3. Rita collected
21 flowers.
Pamela collected
42 flowers.
Flowers collected by Pamela β Flowers collected by Rita
42 flowers β 21 flowers
= 21 flowers
This type of comparison is called comparison by
difference.
4. Rita collected
21 flowers.
Pamela collected
42 flowers.
ππππππππ πππππππππ ππ πΉπππ
ππππππππ πππππππππ ππ π·πππππ
=
ππ
ππ
=
π
π
Rita has collected
π
π
the number of flowers of what
pamela has collected.
5. Rita collected
21 flowers.
Pamela collected
42 flowers.
ππππππππ πππππππππ ππ π·πππππ
ππππππππ πππππππππ ππ πΉπππ
=
ππ
ππ
=
π
π
Pamela has collected twice the number of flowers that
what Rita has collected.
6. Rita collected
21 flowers.
Pamela collected
42 flowers.
ππ
ππ
=
π
π
ππ
ππ
=
π
π
Rita has collected
π
π
the number of
flowers of what pamela has collected.
Pamela has collected twice the number
of flowers that what Rita has collected.
This is known as comparison by division.
8. Comparison by division is called Ratio.
RATIO
In other word, Ratio is a Comparison of two or more
quantities of the same kind by division.
9. Can the following measures be compared with a ratio?
6 yellow fish in an aquarium with 18 fish
Can the following measures be compared with a ratio?
6 yellow fish in an aquarium with 18 fish YES
Soniaβs weight and the number of girls in her class
Can the following measures be compared with a ratio?
6 yellow fish in an aquarium with 18 fish YES
Soniaβs weight and the number of girls in her class NO
Number of matchsticks in a matchbox and number
of matchsticks in a carton full of matchboxes
Can the following measures be compared with a ratio?
6 yellow fish in an aquarium with 18 fish YES
Soniaβs weight and the number of girls in her class NO
Number of matchsticks in a matchbox and number
of matchsticks in a carton full of matchboxes
YES
The size of an ice cube in cm and the temperature
inside the freezer in degree Celsius
Can the following measures be compared with a ratio?
6 yellow fish in an aquarium with 18 fish YES
Soniaβs weight and the number of girls in her class NO
Number of matchsticks in a matchbox and number
of matchsticks in a carton full of matchboxes
YES
The size of an ice cube in cm and the temperature
inside the freezer in degree Celsius
NO
10. Representation of a Ratio.
There are three ways of representing a Ratio.
In fraction form Using colon (:)
Using the word βtoβ
11. Representation of a Ratio.
In fraction form
ππ
ππ
=
π
π
ππ
ππ
=
π
π
12. Representation of a Ratio.
Using the word βtoβ
π
π
= 1 to 2
π
π
= 2 to 1
13. Representation of a Ratio.
Using βcolonβ
π
π
= 1 : 2
π
π
= 2 : 1
14. Do you know?????
If βaβ and βbβ are any two number, then
a : b
First term or Antecedent Second term or Consequent
15. Example
β’ In a fruit basket, there are 20 oranges and 10 pomegranates.
Express it in the form of a ratio.
Solution: In ratio of the number of oranges to the number of pomegranates is:
Using colon (:)
20 : 10
Using the word βtoβ
20 to 10
In fractional form
ππ
ππ
16. Ratio in simplest form
If βaβ and βbβ are any two numbers, then βa : bβ is
said to be its lowest form or simplest form, if a and
b have no common factors except 1.
17. To express a ratio in its simplest form
a) Write the ratio as a fraction
b) Divide the numerator and denominator by their
HCF
c) The answer is a fraction in its lowest form
STEPS
18. Example
Express the ratio 24 : 9 in its simplest form
Solution: Step 1 - Write the ratio as a fraction
Ratio =
ππ
π
Step 3 - The answer is a fraction in its lowest form
=
π
π
= 8 : 3
Step 2 - Divide the numerator and denominator by their HCF
=
ππ / π
π / π
Hence, the ratio of 24 and 9 in its simplest form is 8 : 3
19. Express the following ratios in their simplest forms.
15 and 3
Express the following ratios in their simplest forms.
15 and 3 ππ
π
Express the following ratios in their simplest forms.
15 and 3 ππ
π
=
ππ Γ·π
π Γ·π
Express the following ratios in their simplest forms.
15 and 3 ππ
π
=
ππ Γ·π
π Γ·π
=
π
π
Express the following ratios in their simplest forms.
15 and 3 ππ
π
=
ππ Γ·π
π Γ·π
=
π
π
= 5 : 1
Express the following ratios in their simplest forms.
15 and 3 ππ
π
=
ππ Γ·π
π Γ·π
=
π
π
= 5 : 1
12 and 6
Express the following ratios in their simplest forms.
15 and 3 ππ
π
=
ππ Γ·π
π Γ·π
=
π
π
= 5 : 1
12 and 6 ππ
π
=
ππ Γ·π
π Γ·π
=
π
π
= 2 : 1
80 and 10
Express the following ratios in their simplest forms.
