Class 7 Mathematics Chapter 8 Comparing Quantities

1. Integrated B.Sc. - B.Ed.
Name : SANDHYA
School Of Education
Part 2

2. Identify the Image

3. In the park. a lady had given a kid two chocolates .What is
the ratio to kid to chocolates?

4. In the park. a lady had given a kid two chocolates .What is
the ratio to kid to chocolates?
Ratio of kid to chocolates
= 1:2

5. Later on ,there are five kids and ten chocolates. This is
equally distributed among them.
The ratio of kids to chocolates =
Ratio of kid to
chocolates
= 1:2

6. Later on ,there are five kids and ten chocolates. This is
equally distributed among them.
The ratio of kids to chocolates = 5: 10
Ratio of kid to
chocolates
= 1:2

7. Later on ,there are five kids and ten chocolates. This is
equally distributed among them.
The ratio of kids to chocolates = 5: 10
Ratio of kid to
chocolates
= 1:2

8. Does this ratio - ‘5:10 & 1:2’ represent the same relationship?
The ratio of kids to chocolates = 5: 10
Ratio of kid to
chocolates
= 1:2

9. Equivalent Ratios
Two or more ratios that express the same relation or comparison of numbers are known
as equivalent ratios.
• It is similar to the concept of equivalent fractions.
The equality of two ratios is also known as proportion.
Note: The antecedent and consequent values are different, but still, if we reduce them to
the simplest form, we will get the same value.

10. Equivalent Ratios
For example, to find whether 2:3 and 16:24 are equivalent ratios or not, we
will have to reduce both ratios to their simplest form.

11. Equivalent Ratios
For example, to find whether 2:3 and 16:24 are equivalent ratios or not, we
will have to reduce both ratios to their simplest form.
• 2:3 is already in simplest form as the HCF of 2 and 3 is 1.
The HCF of 16 and 24 is 8.
So, let us divide both these numbers by 8 to find the reduced form. This implies
(16÷8):(24÷8) = 2:3
It is clear that 2:3 and 16:24 results in the same value, therefore they are
equivalent ratios.

12. List some examples from their day to-day life where they
observe equivalent ratios.

13. 𝟏
𝟐
=
𝟐
𝟒
=
𝟒
𝟖
List some examples from their day to-day life where they
observe equivalent ratios.

14. State True or False:
•The antecedent and consequent values are different, but still,
if we reduce them to the simplest form, we will get the same
value.

15. State True or False:
•The antecedent and consequent values are different, but still,
if we reduce them to the simplest form, we will get the same
value. [True]

16. Following is the performance of a cricket team in the matches it
played:
(b.) How can you say so?
Year Wins Losses
Last year 8 2
This Year 4 2

17. Following is the performance of a cricket team in the matches it
played:
(a.)In which year was the record better?
Year Wins Losses
Last year 8 2
This Year 4 2
• Last year, Wins: Losses = 8 : 2 = 4 : 1
• This year, Wins: Losses = 4 : 2 = 2 : 1
Obviously, 4 : 1 > 2 : 1
Hence, we can say that the team
performed better last year.

18. Are the given ratios - 15:10 and 30:15 equivalent
or not?

19. • To find whether the given ratios are equivalent or not.
Let us use the cross multiplication method.
We can write these ratios as
𝟏𝟓
𝟏𝟎
and
𝟑𝟎
𝟏𝟓
𝐬𝐮𝐜𝐡 𝐚𝐬
𝟏𝟓
𝟏𝟎
𝟑𝟎
𝟏𝟓
Now, multiply 15 by 15 and 10 by 30.
• 15 × 15 = 225
• 10 × 30 = 300
Here, 225 ≠ 300.
Therefore, 15:10 and 30:15 are not equivalent ratios.
Are the given ratios - 15:10 and 30:15 equivalent
or not?

20. Encircle the equivalent ratios of 6:5
34:14
30: 25
5:6
60: 72
72:60

21. Ratio of distance of the school from Sneha’s home to the distance of the
school from Ashish’s home is 2 : 1.
(a.)Who lives nearer to the school?

22. Ratio of distance of the school from Sneha’s home to the distance of the
school from Ashish’s home is 2 : 1.
(a.)Who lives nearer to the school?
Ashish lives nearer to the school
(As the ratio is 2 : 1)

23. Ratio of distance of the school from Sneha’s home to the distance of the
school from Ashish’s home is 2 : 1.
(b)Complete the following table which shows some possible distances
that Sneha and Ashish could live from the school.
Distance from Sneha’s home
to school (in km.)
Distance from Ashish’s home
to school (in km.)
10 5
4
4
3
1

24. Ratio of distance of the school from Sneha’s home to the distance of the
school from Ashish’s home is 2 : 1.
(b)Complete the following table which shows some possible distances
that Sneha and Ashish could live from the school.
Distance from Sneha’s
home to school (in km.)
Distance from Ashish’s
home to school (in km.)
10 5
8 4
4 2
6 3
2 1

25. A) 3: 4
B.) 3:2
C.) 4:3
D.) 2:3
• Which ratio is equivalent to 14:21?

26. RECAPITULATION:
• Two or more ratios that express the same relation or comparison of numbers are known as equivalent
ratios.
• In the following figure, encircle the equivalent ratios and simplify also .

27. RECAPITULATION:
• Find two equivalent ratios of 10:11.
• Real life examples of Equivalent Ratios :

28. HOMEWORK:
Q.1) Consider the statement: Ratio of breadth and length of a hall is 2 : 5. Complete the following table that
shows some possible breadths and lengths of the hall.
Q.2) Mother wants to divide Rs36 between her daughters Swati and Warsha in the ratio of their ages. If age
of Swati is 15 years and age of Warsha is 12 years, find how much Swati and Warsha will get.
Q.3) Present age of father is 42 years and that of his son is 14 years. Find the ratio of
(a)Present age of father to the present age of son.
(b) Age of the father to the age of son, when son was 12 years old.
(c) Age of father after 10 years to the age of son after 10 years.
(d) Age of father to the age of son when father was 30 years old.
Breadth of the hall (in metres) 10 40
Length of the hall (in metres) 25 50