What is Percentage?
Percentage means "per hundred." It’s a way to express a number as a fraction of 100. The symbol for percentage is %.
The formula for percentage is: \[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]
Trick 1: Percentage to Fraction Conversion
Converting percentages to fractions simplifies calculations. Here’s a quick shortcut:
Example
- \( 25\% = \frac{25}{100} = \frac{1}{4} \) - \( 75\% = \frac{75}{100} = \frac{3}{4} \)
Trick 2: Fraction to Percentage Conversion
To convert a fraction to a percentage, multiply by 100.
Example
- \( \frac{1}{5} = \frac{1}{5} \times 100 = 20\% \) - \( \frac{3}{8} = \frac{3}{8} \times 100 = 37.5\% \)
Trick 3: Percentage Increase or Decrease
To find the percentage increase or decrease:
\[ \text{Percentage Change} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 \]
Example
If the price of a product increases from ₹500 to ₹600: \[ \text{Percentage Increase} = \left( \frac{600 - 500}{500} \right) \times 100 = 20\% \]
Trick 4: Vedic Math Shortcut for Percentage of a Number
To find \( x\% \) of a number, use this Vedic math trick:
Example
Find 35% of 400. - Break 35% into 30% + 5%. - 30% of 400 = \( \frac{30}{100} \times 400 = 120 \) - 5% of 400 = \( \frac{5}{100} \times 400 = 20 \) - Total = \( 120 + 20 = 140 \)
Practice Problems
Problem 1
If 30% of a number is 45, what is the number?
Problem 2
A number is increased by 20% and then decreased by 10%. What is the net percentage change?
📜 Quiz Instructions
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