FIND THE RATIO OF SHADED PORTION TO THE UNSHADED PORTION

Problem 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 :

	(i) shaded Area : unshaded Area = 3 : 1 (ii) shaded Area : total Area = 3 : 4 (iii) Fraction Form  = 3/4
	(i) shaded Area : unshaded Area = 3 : 2 (ii) shaded Area : total Area = 3 : 5 (iii) Fraction Form  = 3/5
	(i) shaded Area : unshaded Area = 5 : 3 (ii) shaded Area : total Area = 5 : 8 (iii) Fraction Form  = 5/8
	(i) shaded Area : unshaded Area = 5 : 3 (ii) shaded Area : total Area = 5 : 8 (iii) Fraction Form  = 5/8
	(i) shaded Area : unshaded Area = 11 : 5 (ii) shaded Area : total Area = 11 : 16 (iii) Fraction Form  = 11/16
	(i) shaded Area : unshaded Area = 7 : 2 (ii) shaded Area : total Area = 7 : 9 (iii) Fraction Form  = 7/9
	(i) shaded Area : unshaded Area = 7 : 4 (ii) shaded Area : total Area = 7 : 11 (iii) Fraction Form  = 7/11
	(i) shaded Area : unshaded Area = 7 : 3 (ii) shaded Area : total Area = 7 : 10 (iii) Fraction Form  = 7/10

Problem 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 :

a)

(i) By observing the figure,

The ratio of sales of  A to the sales of B

50% : 30%

(ii)

The ratio of sales of A to the total sales.

= 50 : 100

b) 

Fraction Form

50/100 (or) 1/2

Problem 3 :

The column graph represents the results of a survey to determine the method by which students travel to school.

a)  Find the total number of students surveyed.

b)  Write as a ratio:

(i)  Students arriving by car : students who walk

(ii)  Students arriving by bus: total number of students surveyed.

c)  What fraction of the students surveyed travel to school by bus?

Solution :

a)

Number of students surveyed in car = 8

Number of students surveyed in bus = 14

Number of students surveyed in train = 11

Number of students surveyed in walk = 18

Number of students surveyed in bicycle = 13

Total number of students surveyed = 8 + 14 + 11+ 18 + 13

= 64 Students.

b)

(i)

Students arriving by car : students who walk

From (a),

= 8 : 18

(ii)

 Students arriving by bus : total number of students surveyed

From (a),

14 : 64

c)

In fraction form,

From (b),

= 14/64 (or) 7/32

Problem 4 :

Determine whether the ratios are equivalent.

a) 5 : 2 and 30 : 12

b) 6 : 4 and 18 : 6

c) 4 : 3 and 8 : 7

d) 18 : 12 and 3 : 2

Solution :

a) 5 : 2 and 30 : 12

To check if the ratios are equivalent, we have to equate these two ratios.

5/2 = 30/12

5(12) = 30(2)

60 = 60

So, the ratios are equal.

b) 6 : 4 and 18 : 6

6/4 = 18/6

6(6) = 18(4)

36 ≠ 72

So, the ratios are not equal.

c) 4 : 3 and 8 : 7

4/3 = 8/7

4(7) = 8(3)

28 ≠ 24

So, the ratios are not equal.

d) 18 : 12 and 3 : 2

18/12 = 3/2

18(2) = 3(12)

36 = 36

So, the ratios are equivalent.

Problem 5 :

Write two equivalent ratios that have values of 5/7

Solution :

To find equivalent ratios, we have to multiply both numerator and denominator by same number.

(5/7) x (2/2) ==> 10/14

(5/7) x (3/3) ==> 15/21

(5/7) x (4/4) ==> 20/28

So, the equivalent ratios of 5 : 7 are 10 : 14, 15 : 21 and 20 : 28.

Problem 6 :

During a chess match, there are 12 pieces left on the board. The ratio of white pieces to black pieces is 2 : 1. How many white pieces are on the board?

Solution :

Number of pieces left = 12

Ratio between white pieces to black pieces = 2 : 1

Number of white pieces = 2x

Number of black pieces = 1x

2x + 1x = 12

3x = 12

x = 12/3

x = 4

Number of white pieces = 8

Number of black pieces = 4

Problem 7 :

You run at a pace of 2 miles every 17 minutes. Your friend runs at a pace of 3 miles every 24 minutes. Are you and your friend running at the same pace? If not, who is running faster?

Solution :

2 : 17 and 3 : 24

2/17 = 3/24

2(24) = 3(17)

48 ≠ 51

So, you both are not running in the same pace and your friends runs faster.