How to Calculate Percentage: Formula & Solved Examples

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Updated: Jan 12, 2025

Lesson

Lesson Overview

What Is the Percentage?
How to Calculate the Percentage
Difference Between Percentage and Percentile
How to Convert Fractions to Percentages
Solved Examples on Percentage

A percentage is a way to express a number as a fraction of 100. The percentage formula in maths is:

Percentage = (Part / Whole) × 100

Percentages are used to compare quantities, calculate discounts, or find interest rates. This concept helps in real-world tasks like budgeting, calculating sales tax, or determining grade scores.

What Is the Percentage?

Percentage is a way of expressing a number as a fraction of 100.

For example, if Sarah saved 40% of her monthly income, it means she saved 40 out of every 100 units of her income. This is written as 40/100 or as the ratio 40:100. The "%" symbol represents "per hundred" and can be rewritten as "divided by 100" to express it as a fraction or decimal.

Examples of Percentage:

20% = 20/100 ( = 1/5 or 0.2)
50% = 50/100 ( = 1/2 or 0.5)
75% = 75/100 ( = 3/4 or 0.75)
12% = 12/100 ( = 3/25 or 0.12)

Take this quiz -

Percentage Quiz Questions and Answers

How to Calculate the Percentage

Calculating a percentage means determining a portion of a whole, based on a value of 100. There are two common methods to calculate a percentage:

Converting to a Fraction with a Denominator of 100

This method involves finding an equivalent fraction where the denominator is 100. The numerator of this equivalent fraction represents the percentage. This method is suitable when the original fraction's denominator is a factor of 100.

Example:

To express 15 out of 50 as a percentage:

Step 1: Form a fraction: 15/50
Step 2: Multiply the numerator and denominator by 2 to obtain a denominator of 100: (15 x 2) / (50 x 2) = 30/100

Step 3: The numerator represents the percentage: 30%

Part	Whole	Fraction	Equivalent Fraction	Percentage
15	50	15/50	30/100	30%

2. The Unitary Method

This method involves multiplying the fraction by 100 to determine the percentage. This approach is particularly useful when the denominator of the fraction is not a factor of 100.

Example:

To express 12 out of 30 as a percentage:

Step 1: Form a fraction: 12/30
Step 2: Multiply the fraction by 100: (12/30) x 100 = 40%

The unitary method is generally recommended, especially when the denominator is not a factor of 100. Let's look at both methods in practice.

Finding Percentage When the Total is 100

When the total of the items equals 100, calculating the percentage is straightforward. The percentage for each item is simply the number it self.

Example:

Sally bought tiles in three colors. The number of tiles of each color is listed below:

Colour	Number of Tiles	Fraction	Percentage
Yellow	39	39/100	39%
Green	26	26/100	26%
Red	35	35/100	35%

In this case, the total number of tiles is 39 + 26 + 35 = 100. Each number of tiles directly represents the percentage.

Finding Percentage When the Total is NOT 100

If the total number of items doesn't add up to 100, we need to adjust the fractions to get percentages. This can be done using the unitary method or by converting the fraction to have a denominator of 100.

Example:

Emma has a bracelet made up of 8 red beads and 12 blue beads. The total number of beads is 8 + 12 = 20. To calculate the percentage of each color, we use the unitary method.

Colour	Number of Beads	Fraction	Percentage Calculation	Percentage
Red	8	8/20	8/20 × 100	40%
Blue	12	12/20	12/20 × 100	60%

The percentage of red beads is:
8/20 × 100 = 40%

The percentage of blue beads is:
12/20 × 100 = 60%

By using the unitary method, we get the percentage for each color of bead.

Example with Marks Calculation

Example:

If a student scored 35 out of 40 in a test, we need to calculate the percentage. Here, 40 is not a factor of 100, so we use the unitary method.

Percentage = 35/40 × 100 = 87.5%

This shows how the unitary method is useful when the denominator isn't a factor of 100.

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$7th Grade: Math Percentage Quiz!$

7th Grade: Math Percentage Quiz!

Difference Between Percentage and Percentile

While the terms "percentage" and "percentile" sound similar, they represent distinct concepts in mathematics and statistics. Here's a breakdown of their differences:

Feature	Percentage	Percentile
Meaning	Represents a value out of 100.	Represents a rank or position within a dataset.
Symbol	Denoted by %	Denoted by ordinal numbers such as 25th, 50th, or 75th percentile.
Quartiles	Does not include quartiles.	Includes quartiles such as Q1, Q2 (median), and Q3.
Form	Can be written as a ratio or a decimal.	Cannot be expressed as a ratio or decimal.
Basis	Not based on ranking or relative position of values.	Based on the rank or position of a value in a dataset.
Comparison	Focuses on a single value or entity.	Compares one value to the rest of the dataset.
Distribution	Does not rely on data distribution.	Relies on data distribution, often assuming normal distribution.

How to Convert Fractions to Percentages

Converting fractions to percentages means expressing the fraction as a part of 100. This is achieved by multiplying the fraction by 100 and adding the percentage symbol (%).

Steps to Convert Fractions to Percentages

Write the fraction: Start with the given fraction.
Multiply by 100: Multiply the fraction by 100 to convert it into a percentage.
Add the % Symbol: Append the percentage symbol (%) to the result.

Examples

Convert 3/4 into a percentage.
Multiply 3/4 by 100: 3/4 x 100 = 75 percent.
So, 3/4 is equal to 75 percent.
Convert 5/8 into a percentage.
Multiply 5/8 by 100: 5/8 x 100 = 62.5 percent.
Thus, 5/8 equals 62.5 percent.
Convert 7/10 into a percentage.
Multiply 7/10 by 100: 7/10 x 100 = 70 percent.
Hence, 7/10 is equal to 70 percent.