Percentage

In mathematics, a percentage is a figure or ratio that signifies a fraction out of 100, i.e., A fraction whose denominator is 100 is called a Percent. In all the fractions where the denominator is 100, we can remove the denominator and put the % sign.

For example, the fraction 23/100 can be written as 23%. The opposite of this is also true, i.e., any percentage sign can be easily replaced by converting the number into a fraction with the denominator 100. For example, 45% can be converted to a fraction as 45/100.

The word "Percentage" was coined from the Latin word "Percentum" which means "by hundred". It is a dimensionless relation between two numbers. It is often denoted by the sign "%" or percent or pct.

Percentages are used in daily life, helping us understand and compare different quantities easily. Given below are some common applications of percentages in real life:

Percentage Formula

The percentage formula is a formula that is used to find the amount or share of a quantity in terms of a hundred. So, for calculating the percentage, we need three variables. First, the total value V₁, the present value V₂, and the percentage value P. The algebraic equation for this will be:

Percentage (P%) = (Parts (V₂) / Whole (V₁)) × 100

How to Calculate the Percentage of a Number?

Calculating the percentage of a number is very simple, you just need to use the formula mentioned below:

Percent of a Number = Percentage/100 × Number

Example: Calculate 5% of 50

• 5% of 50 = 5/100 × 50
• 5% of 50 = 0.05 × 50
• 5% of 50 = 2.50

Read More about: How to Calculate Percentage.

Percentage Calculator

The Percentage Calculator is a free tool prepared at GeeksforGeeks that is used to find the percentage if two or more numbers are given. Check the percentage calculator below:

Percentage Difference Formula

The Percentage difference or the percentage change formula is calculated when the difference between two values is divided by the average of the same values. We can say that the percentage difference is used to calculate the change in the value over the given period. Mathematically, we can be written as,

Percentage Difference = (Absolute difference / Average) × 100

Example: The Percentage difference between 50 and 100 will be:

= \dfrac{\left|50 - 100\right|}{\frac{50 + 100}{2}} \times 100
= 50/75 ×100
= 66.66%

Also Read,

• Percentage Increase Formula
• Percentage Decrease Formula

Percentage Chart

Let's see the percentage chart of fractions converted into percentages.

Percentage Tricks

There are percentage tricks that can be used while calculating the percentage of numbers. The percentage trick below is the most used:

% x of y = % y of x

Let's Solve 300% of 50.

Solution:

Here, solving 300% of 50 can be a little lengthy and tricky. However, using the trick it can be easily solved,

%x of y = %y of x
300% of 50 = 50% of 300
Now, solving 50% of 300 is relatively is. 50% of 300 is just half of 300. Therefore, 50% of 300 is 150.
Therefore, 300% of 50 is 150.

Read More:

• Tricks for Percentage
• Fractions
• Ratio and Proportions Formula

Solved Example of Percentage

Example 1: Find 15 % of 500.

Solution:

We can find the percentage by formula, 

V₂ = P × V₁
⇒ V₂ = 15% × 500
⇒ V₂ = (15 × 500) / 100 
⇒ V₂ = 75.

Thus, 15% of 500 is 75.

Example 2: What percentage is 1 of 3000?

Solution:

We can find the percentage by formula,

V₂ = P × V₁
⇒ P = V₂ / V₁
⇒ P = 1 / 3000

Thus, P% = 1/3000 × 100
⇒ P% = (1/30)%

Thus, 1 is 0.00333% of 3000.

Example 3: If 10% of x is 900. Find x.

Solution:

We can find the percentage by the formula,

V₂ = P × V₁
⇒ V₁ = V₂ / P
⇒ V₁ = (V₂ × 100 ) / P%
⇒ V₁ = (900 × 100) / 10
⇒ V₁ = 9000

Thus, the value of x is 9000.

Example 4: Find the value of the percentage of green blocks in each case.

Solution:

• In first case, the green blocks are 0, and the total blocks are 36. 
  Therefore, Percentage of green Blocks = 0/36 × 100 = 0%.

• In second case, the green blocks are 18, and the total blocks are 36. 
  Therefore, Percentage of green Blocks = 18/36 × 100 = 50%.

• In third case, the green blocks are 27 and the total bricks are 36. 
  Therefore, Percentage of green Blocks = 27/36 × 100 = 75%.

Practice Problem on Percentages

Question 5 : In school,three rows are formed of the students.First row has 50 % more students than the second row and 
            the third row has 50 % Less students than the second row.
             If the total number of students in all the rows is 900,
             then find the number of students in the third row.

Read More:

• Percentages – Aptitude Questions and Answers
• Problems on Percentage