15 and 3 ππ
π
=
ππ Γ·π
π Γ·π
=
π
π
= 5 : 1
12 and 6 ππ
π
=
ππ Γ·π
π Γ·π
=
π
π
= 2 : 1
80 and 10 ππ
ππ
=
ππ Γ· ππ
ππ Γ·ππ
=
π
π
= 8 : 1
180 and 120
Express the following ratios in their simplest forms.
15 and 3 ππ
π
=
ππ Γ·π
π Γ·π
=
π
π
= 5 : 1
12 and 6 ππ
π
=
ππ Γ·π
π Γ·π
=
π
π
= 2 : 1
80 and 10 ππ
ππ
=
ππ Γ· ππ
ππ Γ·ππ
=
π
π
= 8 : 1
180 and 120 πππ
πππ
=
πππ Γ·ππ
πππ Γ·ππ
=
π
π
= 3 : 2
20. Brain storming
In a class, there are 20 boys and 40 girls.
a) Find the ratio of the number of boys to the number of girls.
b) Find the ratio of the number of boys to the total number of
students.
c) Find the ratio of the number of girls to the total number of
students.
d) Find the ratio of the number of students to the total number of
girls.
21. Brain storming
In a class, there are 20 boys and 40 girls.
a) Find the ratio of the number of boys to the number of girls.
The ratio of the number of boys to the number of girls =
ππ
ππ
Solution : The number of boys = 20
The number of girls = 40
=
ππ
ππ
ππ
ππ
=
π
π
= 1 : 2
22. Brain storming
In a class, there are 20 boys and 40 girls.
b) Find the ratio of the number of boys to the total number of students.
The ratio of the number of boys to the number of students =
ππ
ππ
Solution : The number of boys = 20
Total number of students = 20 + 40 = 60
=
ππ
ππ
ππ
ππ
=
π
π
= 1 : 3
Therefore, the ratio of the number of boys to the number of girls is 1 : 3 in simplest form.
23. Brain storming
In a class, there are 20 boys and 40 girls.
c) Find the ratio of the number of girls to the total number of students.
The ratio of the total number of girls to the number of students =
ππ
ππ
Solution : The number of girls = 40
Total number of students = 20 + 40 = 60
=
ππ
ππ
ππ
ππ
=
π
π
= 2 : 3
Therefore, the ratio of the number of boys to the number of students is 2 : 3 in simplest form.
24. Brain storming
In a class, there are 20 boys and 40 girls.
d) Find the ratio of the number of students to the total number of girls.
The ratio of the total number of students to the number of girls =
ππ
ππ
Solution : The number of girls = 40
Total number of students = 20 + 40 = 60
=
ππ
ππ
ππ
ππ
=
π
π
= 3 : 2
Therefore, the ratio of the number of students to the number of girls is 3 : 2 in simplest form.
25. Determine the ratio of triangles to cube in the rows A, B,C
and D. State which two rows have the same ratio.
A
B
C
D
26. Determine the ratio of triangles to cube in the rows A, B,C
and D. State which two rows have the same ratio.
A π
π
=
π
π
B
π
π
C
π
π
=
π
π
D
π
π
=
π
π
27. Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20 50 to 20
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20 50 to 20 π
π
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20 50 to 20 π
π
Rs 120 to Rs 200 πππ
πππ
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20 50 to 20 π
π
Rs 120 to Rs 200 πππ
πππ
120 : 200
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20 50 to 20 π
π
Rs 120 to Rs 200 πππ
πππ
120 : 200
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20 50 to 20 π
π
Rs 120 to Rs 200 πππ
πππ
120 : 200 120 to 200
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20 50 to 20 π
π
Rs 120 to Rs 200 πππ
πππ
120 : 200 120 to 200 π
π
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20 50 to 20 π
π
Rs 120 to Rs 200 πππ
πππ
120 : 200 120 to 200 π
π
8 hours to 12 hours
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20 50 to 20 π
π
Rs 120 to Rs 200 πππ
πππ
120 : 200 120 to 200 π
π
8 hours to 12 hours π
ππ
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20 50 to 20 π
π
Rs 120 to Rs 200 πππ
πππ
120 : 200 120 to 200 π
π
8 hours to 12 hours π
ππ
8 : 12 8 to 12
Express the following as ratios in different ways.
Fraction Ratio Read as Simplest
form
3 Km to 5 Km π
π
3 : 5 3 to 5 π
π
50 marks to 20
marks
ππ
ππ
50 : 20 50 to 20 π
π
Rs 120 to Rs 200 πππ
πππ
120 : 200 120 to 200 π
π
8 hours to 12 hours π
ππ
8 : 12 8 to 12 π
π
28. RECAP
β’ Ratio is a comparison of two or more quantities of the
same kind by division.
β’ There are three ways of representing a ratio.
In fraction form
Using the word βtoβ
Using colon ( : )
β’ If a and b are any two numbers, then a is said to be
first term or antecedent and b is said to be second term
or consequent.
30. There are 36 bananas,12 oranges and 24
apples in a basket.
Write down the:
a) Ratio of apples to oranges
b) Ratio of bananas to oranges and apples
c) Ratio of oranges to remaining