What are percentages?

Today we are going to know that How to calculate percentage Mathematically, percentages are either numbers or ratios that are expressed as fractions of 100. They are usually denoted as “%” or “percent.” An example of a percentage is 65% or 65 percent. They may be further represented as simple fractions or decimal fractions.

The term “percentage” is formed from two words: “per” and “cent.” Cent is a word with Latin and French origins that means “hundred,” and “percent” means “per hundred.” For example, 50 percent, or 50%, means 50 out of 100 or half of a whole.

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is one of the ways to represent a dimensionless relationship between two numbers; other methods include ratios, fractions, and decimals. Percentages are often denoted by the symbol “%” written after the number. They can also be denoted by writing “percent” or “pct” after the number. For example, 35% is equivalent to the decimal 0.35, or the fractions .

Percentages are computed by multiplying the value of a ratio by 100. For example, if 25 out of 50 students in a classroom are male, . The value of the ratio is therefore 0.5, and multiplying this by 100 yields:

0.5 × 100 = 50

In other words, the ratio of 25 males to students in the classroom is equivalent to 50% of students in the classroom being male.

How to Calculate Percentages

There are many formulas for percentage problems. You can think of the most basic as X/Y = P x 100. The formulas below are all mathematical variations of this formula.

Let’s explore the three basic percentage problems. X and Y are numbers and P is the percentage:

Find P percent of X
Find what percent of X is Y
Find X if P percent of it is Y

How to calculate percentage

Step 1: Identify the number you want to calculate the percentage of. Let’s call this number “X”.

Step 2: Determine the percentage you want to calculate. Let’s call this percentage “P”.

Step 3: Convert the percentage to a decimal by dividing it by 100. This step is necessary because percentages are expressed as parts of 100.

Step 4: Multiply the decimal obtained in Step 3 by the number you want to calculate the percentage of (X).

Step 5: The result of the multiplication in Step 4 is the percentage of X.

1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y

Example: What is 10% of 150?

Convert the problem to an equation using the percentage formula: P% * X = Y
P is 10%, X is 150, so the equation is 10% * 150 = Y
Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10
Substitute 0.10 for 10% in the equation: 10% * 150 = Y becomes 0.10 * 150 = Y
Do the math: 0.10 * 150 = 15
Y = 15
So 10% of 150 is 15
Double check your answer with the original question: What is 10% of 150? Multiply 0.10 * 150 = 15

2. How to find what percent of X is Y. Use the percentage formula: Y/X = P%

Example: What percent of 60 is 12?

Convert the problem to an equation using the percentage formula: Y/X = P%
X is 60, Y is 12, so the equation is 12/60 = P%
Do the math: 12/60 = 0.20
Important! The result will always be in decimal form, not percentage form. You need to multiply the result by 100 to get the percentage.
Converting 0.20 to a percent: 0.20 * 100 = 20%
So 20% of 60 is 12.
Double check your answer with the original question: What percent of 60 is 12? 12/60 = 0.20, and multiplying by 100 to get percentage, 0.20 * 100 = 20%

3. How to find X if P percent of it is Y. Use the percentage formula Y/P% = X

Example: 25 is 20% of what number?

Convert the problem to an equation using the percentage formula: Y/P% = X
Y is 25, P% is 20, so the equation is 25/20% = X
Convert the percentage to a decimal by dividing by 100.
Converting 20% to a decimal: 20/100 = 0.20
Substitute 0.20 for 20% in the equation: 25/0.20 = X
Do the math: 25/0.20 = X
X = 125
So 25 is 20% of 125
Double check your answer with the original question: 25 is 20% of what number? 25/0.20 = 125

What is P percent of X?

Written as an equation: Y = P% * X
The ‘what’ is Y that we want to solve for
Remember to first convert percentage to decimal, dividing by 100
Solution: Solve for Y using the percentage formula
Y = P% * X

Example: What is 10% of 25?

