What is Percentage – Meaning, Formula & Examples

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In mathematics, the word percentage refers to a number(or ratio) that can be expressed as a fraction of $100$. It is represented by the symbol “$\%$”. The term “percentage” was adapted from the Latin word “per centum“, which means “by the hundred”.

In our daily lives, we use percentages all the time without even realizing it. For example, discount percentages while shopping, or while paying interest rates on loans, the concept of percentages is everywhere.

Let’s understand what is percentage and how it is calculated.

What is Percentage?

The word percentage is defined as a part of a whole expressed in hundredths. It is a number in the form of a fraction or a ratio with $100$ as a denominator and is represented by a symbol “$\%$”. The abbreviations used to represent the percentage are ‘pct’ or ‘pc’.

The percentage has no dimensions. It means they are dimensionless numbers. If we say $75\%$ of a number, it implies $75$ percent of its whole. It can even be expressed in both decimal and fraction forms such as $0.75$ or $\frac{75}{100}$.

For example, if your friend scores $80\%$ marks on his math test, it means that he scored $80$ marks out of $100$. In a fraction form, it is written as $\frac{80}{100}$; in a ratio form, it is written as $80:100$. It can also be expressed in decimal form as $0.80$.

Percentage in Math

Each percentage problem has three possible unknowns or variables. These unknowns or variables are

• The percent
• The base
• The part

To solve the percentage problem, you need to recognize these unknown variables.

Let’s consider an example to understand this better.

$80\%$ of $60$ is $48$

Here,

• $80$ is the percent
• $60$ is the base
• $48$ is the part

How to Calculate Part of a Whole?

The percent formula is used to find the part of a whole in terms of $100$. Using this formula, you can represent a number as a fraction of $100$. 

The formula used to calculate the percent of a number is $\text{Part} = \text{Percent} \times \text{Whole}$.

Let’s consider some examples to understand the formula for finding percentages.

Examples

Ex 1: Which number is $25\%$ of $60$?

Here percent = $25$

And, whole = $60$.

Part = $25\% \times 60 = \frac {25}{100} \times 60 = 15$

Therefore, $25%$ of $60$ is $15$.

Ex 2: Which number is $75\%$ of $80$?

Here percent = $75$

And, whole = $80$.

Part = $75\% \times 80 = \frac {75}{100} \times 80 = 60$

Therefore, $75%$ of $80$ is $60$.

How to Calculate Percent of a Whole?

The percent formula is used to find the part of a whole in terms of $100$. Using this formula, you can represent a number as a fraction of $100$. 

The formula used to calculate the percent of a number is $\text{Percent} = \frac{\text{Value}}{\text{Total}} \times 100$.

Let’s consider some examples to understand the formula for finding percents.

Examples

Ex 1: What percent is $24$ of $60$?

Here, value = $24$

Total = $60$

Percent = $\frac{24}{60} \times 100 = \frac{2}{5} \times 100 = 40$

Therefore, $24$ is $40\%$ of $60$.

Ex 2: What percent is $45$ of $135$?

Here, value = $45$

Total = $135$

Percent = $\frac{45}{135} \times 100 = \frac{1}{3} \times 100 = 33.33$

Therefore, $45$ is $33.33\%$ of $135$.

How to Calculate the Whole of a Part?

The percent formula is used to find the part of a whole in terms of $100$. Using this formula, you can represent a number as a fraction of $100$. 

The formula used to calculate the whole of a part is $\text{Whole} = \frac{\text{Part} \times 100}{\text{Percent}}$.

Let’s consider some examples to understand the formula for finding percent.

Examples

Ex 1: For what number $15$ is $25\%$?

Here, part = $15$

And, percent = $25$

Whole = $\frac{15 \times 100}{25} = \frac{1500}{25} = 60$

For $60$, $15$ is $25\%$.

Ex 2: For what number $20$ is $40\%$?

Here, part = $20$

And, percent = $40$

Whole = $\frac{20 \times 100}{40} = \frac{2000}{40} = 50$

For $50$, $20$ is $40\%$.

Difference Between Percent & Percentage

Although the words percent and percentage are frequently used interchangeably and are similar in meaning there lies a difference between these two terms. The only difference that lies is in their usage. The word percent is always used when it is preceded by a numeral. 

Look at the following examples.

I am one hundred percent sure that today it will rain.

$75$ percent of boys failed the math test.

On the other hand, the percentage is used without a numeral preceding it, as in the following sentence:

The percentage of girls joining the armed forces has increased considerably.

Another point of differentiation lies in the fact that the symbol $\%$ can be used to replace percent in a sentence, while it cannot be used in place of percentage.

Conclusion

In mathematics, a percentage is a number or ratio expressed as a fraction of $100$. It is often denoted using the percent sign, “$\%$”. Percentages are a way of representing the parts of a whole.

Practice Problems

1. Express the following percents in fraction
   • $45\%$
   • $52\%$
   • $60\%$
2. Express the following ratios in percent
   • $1:2$
   • $2:3$
   • $4:5$
3. Express the following fractions in percent
   • $\frac{4}{5}$
   • $\frac{1}{4}$
   • $\frac{2}{3}$
4. What is $15%$ of $80$?
5. What is $60%$ of $120$?
6. What percent is $40$ of $60$?
7. What percent is $25$ of $75$?

Recommended Reading

• What is Ratio(Meaning, Simplification & Examples)
• Factors and Multiples (With Methods & Examples)
• Fractions On Number Line – Representation & Examples
• Reducing Fractions – Lowest Form of A Fraction
• Comparing Fractions (With Methods & Examples)
• Like and Unlike Fractions
• Improper Fractions(Definition, Conversions & Examples)
• How To Find Equivalent Fractions? (With Examples)
• 6 Types of Fractions (With Definition, Examples & Uses)
• What is Fraction?  – Definition, Examples & Types
• Mixed Fractions – Definition & Operations (With Examples)
• Multiplication and Division of Fractions
• Addition and Subtraction of Fractions (With Pictures)

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