WRITING RATIO OF SHADED TO UNSHADED AREA

Example 1 :

In each of the following diagrams:

i) Find the ratio of the shaded area to the unshaded area.

ii) Find the ratio of the shaded area to the total area.

iii)  Find the fraction of the total area which is shaded

Solution :

(a) 

(i)  In the first picture out of 4 equal parts, only 3 of them are shaded.

Ratio of shaded to unshaded  =  3 : 1

(ii) Ratio of shaded to total area  =  3 : 4

(iii)  Fractional form of shaded region  =  3/4.

(b) 

(i)  In the first picture out of 6 equal parts, only 5 of them are shaded.

Ratio of shaded to unshaded  =  5 : 1

(ii) Ratio of shaded to total area  =  5 : 6

(iii)  Fractional form of shaded region  =  5/6.

(c) 

(i)  In the first picture out of 8 equal parts, only 3 of them are shaded.

Ratio of shaded to unshaded  =  3 : 5

(ii) Ratio of shaded to total area  =  3 : 8

(iii)  Fractional form of shaded region  =  3/8.

(d) 

(i)  In the first picture out of 9 equal parts, only 3 of them are shaded.

Ratio of shaded to unshaded  =  3 : 6

(ii) Ratio of shaded to total area  =  3 : 9

Since, it can be simplified the answer is 1 : 3

(iii)  Fractional form of shaded region  =  3/9 or 1/3.

(e) 

(i)  In the first picture out of 6 equal parts, only 4 of them are shaded.

Ratio of shaded to unshaded  =  4 : 2

(ii) Ratio of shaded to total area  =  4 : 6

Since, it can be simplified the answer is 2 : 3

(iii)  Fractional form of shaded region  =  4/6 (or) 2/3

(f)  

(i)  In the first picture out of 16 equal parts, only 9 of them are shaded.

Ratio of shaded to unshaded  =  9 : 7

(ii) Ratio of shaded to total area  =  9 : 16

(iii)  Fractional form of shaded region  =  9/16.

Example 2 :

The pie chart represents the sales of three different types of soap powders, A, B and C.

a) Write as a ratio :

i) the sales of A to the sales of B.

ii) the sales of A to the total sales.

b) What fraction of the total sales made is the sales of brand A?

Solution :

i)  50% : 30%

By simplifying we get, 5 : 3.

ii)  Sales of A is 50 and total sales is 100.

=  50 : 100

=  1 : 2

(b)  50/100 (or) 1/2.

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