NCERT Solutions for Class 7 Maths Chapter 8 Exercise 8.2 (Ex. 8.2) Comparing Quantities in PDF file format free to download for session 2022-2023. Solutions are prepared by subject experts using step by step calculation. In class 7 math exercise 8.2, questions are based on the concept of percentage and its application. Here we will learn to convert a simple number or fraction into percentage or percentage to fraction.

## Class 7 Maths Chapter 8 Exercise 8.2 Solution

• ### CBSE NCERT Class 7 Maths Chapter 8 Exercise 8.2 Solution in Hindi and English Medium

 Class: 7 Mathematics Chapter: 8 Comparing Quantities Exercise: 8.2 Hindi and English Medium Solution

### Class 7 Maths Chapter 8 Exercise 8.2 Solution in Videos

#### Percentage

The word ‘per cent’ is derived from Latin phrase ‘per centum’ meaning ‘per hundred’. Per cent is represented by the symbol % and means hundredths too.
Example:
Suppose Ashish obtains 87 marks out of 100 in English. Then, we say that he has obtained 92 per cent marks in English.
Similarly, if there is a box containing 100 toys, out of which 15 toys are defective, we say that 15 per cent of the toys in the box are defective.

##### To Convert a Fraction into a Percentage

RULE: In order to convert a fraction into a percentage multiply the fraction by 100 and put the per cent sign %.

### Convert each of the following fractions into a percentage: (i) 33/100, (ii) ¾ (iii) 7/25 (iv) 11/40

We have:
(i) 33/100 = {(33/100) x 100} % = 33%
(ii) ¾ = {(3/4) x 100} % = 75%
(iii) 7/25 = {(7/25) x 100} % =28%
(iv) 11/40 = {(11/40) x 100} % = 27(1/2) %

### Express each of the following as a ratio: (i) 17 % (ii) 72 % (iii) 12.5 % (iv) 225 %

We have, (i) 17 % = 17/100 = 17 : 100.
(ii) 72 % = 72/100 = 18/28 = 18 : 25.
(iii) 12.5 % = 12.5/100 = 125/1000 = 1/8 = 1 : 8.
(iv) 225 % = 225/100 = 9/4 = 9 : 4

### Convert each of the following into a fraction: (i) 35 % (ii) 56 % (iii) 37.5 % (iv) 140 %

We have:
(i) 35 % = 35/100 = 7/20
(ii) 56 % = 56/100 = 14/25
(iii) 37.5 % = 37.5/100 = 375/1000 = 3/8
(iv) 140 % = 140/100 = 7/5

### Convert each of the following ratios into a percentage: (i) 14 : 25 (ii) 5 : 6 (iii) 111 : 125 (iv) 8 : 5.

We have:
(i) 14 : 25 = 14/25 = (14/25) x 100 % = 56 %
(ii) 5 : 6 = 5/6 = (5/6) x 100 % = 83(1/3) %
(iii) 111 : 125 = 111/125 = (111/125) x 100 % = 88.8 %
(iv) 8 : 5 = 8/5 = (8/5) x 100 % = 160 %

### Convert each of the following into a decimal fraction: (i) 36% (ii) 5.4%

We have:
(i) 36% = 36/100 = 0.36
(ii) 5.4% = 5.4/100 = 54/1000 = 0.054

### Convert each of the following decimal into a percentage: (i) 0.8 (ii) 0.36

We have:
(i) 0.8 = (0.8 x 100) % = 80 %
(ii) 0.36 = (0.36 x 100) % = 36 %

##### To Convert a Percentage into a Fraction

RULE: To convert a percentage into a fraction, we divide it by 100 and remove the sign %.

##### Percentage as a Ratio

A percentage can be expressed as a ratio with its second term 100 and first term equal to the given percentage.

##### To Convert a Given Ratio into a Percentage

RULE First convert the given ratio into fraction, and then multiply the fraction by 100 and put the per cent sign %.

##### To Convert a Given Percentage in Decimal Form

RULE: First convert the given percentage into fraction and then put the fraction into decimal form.

##### To Convert a Given Decimal into a Percentage

RULE: Multiply the given decimal by 100 and put the per cent sign %

### How do I turn a number into a percentage?

To convert a number into percent multiple it by 100 and then add the percent sign. These examples convert the numbers 23 and 158 to percent’s. To convert a number with a decimal into percent, multiply it by 100 and add the percent sign.

### What is percentage formula?

Formula to Calculate Percentage
The Percentage Formula is given as, Percentage = (Value ⁄ Total Value) × 100.

### How do I calculate a percentage between two numbers?

First: work out the difference (increase) between the two numbers you are comparing. Then: divide the increase by the original number and multiply the answer by 100.        