Before understanding how to calculate a percentage, let us know what a percentage is. Percentage means a number or a ratio expressed in terms of fractions of 100. It is denoted using the percentage sign “%”. The abbreviation used to represent the percentage is “pct” or “pc”. In other words, the percent or the percentage is defined as how much of one quantity is made by the different quantity, and it is evaluated at about 100.
Learn more about the percentage here.
In this article, you will learn how to calculate the percentage, how to calculate the percentage increase, decrease and difference along with the respective percentage formulas and examples.
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How to Calculate Percentage Using Formula
We can use the formula to calculate the percentage easily and quickly. The formula to calculate percentage is equal to the ratio of the actual value to the total value multiplied by 100. The percentage formula is:
\(\begin{array}{l}Percentage, % = \frac{Actual Value}{Total Value}\times 100\end{array} \) |
Let us understand this concept and formula with the help of an illustrative example given below:
Example: A circle below has ten divisions, and a few parts are shaded. Calculate the percentage of shaded parts (in the figure) in the circle.
Solution:
Total number of divisions in the circle = 10
Number of shaded parts = 2
We know that,
Percentage, % = (Actual Value / Total Value) × 100
Thus, the percentage of the shaded part of the circle = [(Number of shaded divisions)/ (Total number of divisions)] × 100
= (2/10) × 100
= 20%
Therefore, 20 percent, i.e. 20% of the circle has shaded portions.
Also, try: Percentage Calculator
How to Calculate Percentage of a Number
It is possible to calculate the percentage in three simple steps. They are:
Step 1: Identify the original form of the number, i.e. fraction or decimal. The original format will define the following mathematical operation on the number. Suppose a decimal number is 0.25, which may be the calculated ratio of the values we are comparing, while an example of a fraction is 4/15.
Step 2: Perform the mathematical operation on the number. That means, if the given number is a fraction, convert it to a decimal number. If the given number is a decimal number, then leave it as it is.
For example, 4/15 = 0.267
Step 3: Multiply the result obtained in the previous step by 100 and the resulted value should be expressed as a percentage. For example, 0.267 × 100 = 26.7%.
Learn how to convert decimal to fraction here.
Alternative Method:
We can also calculate the percentage of a number by changing the number into a fraction with the denominator 100. This can be understood in a better way from the example given below:
Example:
Convert 3/20 to a percentage.
Solution:
The given fraction is 3/20.
Let us convert the denominator to 100.
(3/20) × (5/5) = 15/100
Now, multiply the result by 100.
(15/100) × 100 = 15
Therefore, 3/20 = 15%
Note: This method of calculating the percentage is applicable only when the denominator is a factor of 100. Otherwise, we can use the regular method to calculate the percentage.
How to Calculate Percentage of Marks
Most of the students get a question on how to calculate the percentage of marks obtained in exams. Here is the answer to this question along with the example. Two simple steps give you the percentage of marks. They are:
Step 1: Divide the obtained marks by the maxim marks of the test.
Step 2: Multiply the result by 100.
Go through the example given below to understand the process of finding the percentage of marks.
Example 1: A student scored 1156 marks in the examination out of 1200 marks. Calculate the percentage of marks secured by the student.Go through the example given below to understand the process of finding the percentage of marks.
Solution:
Number of marks scored = 1156
Maximum marks = 1200
Percentage of marks =(1156/1200) × 100
Percentage= 0.9633…. × 100
Therefore, the percentage of marks obtained is 96.3%
How to Calculate Percentage Change
Let’s learn how to calculate the percentage difference between two numbers. The percentage difference is the variation in the value of a number or quantity over a while in terms of percentage.
The formula gives Percentage change (Or Percentage difference) is:
% change =[(Change in Value) / Original Value] × 100
Here,
Change in Value = New value – Original value
The change in the value could be positive or negative. Positive difference means there is a percentage increase in the value, otherwise, it is called percentage decrease.
Thus, there are two types of percentage change in mathematics. They are:
- Percentage increase
- Percentage decrease
How to Calculate Percentage Increase
When the new value is greater than the original value, the percentage change in the value shows the percent increase in the original number. This can be calculated as:
\(\begin{array}{l}Percent~Increase(%Increase)=\frac{Increase~ in~ value}{Original~ value}\times 100\end{array} \) |
Here,
Increase in value = New value – Original value
How to Calculate Percentage Decrease
When the new value is lesser than the original value, the percentage change in the value shows the percent decrease in the original number. The formula for percentage increase is given by:
\(\begin{array}{l}Percent~Decrease(%Decrease)=\frac{Decrease~ in~ value}{Original~ value}\times 100\end{array} \) |
Here,
Decrease in value = Original value – New value
Also check: Percentage Increase and Decrease
There exists one more change in a percentage called percentage error. Generally, this kind of error occurs when we deal with weights.
Percentage Error Formula
Difference Between Percentage and Percentile
In most cases, many people might get confused with percentage and percentile. Both are different. Here, the difference between percentage and percentile is given in detail.
Percentage | Percentile |
The percentage represents the number out of 100 | Percentile is not a number out of 100 |
It can be written as ratios or proportions | It cannot be written as ratios or proportions |
A percentage is obtained by multiplying the ratio of two numbers with 100 | A percentile is a percentage of values that can be found below a specific value |
It is not based on ranking numbers | It is based on ranking numbers |
It is written in the form of x% | It is written in the form of xth |
It is based on one case | Comparison of one case with other |
It does not rely on the normal distribution | It relies on the normal distribution |
Also, read: Difference Between Percentage And Percentile
Solved Examples of Calculating the Percentage
Question 1: There are 120 students in a class. Out of them, 60 students are boys. Find the percentage of boys in the class.
Solution:
Given:
Total number of students in class = 120
Number of boys in class = 60
Therefore, the percentage of boys in class = ( 60 × 100)/120
= 600/12 = 50
So, the percentage of boys in class = 50%
Question 2: Find 25 % of 10.
Solution:
Remember that “of” means “times”
So, 25% of 10 = (25/100) × 10
0.25 × 10 = 2.5
Therefore, 25% of 10 is 2.5.
Question 3: Find the percentage of the ripened apples, if the number of ripe apples is 10 and the total number of apples in the basket are 60.
Solution: Given, the total number of apples = 60
Number of ripe apples = 10
Percentage of ripe apples = (10/60) × 100
= (1/6) × 100
= 16.666666
=16.67%
Question 4: There are 150 people present in a cinema hall. The number of men is 80 and the number of women is 70 in the hall. Calculate the percentage of men present in the hall.
Solution: Total number of people present in cinema hall = 150
Number of men = 80
Percentage of men = (80 x 100)/150
= 53.33%
Question 5: What is 15% of 75 equal to?
Solution: 15% of 75 = (15/100) × 75 = 11.25
Practice Problems
- Jaanu scored 34, 65, 58, 70, 50 in 5 subjects of a monthly test in which the maximum marks for each subject is 100. Calculate the percentage of marks scored in 5 subjects.
- The price of a toy was increased by 30% to Rs. 120. What was the original price?
- Convert the fraction 7/18 to a percentage.
- A student increased the value of a number from 65 to 110. Find the percentage change in the number.
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