# How to Calculate Percentage

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## How to Find Percentage: The Method

Before learning how to find the percentage of something- marks, a section of the population or quantity, etc, it is important to first understand the concept of percentage. Percentage of any number is the value of that particular number out of hundred. It defines the ratio of a value to the complete value multiplied by 100. The percentage can be also referred to as per cent and is denoted by ‘%’.  The percentage represents "per one hundred" and denotes a piece of a total amount.

### Percentage Explanation with Examples

For example, 20% represents 20 out of 100, or 20 percent of the total amount. The percentage may also be cited as "out of 100" or "for every 100."

For example, we can say "Kalpana ate 20 out of 100 chocolates" or we can also mention "Kalpana ate 20% of the chocolate”.

There are a few different ways to write a percentage. One way to represent a percentage is to portray it as a decimal.

For example, 50% could also be written as 0.50. One can find the decimal version of a per cent by dividing the percentage by 100.

The concept of percentage is used in our day to day life to measure the tendency of value with respect to the original value. Computation of profit and loss percentage marks obtained by the students, tax to be paid, increment or depreciation of value are all estimated with the formula on how to calculate the percentage.

### Formula of Percentage

To know how to do percentages, it is necessary to know the formula. The formula to calculate percentage is represented by the ratio of the original value to the total value multiplied by 100. The formula is:

Percentage, % = $\frac{Value}{\text{Total Value}}$ x 100

The following strategies are implemented to determine how to get a percentage of something:

1. Establish the whole or total amount of what you want to find a percentage for.

2. Divide the number that is targeted to establish the percentage for.

3. Find the product of the value of the above ratio with 100.

To understand how to calculate the percentage of a number let us look into an example where we will be using a formula illustratively.

Example: A rectangle is divided into 12 equal parts. A few parts are shaded. Find the percentage of the shaded region in the rectangle.

Solution: Total number of divisions in the rectangle = 12

Number of shaded parts = 3

The formula is:

Percentage, % = $\frac{Value}{\text{Total Value}}$ x 100

Thus, the percentage of the shaded region of the rectangle = $\frac{\text{Number of shaded parts}}{\text{Total number of divisions}}$ x 100

= $\frac{3}{12}$ x 100

= 25%

## Did You Know

### 1. How to Find the Percentage of a Number

Commonly, there are two different formats to find the percentage of a number:

• Decimal form – One must multiply the given decimal number by 100.  Like if we take 0.23, the percentage will be 0.23 × 100 = 23%

• Fraction form: In this case, we must convert the fraction into decimal value by dividing the numerator by the denominator and then multiply with 100.

This formula can be used to find the percentage of marks, discount etc.

## 2. What is the Percentage Change Formula

Percentage change = $\frac{\text{New Value - Original Value}}{\text{Original Value}}$ x 100

Changes can be reflected by two different types:

### a. Percentage Increase

In this case, the new value is greater than the actual value. It can be calculated as:

Increase in Value = New Value – Original Value

% Increase = $\frac{\text{Increase in Value}}{\text{Original Value}}$ x 100

### b. Percentage Decrease

In this case, the new value is greater than the actual value. It can be calculated as:

The decrease in Value = Original Value – New Value

% Decrease = $\frac{\text{Decrease in Value}}{\text{Original Value}}$ x 100

### 3. How To Calculate Percentage Discount?

To calculate the percentage of discount received in case of a purchase, one must take into account the discount amount and the marked price.

% Discount = $\frac{\text{Discount Amount}}{\text{Marked Price}}$ x 100

Where, Discount Amount = Selling Price – Marked Price.

### 4. How to Find Percentage of Marks?

To find the percentage of marks obtained, one must take into account the marks obtained and total marks allotted for the test.

% Marks = $\frac{\text{Marks Obtained}}{\text{Total Marks}}$ x 100

### 5. How To Calculate Percentage With Calculator

There is ‘%’ sign in a calculator. Suppose you need to find 5% of 50, you need to type:

5%50

The press ‘=’ to get the answer i.e. 2.5

If you know how to find out the percentage, it will give you a huge advantage in business, calculating tips in restaurants, finding out the nutritional content of your food, or even determining statistics of your academic performance.

1. How to Check Percentage and Percentile Difference?

Ans: The following differences determine percentage and percentile:

 Percentage Percentile The percentage determines the value of some number out of 100 Percentile is not calculated as a value out of 100 Ratios or proportions can be used to represent a percentage Ratios or proportions cannot be used to represent a percentile The ratio of the value by the total value multiplied by 100, gives the percentage A percentile is a percentage of values that can originate lower than a precise value It is not related to ranking numbers It is related to ranking numbers The format is expressed as x% The format is expressed as x-th Only one case is represented by it It compares one case with another. A normal distribution is not required for this A normal distribution is required to determine this

2. In a Picnic Held By School, 250 Students ate Vegetarian Meal Whereas 750 of them Took Non-vegetarian Meal. Show How to Take Percentage of the Following:

1. Vegetarian students

2. Non-vegetarian students

Ans: The number of students that ate vegetarian = 250

The number of students that ate non-vegetarian = 750

The total number of students that went for the picnic = Vegetarian students + Non-vegetarian students

=  250 + 750

=  1000

According to the formula:

Percentage, % = Value / Total Value x 100

1. Percentage of vegetarian students = Number of vegetarian students / Total number of students x 100

= 250 / 1000 x 100

= 25%

1. Percentage of vegetarian students = Number of non-vegetarian students / Total number of students x 100

= 750 / 1000 x 100

= 75%