CBSE Class 8 Math: Percentage
By Pratap Sanjay Sir
Introduction to Percentage
➥ The word ‘percent’ is derived from the Latin phrase “Percentum” which means per hundred.
➥ A percentage is a fraction with a denominator of one hundred and is denoted by the symbol ‘%’.
Definitions
Percentage:⟹ A ratio expressed as a fraction of 100. Example: 50% means 50 out of 100.
Percent:⟹ The symbol (%) used to denote a percentage.
Increase:⟹ When a value goes up. For example, an increase from 20 to 25 is a 25% increase.
Decrease:⟹ When a value goes down. For example, a decrease from 25 to 20 is a 20% decrease.
Profit:⟹ The amount gained. It is calculated as the selling price minus the cost price.
Loss:⟹ The amount lost. It is calculated as the cost price minus the selling price.
Discount:⟹ A reduction in price. It is usually given as a percentage of the original price.
Properties of Percentages
- Conversion: Percentages can be converted to fractions and decimals.
For example, 25% = 1/4 = 0.25. - Addition and Subtraction: Percentages can be added or subtracted when calculating increases or decreases.
- Multiplication and Division: Percentages are often used in multiplication and division to calculate profit, loss, or discount.
Examples of Percentage Calculations
Example 1: Conversion of Percent into Fraction
Express 25% as a fraction.
Solution: 25% = ( frac{25}{100} = frac{1}{4} )
Example 2: Conversion of Fraction into Percent
Convert ( frac{3}{8} ) into a percentage.
Solution: Required percentage = ( frac{3}{8} times 100 = 37.5% )
Example 3: Conversion of Percent into Decimal
Express 18% as a decimal.
Solution: Required decimal = ( frac{18}{100} = 0.18 )
Example 4: Calculating Percentage
What is 20% of 50?
Solution: ( frac{20}{100}times 50 = 10)
Example 5: Percentage Increase
If the price of a book increases from ₹200 to ₹250, what is the percentage increase?
Solution: Increase = 250 - 200 = 50
Percentage Increase = ( frac{50}{200} times 100 = 25% )
Example 6: Percentage Decrease
If the price of a book decreases from ₹250 to ₹200, what is the percentage decrease?
Solution: Decrease = 250 - 200 = 50
Percentage Decrease = ( frac{50}{250} times 100 = 20% )
Example 7: Profit Percentage
If a product is bought for ₹150 and sold for ₹180, what is the profit percentage?
Solution: Profit = 180 - 150 = 30
Profit Percentage = ( frac{30}{150} times 100 = 20% )
Example 8: Loss Percentage
If a product is bought for ₹200 and sold for ₹160, what is the loss percentage?
Solution: Loss = 200 - 160 = 40
Loss Percentage = ( frac{40}{200} times 100 = 20% )
Example 9: Discount Calculation
If a product costs ₹500 and is sold at a 10% discount, what is the selling price?
Solution: Discount = ( frac{10}{100} times 500 = 50 )
Selling Price = 500 - 50 = 450
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