proportion and its types, mathematics 8

Proportion

Objectives

After this presentation students will be

able to

Define proportion

Define types of proportion

Define compound proportion

+ Exercises

Proportion

Proportion: The equality of two ratios

is called proportion.

For Example:

2 : 3 = 6 : 9 or 2 : 3 : : 6 : 9

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

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.

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.

Find the value of X From the

following proportions1. 1 : 2 = 3 : x

Solution:

1x X = 2 x 3

X = 6

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

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

Compound Proportion

If more than one proportion are used

in any problem then it is called a

compound proportion .

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 ?

Solut ion:

days horses food (bags)

20 36 200

45 45 X

36 200 20 200

45 X 45 X-

1-2

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

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.