Calculating Percentage: Formula, Steps, and Examples

Before delving into the intricacies of calculating a percentage, let's first grasp the concept of a percentage itself. A percentage refers to a numerical value or a ratio that is expressed as a fraction out of 100. It is denoted by the symbol "%". The abbreviation "pct" or "pc" is used to represent the term "percentage". To put it simply, a percentage signifies the proportion of one quantity in relation to another quantity, and it is typically evaluated in relation to 100.

Expand your understanding of the concept of percentage here.

Within this article, you will gain insights on the process of calculating percentages, including how to determine percentage increases, decreases, and differences. Alongside, we will also explore the respective percentage formulas and provide illustrative examples.

Calculating Percentages Using a Formula

Calculating percentages can be done swiftly and conveniently with the help of a formula. The formula used to calculate percentages involves dividing the actual value by the total value and multiplying the result by 100. This percentage formula is expressed as:

\(\begin{array}{l}Percentage = \frac{Actual\ Value}{Total\ Value} \times 100\end{array}\)

We can enhance our understanding of this concept and the formula by examining a practical example presented below:

Example: Consider a circle with ten divisions, wherein a few portions are shaded. Your task is to determine the percentage of shaded sections in the circle.

Solution:

Total number of divisions in the circle = 10

Number of shaded sections = 2

We are aware that:

Percentage, % = (Actual Value / Total Value) × 100

Hence, the percentage of shaded portions in the circle can be calculated as follows:

= [(Number of shaded divisions) / (Total number of divisions)] × 100

= (2/10) × 100

= 20%

Consequently, 20 percent or 20% of the circle contains shaded portions.

Additionally, you can try utilizing the Percentage Calculator to further reinforce your understanding.

Determining the Percentage of a Number

To calculate percentages, you can follow three simple steps:

Step 1: Identify the original representation of the number, which can either be a fraction or a decimal. This original format will dictate the subsequent mathematical operation performed on the number. For instance, a decimal number might be 0.25, representing the computed ratio of the values being compared, while a fraction could be 4/15.

Step 2: Carry out the necessary mathematical operation on the number. This entails converting a fraction into a decimal if the given number is in fraction form. If the number is already in decimal form, it remains unchanged.

For example, 4/15 = 0.267

Step 3: Multiply the result obtained from the previous step by 100 to express it as a percentage. For example, 0.267 multiplied by 100 equals 26.7%.

By following these steps, you will be able to accurately calculate percentages.

Discover the process of transforming decimals into fractions by visiting this link.

An alternate approach:

We can also determine the proportion of a number by converting it into a fraction with a denominator of 100. The following example will provide a clearer understanding:

Example:

Transform 3/20 into a percentage.

Resolution:

The given fraction is 3/20.

Let's convert the denominator to 100.

(3/20) × (5/5) = 15/100

Next, multiply the result by 100.

(15/100) × 100 = 15

Therefore, 3/20 is equal to 15%.

Note: This method of calculating percentages applies only when the denominator is a factor of 100. Otherwise, the standard method should be used.

The Process of Percentage Calculation for Marks

Many students often wonder how to calculate the percentage of marks obtained in exams. The answer, along with an example, can be found below. The calculation involves two simple steps:

Step 1: Divide the obtained marks by the maximum marks of the test.

Step 2: Multiply the result by 100.

To comprehend the process of finding the percentage of marks, refer to the following example:

Example 1: A student scored 1156 marks out of 1200 marks in an examination. Calculate the percentage of marks secured by the student.

Resolution:

Number of marks scored = 1156

Maximum marks = 1200

Percentage of marks = (Marks obtained/Maximum marks) × 100

Percentage of marks = (1156/1200) × 100

Percentage = 0.9633.... × 100

Therefore, the student obtained 96.3% of marks.

Determining Percentage Change

Learn how to calculate the percentage difference between two numbers. Percentage change represents the variation in the value of a number or quantity over a specific period, expressed in terms of percentage.

The formula for percentage change (or percentage difference) is:

% change = [(Change in Value) / Original Value] × 100

The "Change in Value" refers to the difference between the new value and the original value. It can be positive or negative. A positive difference indicates a percentage increase, while a negative difference signifies a percentage decrease.

