## How To Find Percentage

Calculating percentages is an essential skill in various fields, including finance, mathematics, science, and everyday life. Understanding how to find percentages helps you interpret data, make informed decisions, and solve a wide range of problems. In this comprehensive guide, we’ll cover different methods and examples to help you master the art of calculating percentages.

**Method 1: Using the Percentage Formula:**

The most fundamental method to calculate a percentage is by using the percentage formula:

$Percentage=WholePart ×100$

- “Part” refers to the portion you want to find the percentage of.
- “Whole” represents the total or complete quantity.

**Example 1: Calculating a Percentage:**

Suppose you sold 150 items out of a total of 200 items. To find out what percentage of items you sold, use the formula:

$Percentage=200150 ×100=75%$

**Method 2: Calculating Percentage Change:**

You can use percentages to determine the change between two values. The percentage change formula is:

$Percentage Change=Old ValueNew Value−Old Value ×100$

**Example 2: Calculating Percentage Change:**

If the temperature increased from 20°C to 25°C, you can calculate the percentage change:

$Percentage Change=20− ×100=25%increase$

**Method 3: Finding a Percentage of a Number:**

When you need to find a certain percentage of a given number, use this formula:

$Percentage of Number=100Percentage ×Number$

**Example 3: Finding Percentage of a Number:**

To calculate 20% of 500:

$Percentage of Number=10020 ×500=100$

**Method 4: Calculating Final Value with Percentage Increase/Decrease:**

When you have an initial value and want to find the final value after a percentage increase or decrease, use these formulas:

- For an increase: $Final Value=Initial Value+(100Percentage Increase ×Initial Value)$
- For a decrease: $Final Value=Initial Value−(100Percentage Decrease ×Initial Value)$

**Example 4: Calculating Final Value with Percentage Decrease:**

If the price of a product decreased by 15% from $200:

$Final Value=200−(10015 ×200)=170$

**Method 5: Finding the Original Value:**

When you have the final value after a percentage increase or decrease and want to find the original value, use these formulas:

- For an increase: $Original Value=+100Percentage Increase Final Value $
- For a decrease: $Original Value=−100Percentage Decrease Final Value $

**Example 5: Finding Original Value after Percentage Increase:**

If the final value is $300 after a 20% increase:

$Original Value=+10020 300 =250$

**Method 6: Calculating Percentage Increase/Decrease Between Two Values:**

To find the percentage increase or decrease between two values, use this formula:

$Percentage Change=Old ValueNew Value−Old Value ×100$

**Example 6: Finding Percentage Increase/Decrease:**

If your monthly expenses increased from $500 to $600:

$Percentage Change=500− ×100=20%increase$

**Method 7: Finding the Percentage Increase/Decrease Relative to the Original:**

This method calculates the percentage increase or decrease relative to the original value. The formula is:

$Percentage Increase/Decrease=Original ValueDifference ×100$

**Example 7: Finding Percentage Increase/Decrease Relative to Original:**

If a stock’s price increased from $50 to $60:

$Percentage Increase/Decrease=50− ×100=20%increase$

**Method 8: Finding the Percentage Difference Between Two Quantities:**

This method calculates the percentage difference between two quantities, regardless of increase or decrease. The formula is:

$Percentage Difference=AverageDifference ×100$

**Example 8: Finding Percentage Difference:**

If the rainfall in January was 40 mm and in February was 60 mm:

$Percentage Difference=2+ − ×100=50%$

**Method 9: Calculating Compound Interest:**

When dealing with financial calculations, such as compound interest, you can calculate the final amount using the formula:

$Final Amount=Principal×(1+100Rate )_{Time}$

**Example 9: Calculating Compound Interest:**

If you invest $1000 at an annual interest rate of 5% for 3 years:

$Final Amount=1000×(1+1005 )_{3}=1157.63$

**Method 10: Calculating Percentage Contribution:**

When analyzing data, you might want to calculate the percentage contribution of a value to a total. The formula is:

$Percentage Contribution=TotalValue ×100$

**Example 10: Calculating Percentage Contribution:**

If a company’s revenue is $800,000 out of a total industry revenue of $4,000,000:

$Percentage Contribution=4000000800000 ×100=20%$

**Method 11: Calculating Tax and Discounts:**

In business and personal finance, percentages are often used to calculate taxes and discounts. For instance, to calculate the final price after applying a discount, you can use:

$Final Price=Original Price×(1−100Discount Percentage )$

**Example 11: Calculating Final Price with Discount:**

If an item originally costs $200 and there’s a 15% discount:

$Final Price=200×(1−10015 )=170$

**Method 12: Weighted Averages:**

In statistics, calculating weighted averages involves using percentages to give different values different levels of importance. The formula is:

$Weighted Average=Sum of Weights× $

**Example 12: Calculating Weighted Average:**

If you have three test scores: 85 (weight 2), 70 (weight 1), and 95 (weight 3):

$Weighted Average=++(×)+(×)+(×) =88$

**Practical Applications:**

- Calculating sales tax or discounts while shopping.
- Analyzing data and trends in business and finance.
- Determining grades and performance in education.
- Understanding health metrics like body fat percentage.
- Calculating population growth rates in demography.
- Analyzing scientific experiments and research data.
- Budgeting and financial planning.
- Calculating proportions in recipes and cooking.

**Conclusion:**

Calculating percentages is a fundamental skill that’s applicable in various scenarios. Whether you’re analyzing data, making financial decisions, or solving mathematical problems, understanding how to find percentages is crucial. By using the formulas and examples provided in this guide, you’ll be equipped to confidently calculate percentages, interpret results, and apply this knowledge to different situations in your academic, professional, and personal life.