Written using the percentage formula: Y = 10% * 25
First convert percentage to a decimal 10/100 = 0.1
Y = 0.1 * 25 = 2.5
So 10% of 25 is 2.5

Y is what percent of X?

Written as an equation: Y = P% ? X
The ‘what’ is P% that we want to solve for
Divide both sides by X to get P% on one side of the equation
Y ÷ X = (P% ? X) ÷ X becomes Y ÷ X = P%, which is the same as P% = Y ÷ X
Solution: Solve for P% using the percentage formula
P% = Y ÷ X

Example: 12 is what percent of 40?

Written using the formula: P% = 12 ÷ 40
P% = 12 ÷ 40 = 0.3
Convert the decimal to percent
P% = 0.3 × 100 = 30%
So 12 is 30% of 40

Y is P percent of what?

Written as an equation: Y = P% * X
The ‘what’ is X that we want to solve for
Divide both sides by P% to get X on one side of the equation
Y ÷ P% = (P% × X) ÷ P% becomes Y ÷ P% = X, which is the same as X = Y ÷ P%
Solution: Solve for X using the percentage formula
X = Y ÷ P%

Example: 9 is 60% of what?

Writen using the formula: X = 9 ÷ 60%
Convert percent to decimal
60% ÷ 100 = 0.6
X = 9 ÷ 0.6
X = 15
So 9 is 60% of 15

What percent of X is Y?

Written as an equation: P% * X = Y
The ‘what’ is P% that we want to solve for
Divide both sides by X to get P% on one side of the equation
(P% * X) ÷ X = Y ÷ X becomes P% = Y ÷ X
Solution: Solve for P% using the percentage formula
P% = Y ÷ X

Example: What percent of 27 is 6?

Written using the formula: P% = 6 ÷ 27
6 ÷ 27 = 0.2222
Convert decimal to percent
P% = 0.2222 × 100
P% = 22.22%
So 22.22% of 27 is 6

P percent of what is Y?

Written as an equation: P% × X = Y
The ‘what’ is X that we want to solve for
Divide both sides by P% to get X on one side of the equation
(P% × X) ÷ P% = Y ÷ P% becomes X = Y ÷ P%
Solution: Solve for X using the percentage formula
X = Y ÷ P%

Example: 20% of what is 7?

Written using the formula: X = 7 ÷ 20%
Convert the percent to a decimal
20% ÷ 100 = 0.2
X = 7 ÷ 0.2
X = 35
So 20% of 35 is 7.

P percent of X is what?

Written as an equation: P% * X = Y
The ‘what’ is Y that we want to solve for
Solution: Solve for Y using the percentage formula
Y = P% * X

Example: 5% of 29 is what?

Written using the formula: 5% * 29 = Y
Convert the percent to a decimal
5% ÷ 100 = 0.05
Y = 0.05 * 29
Y = 1.45
So 5% of 29 is 1.45

Y of what is P percent?

Written as an equation: Y / X = P%
The ‘what’ is X that we want to solve for
Multiply both sides by X to get X out of the denominator
(Y / X) * X = P% * X becomes Y = P% * X
Divide both sides by P% so that X is on one side of the equation
Y ÷ P% = (P% * X) ÷ P% becomes Y ÷ P% = X
Solution: Solve for X using the percentage formula
X = Y ÷ P%

Example: 4 of what is 12%?

Written using the formula: X = 4 ÷ 12%
Solve for X: X = Y ÷ P%
Convert the percent to a decimal
12% ÷ 100 = 0.12
X = 4 ÷ 0.12
X = 33.3333
4 of 33.3333 is 12%

What of X is P percent?

Written as an equation: Y / X = P%
The ‘what’ is Y that we want to solve for
Multiply both sides by X to get Y on one side of the equation
(Y ÷ X) * X = P% * X becomes Y = P% * X
Solution: Solve for Y using the percentage formula
Y = P% * X

Example: What of 25 is 11%?