Hence, there are two types of percentage change in mathematics:

• Percentage increase
• Percentage decrease

Calculating Percentage Increase

When the new value is greater than the original value, the percentage change reflects the percent increase in the original number. The calculation can be done using the following formula:

Percent Increase = (Increase in value / Original value) × 100

In this case,

The increase in value is equal to the new value minus the original value.

How to Calculate Percentage Decrease

When the original value is greater than the new value, the percentage change in value represents the decrease in the original number. The formula for calculating percentage decrease is as follows:

In this case,

The decrease in value is equal to the original value minus the new value.

Also check: Percentage Increase and Decrease

There is another type of percentage called percentage error, which usually occurs when dealing with weights.

Percentage Error Formula

\(\begin{array}{l} Percentage\ Error = \frac{Error}{Real ~value}\times 100\end{array} \)

In this case,

The difference between percentage and percentile can often confuse many individuals. It is important to note that these two concepts are different. Here, we will provide a detailed explanation of the difference between percentage and percentile.

Percentage

Percentile

The percentage represents a number out of 100.

Percentile is not a number out of 100.

It can be expressed as ratios or proportions.

It cannot be expressed as ratios or proportions.

A percentage is obtained by multiplying the ratio of two numbers by 100.

A percentile represents a percentage of values that can be found below a specific value.

It is not based on ranking numbers.

It is based on ranking numbers.

It is written in the form of x%.

It is written in the form of xth.

It is based on a single case.

It involves comparing one case with others.

It does not rely on the normal distribution.

It relies on the normal distribution.

Also, read: Difference Between Percentage And Percentile

Solved Examples of Calculating the Percentage

Question 1: In a class, there are 120 students. Out of these, 60 students are boys. Calculate the percentage of boys in the class.

Solution:

Given:

Total number of students in the class = 120

Number of boys in the class = 60

\(\begin{array}{l}\text{Therefore, the percentage of boys in the class} = \frac\times 100\end{array} \)

= 600/12 = 50

So, the percentage of boys in the class is 50%.

Question 2: Find 25% of 10.

Solution:

Remember that "of" means "times."

So, 25% of 10 = (25/100) × 10

0.25 × 10 = 2.5

Therefore, 25% of 10 is equal to 2.5.

Question 3: Find the percentage of ripe apples, given that there are 10 ripe apples out of a total of 60 apples in the basket.

Reformulated passage:

Finding the Solution:

Given the total quantity of apples is 60

The number of fully ripened apples is 10

To determine the percentage of fully ripened apples, we use the following formula:

(10/60) × 100

which simplifies to:

(1/6) × 100

resulting in:

16.666666

Thus, the percentage of fully ripened apples is 16.67%.

Question 4:

In a cinema hall, there are a total of 150 people present, consisting of 80 men and 70 women. To calculate the percentage of men in the hall, we can use the following equation:

(Total number of men / Total number of people) × 100

which gives us:

(80 x 100)/150

as a result:

53.33%

Question 5:

The task is to determine 15% of 75. To solve this, we multiply the decimal equivalent of 15% (15/100) with 75, resulting in:

(15/100) × 75 = 11.25

Practice Problems:

1. Jaanu achieved the following scores in 5 subjects of a monthly test, where the maximum marks for each subject is 100: 34, 65, 58, 70, 50. To find the percentage of marks scored in all 5 subjects, we will calculate the average percentage.

2. If the price of a toy was increased by 30% to reach Rs. 120, we can determine the original price by reversing the percentage increment calculation.

3. Transforming the fraction 7/18 into a percentage.

4. A student increased the value of a number from 65 to 110. To find the percentage change in the number, we need to compute the relative difference between the two values.

If you want to explore more intriguing mathematical topics, feel free to visit BYJU’S – The Learning App, where you can also find captivating instructional videos.

Frequently Asked Questions on Finding Percentage:

What is the concept of percentage?

Percentage is a dimensionless ratio that compares two numbers, indicating the difference between them or comparing them to a common scale.

What is the formula to convert percent into decimal form?

To convert a percent into its decimal form, the steps are as follows: remove the percent symbol (%), divide by 100, and express the resulting fraction as a decimal.

Is it possible for a percentage to exceed 100?

Certainly. A percentage can be greater than 100 if the value being measured surpasses the total value.

How can I calculate x percent of y?

To determine x percent of y, divide x by 100 and then multiply the resulting decimal by y. The product obtained will represent x% of y.