The document explains the concept of proportion, defining it as the equality of two ratios and discussing types such as direct and inverse proportions. It details elements of proportion, including extremes and means, and illustrates how to solve proportion-related problems through exercises. Additionally, it emphasizes the utility of proportion in solving real-life problems and mathematical calculations.

2. Proportio
n

3. Objectives
 After this presentation students will be
able to
 Define proportion
 Define types of proportion
 Define compound proportion
 + Exercises

4. Proportion
 Proportion: The equality of two ratios
is called proportion.
 For Example:
2 : 3 = 6 : 9 or 2 : 3 : : 6 : 9

5. Elements of Proportion
1. It consist four terms. The first and
fourth terms are called extremes.
While the second and third terms are
called means.
2. The product of means is always
equal to the product of extremes.
This property enables to find missing
term out of the fourth terms

6. Two kinds of Proportion
1. Direct Proportion:
Direct proportion is that when one
quantity increases, other one
quantity also increases .
Or
when one quantity decreases , other
one quantity also decreases.

7. Two kinds of Proportion
2. Inverse proportion:
Inverse proportion is that when one
quantity increases and other one
quantity decreases.
Or
when one quantity decreases and other
one quantity increases.

8. Find the value of X From the
following proportions
1. 1 : 2 = 3 : x
Solution:
1x X = 2 x 3
X = 6

9. Q:7. 11 and 27 are the extremes of a
proportion. If one of the means is 9, find the
other?
Solution:
11 : 9 : : X : 27
9 x X = 27 x 11

10. Q:14 . In a fort 600 persons have food provision for
27 days and after 10 days 80 more persons joined
them. For how many days will the same food
provision be sufficient for 25 days?
 Solution:
persons days
600 : 17
680 : X
600:680 : : X:17
680 x X = 600 x 17
X = 600 x 17 X = 15 days
680

11. Compound Proportion
 If more than one proportion are used
in any problem then it is called a
compound proportion .

12. Exercise 4.2
 Q no. 3 If food provision of 200 bags is
sufficient for 36 horses for 20 days, find
how much provision of bags will be
sufficient for 45 horses in 45 days ?

13. Solution:
days horses food (bags)
20 36 200
45 45 X
36 200 20 200
45 X 45 X
-
1
-2

14. 36 : 45 : : 200 : X
20 : 45 : :200 : X
36 : 45
20 : 45
: : 200 : X
36 x 20 x X = 45 x 45 x 200
X = 45 x 45 x 200
36 x 20
X = 405000
720
X = 562.5 bags

15. Conclusion
 Proportion is more effective tool with
the help of proportion we solve the
daily life problems and also
mathematical proportion. The equality
of two ratios is called proportion.