Mastering Percentage Calculations: Formulas and Methods

Calculating percentages involves finding a specified portion or fraction of a whole, often expressed as a percentage value. Here are some common methods and formulas for calculating percentages:

1. Percentage of a Whole (Part/Whole x 100):

• To find what percentage one number (the "part") represents of another number (the "whole"), use the following formula:

  $\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100$

• For example, if you have 25 apples out of a total of 100 apples, the percentage of apples you have is $(25 / 100) \times 100\% = 25\%$.

2. Percentage Change or Increase/Decrease:

• To calculate the percentage change between two values, use the following formula:

  $\text{Percentage Change} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100\%$

• If a product's price increased from $50 to $60, the percentage increase is $(60 - 50) / 50 \times 100\% = 20\%$.

3. Finding a Percentage of a Number:

• To find what a specific percentage of a number is, use the following formula:

  $\text{Result} = \frac{\text{Percentage}}{100} \times \text{Number}$

• If you want to find 15% of 200, the calculation is $(15 / 100) \times 200 = 30$.

4. Calculating the Original Value (Reverse Percentage):

• To find the original value when you know the final value and the percentage change, use the following formula:

  $\text{Original Value} = \frac{\text{Final Value}}{1 + (\text{Percentage Change} / 100)}$

• If a product costs $60 after a 20% discount, you can find the original price as 60 / (1 + 20/100) = $50.

5. Percentage of a Portion of a Whole:

• To find the percentage a part of something represents of a larger whole, use this formula:

  $\text{Percentage} = \frac{\text{Part}}{\text{Whole Part}} \times 100\%$

• For example, if you want to know what percentage of your monthly income is spent on rent, you'd use your monthly rent payment as the "part" and your total monthly income as the "whole."

These formulas and methods are versatile and can be applied in various situations when you need to work with percentages. Whether you're calculating discounts, tax amounts, percentage growth, or other percentage-related problems, these formulas will help you find the answers you need.