# Percentage

The term “percentage” refers to a way of expressing a fraction or proportion as a number out of 100. It is commonly used to compare or represent parts of a whole in various contexts.

In mathematics and statistics, percentages are used to quantify relative values, rates, or proportions. They allow for easy comparison and understanding of proportions on a standardized scale.

The word “percentage” is derived from the Latin word “per centum,” which means “by the hundred.” The symbol “%” is used to represent a percentage. For example, 50% represents 50 out of 100, or half of the whole.

Percentages are frequently used in everyday life, such as when calculating discounts, expressing interest rates, analyzing statistics, or understanding proportions in various fields like finance, economics, science, and social sciences.

By converting numbers into percentages, it provides a more intuitive representation that is easily comprehensible and comparable across different values and contexts.

Let’s take some example to discuss more on the basics of percentage. John got 86 marks out of 100 in a math exam, then the percent of mark in mathematics = 86100 = 86 %

Bob got 91 marks out of 100 in the same exam, then the percent of mark = 91100 = 91%
Since 91% is greater than 86%, we conclude that Bob’s performance is better than John in mathematics exam. The use of percent makes comparison easier as it is just like comparing whole numbers.

#### How Percentage Calculated ?

Percentages are calculated by expressing a part or fraction of a whole as a portion of 100. Here’s the general formula for calculating a percentage:

Percentage = (Part / Whole) * 100

To calculate a percentage, follow these steps:

Determine the “part” you want to express as a percentage.
Determine the “whole” or the total value of which the part is a portion.
Divide the part by the whole.
Multiply the result by 100 to convert it into a percentage.
For example, let’s say you have 25 apples out of a total of 100 apples, and you want to calculate the percentage of apples you have. Using the formula:

Percentage = (25 / 100) * 100
Percentage = 0.25 * 100
Percentage = 25%

So, in this case, you have 25% of the total apples.

You can also use this formula in reverse to find the part from a given percentage. For example, if you know that 40% of a value is 80, you can calculate the original value by rearranging the formula:

Part = (Percentage / 100) * Whole

Using the given values:

Part = (40 / 100) * Whole
80 = 0.4 * Whole

To solve for Whole, divide both sides by 0.4:

Whole = 80 / 0.4
Whole = 200

So, in this case, the whole value is 200.

A. 6%
B. 10%
C. 60%
D. 90% A. 8 %
B. 15 %
C. 27 %
D. 35 %

Explaination:

Students passed in English = 80%
Students passed in Math’s = 85%
Students passed in both subjects = 73%
Then, number of students passed in at least one subject
= (80+85)-73
= 92%. [The percentage of students passed in English and Maths individually, have already included the percentage of students passed in both subjects. So, We are subtracting percentage of students who have passed in both subjects to find out percentage of students at least passed in one subject.]

Thus, students failed in both subjects = 100-92 = 8%.

A. 0.2
B. 0.02
C. 0.005
D. 0.05

Explanation: A. 53,900
B. 54,000
C. 54,080
D. 54,900

Explanation: A. 1762
B. 1635
C. 441
D. 139

Explanation: A. 17.5%
B. 16 3/7 %

C. 18.5%

D. 18.25% 