
7
4
=
𝑦+2
𝑦−4
TASK 2
B. Determine the given ratios then set up
proportion.
1. In a photograph, a basketball player Vin is 7 cm tall
and Mar is 11 cm tall. Vin’s actual height is 168 cm.
What is Mar’s actual height?
Solving World Problems
In a photograph, a basketball player Vin is 7 cm tall
and Mar is 11 cm tall. Vin’s actual height is 168 cm.
What is Mar’s actual height?
Solution: Let 𝑥 be the actual height of Mar in cm.
7
168
=
11
𝑥
7x = 168(11)
7x = 1,848
𝑥 = 264 𝑐𝑚
Mar’s actual height is 264 𝑐𝑚