Class 7 - Percentages: Meaning, Formula and Solved Examples

Percentages are a key concept in Class 7 Mathematics that help express numbers as parts of 100. They are widely used in everyday life, such as calculating marks, discounts, interest, data representation,etc. Understanding percentages makes it easier to compare quantities in a standardized form. In this guide, you will learn how to convert fractions and decimals into percentages, calculate percentage values, and solve different types of problems step by step with clear explanations and simple examples.

Table of Contents

• What is a Percentage?
• Percentage Formula
• Converting Fractions to Percentages
• Converting Decimals to Percentages
• Converting Percentages to Fractions
• Converting Percentages to Decimals
• Converting Ratios to Percentages
• Finding the Percentage of a Given Quantity
• Expressing One Quantity as a Percentage of Another
• Percentage Increase and Decrease
• Percentage Chart: Fractions to Percentages
• Solved Examples on Percentages
• Practice Problems on Percentages

What is a Percentage?

The word ‘percent’ comes from the Latin phrase per centum, which means ‘per hundred’ or ‘out of 100’. So a percentage is simply a way of expressing a number as a part of 100. The symbol ‘%’ reads per cent. Percentages have no unit, they are just pure numbers.

Example:

• 50% means 50 out of 100, half of any quantity.

• 100% means the whole thing.

• 25% means one quarter.

• 1% means one hundredth.

Percentage Formula

The basic formula to find what percentage a value is of a total:

Percentage = (Value / Total Value) × 100

Or, when you want to find a percentage of a number:

P% of a number = (P / 100) × Number

Converting Fractions to Percentages

Here are the simple steps to convert fractions to percentages:

Step 1: Find the equivalent fraction with the denominator as 100.

Step 2: Write the numerator with % symbol.

Alternatively, 

Fraction → Percentage: (Numerator / Denominator) × 100 

Example 1: Convert 25to percentage.
 25=2×205×20=40100=40

Example 2: Convert 5/8 to a percentage. 
 58×100=500/8=62.5

Converting Decimals to Percentages

Here are the simple steps to convert decimals to percentages:

Step 1: Multiply the decimal with 100.

Step 2: Place the % symbol next to the number.

Formula: Decimal × 100 = Percentage

Example: Convert the following decimals to percentages. (a) 0.67 (b) 0.07

(a) 0.67 = 0.67 × 100 = 67%

(b) 0.07 = 0.07 × 100 = 7%

Converting Percentages to Fractions

Here are the simple steps to convert percentages to fractions:

Step 1: Remove the % symbol and write the number as a fraction with the denominator as 100.

Step 2: Simplify the fraction, if possible.

Example 1: Convert 25% to a fraction.

25% = 25/100

HCF of 25 and 100 = 25

25 ÷ 25 = 1, 100 ÷ 25 = 4

25% = 1/4

Example 2: Convert 60% to a fraction.

60% = 60/100

HCF = 20; 60/20 = 3, 100/20 = 5

60% = 3/5

Converting Percentages to Decimals

Here are the simple steps to convert percentages to decimals:

Step 1: Remove the % symbol and write the number as a fraction with the denominator as 100.

Step 2: Write the fraction as a decimal by putting the decimal point by skipping two digits from the ones place of the numerator.

Example: Convert the following percentages to decimals: (a) 6% (b) 37%

(a) 6% = 6/100 = 0.06

(b) 37% = 37/100 = 0.37

Converting Ratios to Percentages

Here are the simple steps to convert ratios to percentages:

Step 1: Write the ratio as a fraction.

Step 2: Multiply the fraction with 100 and put the % symbol next to the product.

Example: Convert the following ratios to percentages: (a) 3:7 (b) 2:5

(a) 3:7 =  37=37×100=3007

(b) 2:5 =  25=25×100=40

Finding the Percentage of a Given Quantity

Here are the simple steps to find the percentages of a given quantity:

Step 1: Write the given percentage as a fraction with the denominator as 100.

Step 2: Multiply the fraction with the given quantity.

X% of Y = (X/100) × Y

Example1: Find 20% of 150.

(20/100) × 150 = 0.2 × 150 = 30

Example 2: Find 15% of ₹2,000.

(15/100) × 2000 = 15 × 20 = ₹300

Expressing One Quantity as a Percentage of Another

Here are the simple steps to express one quantity as a percentages of another:

Step 1: Write the given quantities as fractions.

Step 2: Multiply the fraction with 100 and put the % symbol beside the product.

Example 1: What percentage of 800 m is 40 m?

Let x% of 800 m be 40 m.

x% of 800 m = 40 m

 x100 × 800 = 40

8x = 40

x = 40/8 = 5

Therefore, 5% of 800m is 40m.

Percentage Increase and Decrease

Steps to calculate an increase or a decrease in percent:

Step 1: Check whether there is an increase or a decrease in the given quantity.

Step 2: Write this as fraction with denominator as the original quantity.

Step 3: Multiply the fraction with 100 and put % symbol.

Percentagechange=ChangeOriginal×100

% Increase = [(New Value − Original Value) / Original Value] × 100

% Decrease = [(Original Value − New Value) / Original Value] × 100

Example 1: The price of a notebook increased from ₹40 to ₹50. What is the percentage increase?

Increase in price = 50 − 40 = ₹10

% Increase = (10/40) × 100 = 25%

There is a  25% increase in the price of notebook.

Example 2: A TV was priced at ₹15,000. During a sale, it dropped to ₹12,000. What is the percentage decrease?

Decrease in price = 15,000 − 12,000 = ₹3,000

% Decrease = (3000/15000) × 100 = 20%

There is a  20%  decrease in the price of TV.

Percentage Chart: Fractions to Percentages

Solved Examples on Percentages

Example 1: Meena got 45 out of 50 marks. What is her percentage?

Solution: Given, Meena got 45 out of 50 marks.

(45/50) × 100 = 90%

Meena got 90% marks.

Example 2: Convert 0.65 into a percentage.

Solution: 0.65 × 100 = 65%

Example 3:What percentage of 500 cm is 20 cm?

Solution: Let x% of 500 cm be 20 m.

x% of 500 = 20

(x/100) × 500  = 20

5x = 20

x= 4

Therefore, 4% of 500 cm is 20 cm.

Example 4: The price of petrol increased from ₹90 to ₹99 per litre. Find the % increase.

Solution: Increase in price = 99 − 90 = ₹9

% Increase = (9/90) × 100 = 10%

Example 5: 15% of a number added to 20% of 150 gives 57. Find the number.

Solution: Let the required number be x.

 15% of x + 20% of 150 = 57

(15/100) × x + (20/100)  × 150 = 57

(15/100) × x + 30 = 57

(15/100) × x = 57 - 30 = 27

x = (27 × 100)/15 = 180.

Therefore the required number is 180.

Practice Problems on Percentages

1. Convert 7/25 to a percentage.

2. Convert 68% to a fraction in simplest form.

3. Convert 0.045 to a percentage.

4. Convert 4 : 5 to a percentage (each part).

5. Find 35% of 420.

6. A bag has 5 red and 20 blue pens. What % are red? 

7. 12% of a number is 96. Find the number. 

8. The price of 1 litre of petrol increased from ₹74 to ₹82. Find the percentage increase.

9. The sale of a novel decreased from ₹2000 on the first day to ₹1800 on the next day. Find the percentage decrease.

10. A TV's price increased from ₹12,000 to ₹13,200. Find the % increase.