Exercise 2.1 (Converting Fraction to Percentage, percentage as fraction)

Exercise 2.1

1. In each of the following grid, find the number of coloured squares and express it as a fraction, decimal and percentage.

Solution:

(i) Number of coloured square = 58

Total number of squares = 100

∴ Fraction : 58 / 100

Decimal : 0.58

Percentage : 58%

(ii) Number of coloured square = 53

Total number of squares = 100

∴ Fraction : 53 / 100

Decimal : 0.53

Percentage : 53%

(iii) Number of coloured square = 25

Total number of squares = 50

∴ Fraction : 25 / 50

Decimal : 25/50 × 2/2 = 50 / 100 = 0.50

Percentage : 25/50 × 100/100 = 25/50 × 100 % = 50%

 (iv) Number of coloured square = 17

Total number of squares = 25

∴ Fraction : 17/25

Decimal : 17/25 × 4/4 = 68 / 100 = 0.68

Percentage : 17/25 × 100/100 = 17 / 25 × 100% = 68%

(v) Number of coloured square = 15

Total number of squares = 30

∴ Fraction : 15 / 30

Decimal : 15/30 = 1/2 ×   50/50 = 50/100 = 0.50

Percentage : 15/30 = 15/30 × 100/100 = 15/30 × 100% = 50%

2. A picture of chess board is given. (i) Find the percentage of the white coloured squares. (ii) Find the percentage of grey coloured squares. (iii) Find the percentage of the squares that have the pieces and (iv) The squares that do not have the pieces.

Solution:  

(i) Total number of squares in the chess board = 64

Number of white coloured squares = 32

Percentage = ( 32/64 ) × (100/100)

 = 32/64 × 100% = 50%

(ii) Grey coloured squares = 64

Percentage = 32/64 × 100/100 = 32/64 × 100% = 50%

(iii) Number of squares having pieces = 20

Total number of squares = 64

 Percentage = 20/64 × 100/100 = 20/64 × 100% = 125% / 4 = 31 (1/4)%

 (iv) Number of squares do not have pieces = 44

 Percentage = 44/64 × 100/100 = 44 / 64 = 100% =

= 275% / 4 = 68 (3/4) %

3. A picture of dart board is given. Find the percentage of white coloured portion and black coloured portion.

Solution:

Total sector = 20

White coloured sector = 10

Black coloured sector = 10

Percentage of white : 10/20 × 100/100

Decimal : 10/20 × 100% = 50%

Percentage of black colour : 10/20 × 100/100

Decimal : 10/20 × 100% = 50%

4. Write each of the following fraction as percentage.

(i) 36/50 (ii) 81/30 (iii) 42/56 (iv) 2 (1/4) (v) 1 (3/5)

Solution:  

(i) 36/50 = (36/50 ) × 100/100 = 36/50 × 100% = 72%

(ii) 81/30 = ( 81/30) × 100/100 = 81/30 × 100% = 270%

(iii) 42/56 =( 42/56) × 100/100 = 42/56 × 100% = 21/28 × 100% = 75%

(iv) 2 (1/4 ) = 9/4 = 9/4 × 100/100 = (9/4) × 100% = 225%

(v) 1 (3/5) = 8/5 = 8/5 × 100/100 = 8/5 × 100% = 160%

5. Anbu scored 436 marks out of 500 in his exams. What was the percentage he scored?

Solution:

Total marks = 500;

Anbu's Score = 436

Percentage = (436/500) × 100/100 = ( 436/500 ) × 100% = 87.2%

Anbu's Score = 87.2%

6. Write each of the following percentage as fraction.

(i) 21%  (ii) 93.1%  (iii) 151%  ( iv) 65%  (v) 0.64%

Solution:

(i) 21% = 21/100

(ii) 93.1% = 93.1/100 = [93.1 × 10 ] / [100 × 10] = 931/1000

(iii) 151% = 151/100

(iv) 65% = 65/100 = 13/20

(v) 0.64% = [0.64 × 100] / [100 × 100] = 64/10000 = 4/625

7. Iniyan bought 5 dozen eggs. Out of that 5 dozen eggs, 10 eggs are rotten. Express the number of good eggs as percentage.

Solution:

1 dozen eggs = 12

5 dozen = 5 × 12

Total eggs = 60 eggs

Rotten eggs = 10

Good eggs = 60 – 10 = 50

Fraction of good eggs = 50/60

Percentage of good eggs = ( 50/60) × 100/100 = (50/60) × 100% = 83.33%

Percentage of good eggs = 83. 33%

8. In an election, Candidate X secured 48% of votes. What fraction will represent his votes?

Solution:  

Percentage of votes × secured = 48% = 48/100

Fraction of votes × secured = 12/25

9. Ranjith’s total income was ₹ 7,500. He saved 25% of his total income. Find the amount saved by him.

Solution:

Total income of Ranjith = ₹ 7500

His savings = 25% of 7500 = 25/100 of 7500 = (25/100 )x 7500 = ₹ 1,875

∴ Amount saved by Ranjith = ₹1,875

Objective type Questions

10. Thendral saved one fourth of her salary. Her savings percentage is

 (i) 3/4 %

(ii) 1/4  %

(iii) 25%

(iv) 1%

Solution: 1/4 × 100/100 = 1/4 × 100% = 25%

[Answer: (iii) 25%]

11.  Kavin scored 15 out of 25 in a test. The percentage of his marks is

 (i) 60%

(ii) 15%

(iii) 25%

(iv) 15/25

Solution: 15/25 × 100/100 = 15/25 × 100% = 60%

[ Answer: (i) 60% ]

12. 0.07% is 7

(i) 7/10  

(ii) 7/100  

(iii) 7/1000  

(iv) 7/10,000

Solution: 0.07% = 0.07 / 100 = ( [7/100] / 100 ) = 7 / (100 × 100) = 7 / 10,000

 [Answer: (iv) 7 / 10,000]

ANSWER:

Exercise 2.1

1. (i) 58/100, 0.58, 58% (ii) 53/100, 0.53, 53% (iii) 25/50 , 0.50, 50% (iv) 17/25 ,0.68, 68%  (v) 15/30 , 0.50, 50%

2. (i) 50% (ii) 50% (iii) 31 (4/16)% (iv) 68 (12/16)%

3. White colour– 50% ;  Black colour – 50 %

4. (i) 72% (ii) 270% (iii) 75% (iv) 225% (v) 160%

5. 87.2 %

6. (i) 21/100 (ii) 931/1000 (iii) 151/100 (iv) 13/20 (v) 4/625

7. 83.33%

8. 12/25

9. ₹ 1, 875

Objective type questions

 10.(iii) 25%

11. (i) 60%

12. (iv) 7/10,000