Written using the formula: Y = 11% * 25
Convert the percent to a decimal
11% ÷ 100 = 0.11
Y = 0.11 * 25
Y = 2.75
So 2.75 of 25 is 11%

Y of X is what percent?

Written as an equation: Y / X = P%
The ‘what’ is P% that we want to solve for
Solution: Solve for P% using the percentage formula
P% = Y / X

Example: 9 of 13 is what percent?

Written using the formula: P% = Y / X
9 ÷ 13 = P%
9 ÷ 13 = 0.6923
Convert decimal to percent by multiplying by 100
0.6923 * 100 = 69.23%
9 ÷ 13 = 69.23%
So 9 of 13 is 69.23%

Percentage Chart

The percentage chart is given here for fractions converted into percentages.

S.no	Ratio	Fraction	Percent(%)	Decimal
1	1:1	1/1	100	1
2	1:2	1/2	50	0.5
3	1:3	1/3	33.333	0.3333
4	1:4	1/4	25	0.25
5	1:5	1/5	20	0.20
6	1:6	1/6	16.667	0.16667
7	1:7	1/7	14.285	0.14285
8	1:8	1/8	12.5	0.125
9	1:9	1/9	11.111	0.11111
10	1:10	1/10	10	0.10
11	1:11	1/11	9.0909	0.0909
12	1:12	1/12	8.333	0.08333
13	1:13	1/13	7.692	0.07692
14	1:14	1/14	7.142	0.07142
15	1:15	1/15	6.66	0.0666

Learn Definition of Fraction in hindi

Problem Theory	Example
What is P percent of X? Written as an equation: Y = P% * X The ‘what’ is Y that we want to solve for Remember to first convert percentage to decimal, dividing by 100 Solution: Solve for Y using the percentage formula *Y = P% X**	Example: What is 10% of 25? Written using the percentage formula: *Y = 10% 25** First convert percentage to a decimal 10/100 = 0.1 Y = 0.1 * 25 = 2.5 So 10% of 25 is 2.5
Y is what percent of X? Written as an equation: Y = P% ? X The ‘what’ is P% that we want to solve for Divide both sides by X to get P% on one side of the equation Y ÷ X = (P% ? X) ÷ X becomes Y ÷ X = P%, which is the same as P% = Y ÷ X Solution: Solve for P% using the percentage formula P% = Y ÷ X	Example: 9 is 60% of what? Writen using the formula: X = 9 ÷ 60% Convert percent to decimal 60% ÷ 100 = 0.6 X = 9 ÷ 0.6 X = 15 So 9 is 60% of 15
What percent of X is Y? Written as an equation: P% * X = Y The ‘what’ is P% that we want to solve for Divide both sides by X to get P% on one side of the equation (P% * X) ÷ X = Y ÷ X becomes P% = Y ÷ X Solution: Solve for P% using the percentage formula P% = Y ÷ X	Example: What percent of 27 is 6? Written using the formula: P% = 6 ÷ 27 6 ÷ 27 = 0.2222 Convert decimal to percent P% = 0.2222 × 100 P% = 22.22% So 22.22% of 27 is 6
P percent of what is Y? Written as an equation: P% × X = Y The ‘what’ is X that we want to solve for Divide both sides by P% to get X on one side of the equation (P% × X) ÷ P% = Y ÷ P% becomes X = Y ÷ P% Solution: Solve for X using the percentage formula X = Y ÷ P%	Example: 20% of what is 7? Written using the formula: X = 7 ÷ 20% Convert the percent to a decimal 20% ÷ 100 = 0.2 X = 7 ÷ 0.2 X = 35 So 20% of 35 is 7.
Y of what is P percent? Written as an equation: Y / X = P% The ‘what’ is X that we want to solve for Multiply both sides by X to get X out of the denominator (Y / X) * X = P% * X becomes Y = P% * X Divide both sides by P% so that X is on one side of the equation Y ÷ P% = (P% * X) ÷ P% becomes Y ÷ P% = X Solution: Solve for X using the percentage formula X = Y ÷ P%	Example: 4 of what is 12%? Written using the formula: X = 4 ÷ 12% Solve for X: X = Y ÷ P% Convert the percent to a decimal 12% ÷ 100 = 0.12 X = 4 ÷ 0.12 X = 33.3333 4 of 33.3333 is 12%
Y of X is what percent? Written as an equation: Y / X = P% The ‘what’ is P% that we want to solve for Solution: Solve for P% using the percentage formula P% = Y / X	Example: 9 of 13 is what percent? Written using the formula: P% = Y / X 9 ÷ 13 = P% 9 ÷ 13 = 0.6923 Convert decimal to percent by multiplying by 100 0.6923 * 100 = 69.23% 9 ÷ 13 = 69.23% So 9 of 13 is 69.23%
What of X is P percent? Written as an equation: Y / X = P% The ‘what’ is Y that we want to solve for Multiply both sides by X to get Y on one side of the equation (Y ÷ X) * X = P% * X becomes Y = P% * X Solution: Solve for Y using the percentage formula *Y = P% X**	Example: What of 25 is 11%? Written using the formula: *Y = 11% 25** Convert the percent to a decimal 11% ÷ 100 = 0.11 Y = 0.11 * 25 Y = 2.75 So 2.75 of 25 is 11%
P percent of X is what? Written as an equation: P% * X = Y The ‘what’ is Y that we want to solve for Solution: Solve for Y using the percentage formula *Y = P% X**	Example: 5% of 29 is what? Written using the formula: *5% 29 = Y** Convert the percent to a decimal 5% ÷ 100 = 0.05 Y = 0.05 * 29 Y = 1.45 So 5% of 29 is 1.45

