How to Calculate Percentage

How to Calculate  Percentage is a very important mathematical application applied both in academia and in everyday life. A percentage is a fraction of something whole, described in terms of 100. From exam scores to calculating discounts while shopping or figuring out interest rates, percentages find their use everywhere. The method of calculating a percentage usually includes multiplying the value with the percentage and dividing by 100. Proficiency in this concept helps to simplify comparing amounts, comprehending proportions, and solving problems easily.

 

Table of Contents

• What is a Percentage?
• Percentage Formula
• How to Find Percentage
• Percentage Increase & Decrease
• Percentage Change Formula
• Percentage Difference
• Fraction to Percentage
• Percentage Table
• Percentage vs Per Cent
• How to Calculate Marks Percentage
• Percentage in Maths - Real Life Applications
• Tricks to Calculate Percentage
• Solved Examples
• Common Misconceptions about How to Calculate Percentage
• Conclusion
• FAQs On How to Calculate Percentage

 

What is a Percentage?

A percentage is a number expressed as a fraction of 100. It is denoted using the % symbol.

Examples:

• 40% = 40/100 = 0.4

• 75% = 75/100 = 0.75

Knowing how to calculate percentage helps in understanding parts of a whole in real-life contexts.

 

Percentage Formula

The percentage formula is used to find a portion of a total in terms of 100. It is a simple way to compare quantities or show proportions.

The basic percentage formula is:

Percentage=(PartWhole)×100

 

Example:

The formula is to divide the portion by the whole and then multiply by 100 to obtain the result as a percentage.

For instance, if you obtained 45 marks out of 50,

Percentage=4550×100=90%

 

How to Find the Percentage of a Number

To find the percentage of a number, use this formula:

Percentage of a number = (Given % × Number) / 100

Example:
What is 20% of 150?
= (20% × 150) / 100 = 30

 

Percentage Increase and Decrease

What is Percentage Increase?

The Percentage Increase is used when the new value is greater than the original value. It helps us understand how much a quantity has grown in terms of percentage

 

Percentage Increase Formula:

Percentage Increase = ((New Value - Original Value) / Original Value) × 100

Example:
Original Price = ₹200
New Price = ₹250

Increase = (250−200/200)×100
              = 25%

So, the price increased by 25%.

 

What is Percentage Decrease?

Percentage Decrease is used when the new value is less than the original value. It shows how much a quantity has reduced as a percentage of its original amount.

 

Percentage Decrease Formula:

Percentage Decrease = ((Original Value - New Value) / Original Value) × 100

Example:
Original value = 120
New value = 90

Percentage Decrease =(120 - 90/120)×100

                                     =30/120×100

                                     =25%

Percentage Change Formula

To determine how much a value has changed from its initial value, the percentage change formula is utilised. If the result is positive, it shows the percentage increase; if it is negative, it  show the percentage decrease.
This formula helps to find the overall change, either an increase or a decrease:

Percentage Change = (Change in Value / Original Value) × 100

Where Change in Value = New Value - Old Value

 

Percentage Difference

The difference between the two values in relation to their average is compared using the percentage difference. It displays the difference between the two values as a percentage of their average.

Explanation:

• Take the absolute difference between the two values.

• Divide it by their average.

• Multiply by 100 to get the percentage.

Percentage Difference Formula:

Used to compare two values

Percentage Difference = (|A - B| / ((A + B) / 2)) × 100

Example:
A = 60, B = 80
Difference = (20 / 70) × 100 = 28.57%

 

Fraction to Percentage

A fraction is a portion of a whole, whereas a percentage is a number out of 100. To convert a fraction to percentage, a fraction is simply multiplied by 100 to become a percentage. This makes the fraction easier to understand in real-world contexts, such as comparisons, discounts, or markings, by expressing it in terms of 100.

(Fraction) × 100 = Percentage

Example:
(3/4) × 100 = 75%

Common Table:

 

 

Percentage Table

Use this for quick reference:

 

 

Percentage vs Per Cent

Although the terms percentage and per cent are often used interchangeably, there is a slight difference in how and when they are used.

• A percentage is a mathematical concept used to express a number as a fraction of 100.

• Per cent (written as two words) means "per hundred" and is more commonly used in general English writing or formal texts.

 

Percentage

• "Percentage" is usually used when talking about the concept in general, or when no specific number is mentioned.
  
  Examples:

• The percentage of students who passed has increased.

• A large percentage of rainfall occurs in July.

 

Per cent

• "Per cent" is used when referring to a specific value or statistical figure and is often followed by a number.
  
