## Introduction

Percentage is a mathematical concept used to represent parts of a whole as a fraction of 100. Understanding how to calculate percentages is crucial in everyday life, from budgeting to shopping to career growth. There are various methods to calculate percentages, and this article will discuss each one in detail, including the basic formula method, proportion method, percentage change method, percentage of total method, discounted percentage method, and the reverse percentage method.

## The Basic Formula Method

The basic formula method is the most commonly used method to calculate percentage and is applicable to find the percentage of a number in relation to another. Here’s how to do it:

**Step 1:** Identify the numbers you need for the calculation. One number will represent the part of the whole, and another number will represent the whole.

**Step 2:** Divide the part of the whole by the whole number.

**Step 3:** Multiply the result by 100 to get the percentage.

For example, if you want to find what percentage of the test questions you got correct out of 50 total questions:

**Step 1:** Let’s say you got 40 questions correct. Then, the number representing the part of the whole is 40, and the number representing the whole is 50.

**Step 2:** Divide 40 by 50: 40/50 = 0.8.

**Step 3:** Multiply the result by 100: 0.8 x 100 = 80%. Therefore, you got an 80% score on the test.

## The Proportion Method

The proportion method is a way to calculate percentages when dealing with ratios and proportions.

**Step 1:** Determine the ratio in the problem and convert it to a fraction.

**Step 2:** Simplify the fraction if necessary.

**Step 3:** Multiply the numerator and denominator of the fraction by the same number to get a new fraction, where the denominator is 100.

**Step 4:** Convert the numerator to a percentage.

For example, let’s say a basket contains 6 red apples and 4 green apples. What percentage of apples is red?

**Step 1:** The ratio of red to total apples is 6:10, which simplifies to 3:5 as a fraction.

**Step 2:** The fraction doesn’t simplify further.

**Step 3:** Multiply the numerator and denominator by 20 to get 60/100.

**Step 4:** Convert the numerator to a percentage: 60% of the apples in the basket are red.

## The Percentage Change Method

The percentage change method is used to calculate the increase or decrease in a number over a certain period of time.

**Step 1:** Determine the initial number and the final number.

**Step 2:** Find the difference between these two numbers.

**Step 3:** Divide the difference by the initial number.

**Step 4:** Multiply the result by 100.

For example, let’s say that you invested $500 in a stock, and after six months, it is now valued at $700. Therefore, the percentage increase in the value of your investment is:

**Step 1:** The initial investment is $500, and the final value is $700.

**Step 2:** The difference between the two numbers is $700-$500=$200.

**Step 3:** Divide the difference by the original value: $200/$500=0.4.

**Step 4:** Multiply the result by 100: 0.4 x 100 = 40%. Therefore, there was a 40% increase in the value of your investment.

## The Percentage of Total Method

The percentage of total method is used to calculate a percentage based on a value’s proportion in relation to a total value.

**Step 1:** Determine the value you want to express as a percentage and the total value.

**Step 2:** Divide the value you want to express as a percentage by the total value.

**Step 3:** Multiply the result by 100 to get the percentage.

For example, let’s say that you spent $50 on groceries out of your monthly budget of $200. The percentage of your budget spent on groceries is:

**Step 1:** The value you want to express as a percentage is $50, and the total value is $200.

**Step 2:** Divide the value you want to express as a percentage by the total value: $50 / $200 = 0.25.

**Step 3:** Multiply the result by 100: 0.25 x 100 = 25%. Therefore, you spent 25% of your monthly budget on groceries.

## The Discounted Percentage Method

The discounted percentage method is used to determine how much you will save or spend on a sale item.

**Step 1:** Determine the original price of the product and the discount percentage.

**Step 2:** Multiply the original price by the discount percentage as a decimal (i.e., divide the percentage by 100).

**Step 3:** Subtract the result from Step 2 from the original price to obtain the discounted price.

For example, let’s say you are interested in purchasing a dress originally priced at $100, which is now on sale for 20% off. Here’s how to determine the final cost:

**Step 1:** The original price is $100, and the discount is 20%.

**Step 2:** Multiply the original price by the discount percentage as a decimal: $100 x 0.20 = $20.

**Step 3:** Subtract $20 from the original price to arrive at the discounted price: $100 – $20 = $80. Therefore, the discounted price of the dress is $80.

## The Reverse Percentage Method

The reverse percentage method is used to determine the original value of a number after a percentage increase or decrease.

**Step 1:** Determine the final value and the percentage increase or decrease.

**Step 2:** Convert the percentage increase or decrease to a decimal and add or subtract it from 1.

**Step 3:** Divide the final value by the result of Step 2.

For example, if an item initially cost $100 and now it’s marked down 15%, the original price of the item can be calculated as follows:

**Step 1:** The final price of the item is $85, and the discount is 15%.

**Step 2:** Convert the percentage discount to a decimal and subtract it from 1: 1-0.15 = 0.85.

**Step 3:** Divide the final price by the result of Step 2: $85/0.85 = $100. Therefore, the original price of the item was $100.

## Conclusion

Calculating percentages is essential in many aspects of everyday life. From understanding your monthly budget to determining the value of investments, percentages are a fundamental part of our daily calculations. Understanding how to use each of the various methods helps us better manage our finances and assess the impact of changes in value. By using the tips we have covered, you will be able to calculate percentages with ease in no time.