Percentage mock test in hindi

Percentage Difference Formula

If we are given with two values and we need to find the percentage difference between these two values, then it can be done using the formula

\begin{array}{l}Percentage~Difference = \frac{\left|N_{1}-N_{2}\right|}{\left[\frac{\left(N_{1}+N_{2}\right)}{2}\right]} \times 100\end{array}

For example, if 20 and 30 are two different values, then the percentage difference between them will be:

\begin{array}{l}Percentage~Difference = \frac{\left|20-30\right|}{\left[\frac{\left(20+30\right)}{2}\right]} \times 100\end{array}

Percentage Increase and Decrease

The percentage increase is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.

% increase = [(New number – Original number)/Original number] x 100

where,

increase in number = New number – original number

Similarly, a percentage decrease is equal to the subtraction of a new number from the original number, divided by the original number and multiplied by 100.

% decrease = [(Original number – New number)/Original number] x 100

Where decrease in number = Original number – New number

percentage calculator | percentage formula |how to define percentage in math

How to calculate percentage of marks

To calculate percentage of marks, divide the obtained marks by total marks and multiply the result by 100.

Percentage = (Obtained marks / Total marks) x 100

Determine the total marks possible for the exam or assessment.
Add up the marks obtained in each subject or category.
Divide the obtained marks by the total marks.
Multiply the result by 100 to convert it to a percentage.
Round the result to desired decimal places if necessary.

Frequently asked question about percentage

What is the definition of percentage?
- Percentage is a fraction or ratio that represents a part of a whole. It is expressed as a number between 0 and 100.
How do you convert a fraction to a percentage?
- To convert a fraction to a percentage, multiply the fraction by 100 and add the percent symbol (%).
How do you convert a decimal to a percentage?
- To convert a decimal to a percentage, multiply the decimal by 100 and add the percent symbol (%).
How do you convert a percentage to a fraction?
- To convert a percentage to a fraction, divide the percentage by 100 and simplify the fraction if necessary.
What is the difference between percentage and percentage point?
- Percentage is a number that represents the ratio of a part to a whole expressed as a fraction of 100. Percentage point is the difference between two percentages.