  Examples:

• 80 per cent of the population owns a smartphone.

• Only 5 per cent of the class failed the test.
  
  

 

With Symbol (%)

When using the symbol %, we use numerals (not words like "per cent").

Examples:

• Correct: 25% of the work is done.

• Incorrect: 25 per cent (%) of the work is done.
  
  

Example:
75 percent = 75 per 100 = 75%

 

How to Calculate Marks Percentage

The mark's percentage tells us how much a student scored out of the total marks, expressed in terms of 100. It helps us easily understand performance in exams or tests.

Formula:

Marks Percentage = (Marks Obtained / Total Marks) × 100

Step-by-Step Example:

Let’s say a student got 460 marks out of 500.

Step 1: Divide the marks obtained by the total marks

460÷500=0.92

Step 2: Multiply the result by 100

0.92×100=92%

So, the student’s mark percentage is 92%.

 

 

Tricks to Calculate Percentage

• 10% of a number = divide by 10
  Example: 10% of 200 = 20

• 5% = Half of 10%
  Example: 5% of 200 = 10

• 15% = 10% + 5%
  Example: 15% of 300 = 30 + 15 = 45

• 25% = 1/4 of the number

• 20% = 10% × 2

These tricks make percentage calculation faster and easier.

 

Solved Examples

Example 1:
Question: What is 25% of 200?

Given:
Percentage = 25%
Whole value = 200

To Find:
Part (value)

Solution:
Using the formula:
Percentage = (Part / Whole) × 100
25% = (Part / 200) × 100
Part = (25% × 200) / 100
Part = 50

Answer: 25% of 200 is 50.

 

Example 2:
Question: 45 is what percent of 150?

Given:
Part = 45
Whole = 150

To Find:
Percentage

Solution:
Using the formula:
Percentage = (Part / Whole) × 100
Percentage = (45 / 150) × 100
Percentage = 30%

Answer: 45 is 30% of 150.

 

Example 3:
Question: A student scored 45 marks out of 60 in a test. Find the percentage.

Given:

• Marks Obtained = 45

• Total Marks = 60
  
  

To Find:
Percentage of marks.

Solution:
Percentage = (Marks Obtained / Total Marks) × 100
Percentage = (45 / 60) × 100
Percentage = 0.75 × 100
Percentage = 75%

Final Answer: The student scored 75% marks.

 

Common Misconceptions about How to Calculate Percentage

• The percentage is Always Out of 100 Only
  Although percentages are based on 100, people frequently mistake them for fixed values. Context is important because, for instance, 20% of 50 and 20% of 200 are different.

• Percentage Increase and Decrease Use the Same Formula
  Remember:

• Increase = ((New - Original) / Original) × 100

• Decrease = ((Original - New) / Original) × 100

• Confusing Percentage Change with Absolute Difference
  Saying “It increased by 10” vs. “It increased by 10%” has a big difference. Always clarify if it's a percentage or an absolute number.

• Ignoring the Base Value in Calculations
  Many mistakes happen by using the wrong base. For example, when comparing two values for percentage difference, use the average of the two, not just one.

• Believing 100% is Always the Maximum
  In growth scenarios, values can exceed 100%. For instance, a profit that doubles the investment is a 100% increase, not a maximum.

 

Conclusion

Now you know how to calculate percentages in various scenarios such as marks, discounts, and data comparison. Mastering the percentage formula, percentage of a number, percentage increase/decrease, and using tricks can make you quicker and more confident in solving mathematical problems.

 

Frequently Asked Questions On How to Calculate Percentage

1. How to calculate a percentage formula?

Answers: To calculate a percentage, use the formula:

Percentage = (Part / Whole) × 100

Example: If 40 is out of 80, then: (40 ÷ 80) × 100 = 50%

 

2. How much is 20% out of 70?

Answers: To find 20% of 70:

(20 × 70) ÷ 100 = 14

 

3. How do I calculate a percentage in numbers?

Answers: To calculate a percentage of any number:

(Percentage × Number) ÷ 100

Example: 25% of 160 = (25 × 160) ÷ 100 = 40

 

4. What is 30% out of 300?

Answers: 30% of 300 = (30 × 300) ÷ 100 = 90

 

5. How to solve 30% of 150?

Answers: 30% of 150 = (30 × 150) ÷ 100 = 45

 

6. What is 120 out of 300?

Answers: To find what percentage 120 is of 300:

(120 ÷ 300) × 100 = 40%

 

Understanding how to calculate a percentage is just the beginning. Explore more maths concepts to boost your confidence and accuracy in problem-solving with Orchids The International School!