1481 LearnersLast updated on June 10th, 2025
Percentage
A percentage is a way of expressing a number or ratio as a fraction of 100. The word percentage comes from the Latin word “per centum,” meaning “by the hundred.” In our daily lives, we use percentages to calculate discounts, interest rates, taxes, and more.
What is Percentage in Math?
A percentage expresses a number or ratio as a part of a whole (100). A percentage is represented by the symbol %, which is read as ‘percent.’ It is calculated by dividing the part by the total and multiplying it by 100.
That is, percentage = part/total × 100
A percentage is defined as a fraction out of 100. The word came from the Latin word “Percentum” meaning by hundred. It is always denoted by % or percent. It is used for finding the share or amount of a quantity out of 100. Percentage is used in data sufficiency, data interpretation, or simplification. Percentage has no dimension, if it is said 30% of a number, it means 30% of the whole. Therefore, it can be written as 30/100 in fraction and 30:100 in ratio.
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Methods to Calculate the Percentage
In this section, let’s discuss methods to calculate percentages. Here are a few methods:
- Using the Percentage Formula
- Converting to Fractions or Decimals
Using the Percentage Formula
Percentage is the part by total multiplied by 100. That is, percentage = Part/Total × 100 by following these steps, we can find the percentage.
When finding the percentage using the formula, we substitute the values in the formula. That is percentage = Part/Total × 100
For instance, if a student scores 25 out of 50, find the percentage of it.
To find the percentage, we apply the formula, Part/Total × 100
Here, part = 25
Total = 50
So, the percentage = 2550 × 100 = 50%
Converting to Fractions or Decimals
Here, we learn how to convert fractions or decimals into percentages.
When converting a fraction to a percentage, we simply multiply the number with 100. That is if 35 students out of 50 choose football then the percentage of students who choose football is
35/50 × 100 = 70%.
When converting a decimal to a percentage, we multiply the number by 100. That is 0.57 in percentage is 0.57 × 100 = 57%.
Tips and Tricks for Calculating the Percentage
Tips and tricks can make it easier to find the percentage. In this section, let’s discuss a few tips and tricks to master percentage.
Using the formula effectively: When applying the percentage formula that is Part/Total × 100, here part is the value we consider and the total is the overall value.
Rounding the value for easy calculation: For easier calculation of percentage, we can round the value. That is 48% can be rounded to 50%.
Memorizing a few basic percentages: Mostly percentages are converted into fractions. So basic fractions should be memorized -
50% = 1/2
25% = 1/4
20% = 1/5
10% = 1/10
Common Mistakes and How to Avoid Them in Percentage
When finding the percentage, students make some common errors. So to master percentage let’s learn a few common mistakes and the ways to avoid them.
Mistake 1
Not multiplying by 100
When finding the percentage students forget to multiply the value by 100. To avoid errors students should understand the concept of percentage and use the correct formula which is percentage = Part/Total × 100
Mistake 2
Ignoring the decimal place
When converting the value to a percentage forget the decimal places. So to avoid errors students should add the decimal points to give an accurate percentage.
Mistake 3
Errors while converting between percentages and decimals
Errors are common when converting between percentages and decimals. For instance, converting 0.5 as 5% instead of 50%. When converting from decimal to percentage multiply it by 100. Divide it by 100 when converting from percent to decimal.
Mistake 4
Forget to add the symbol(%) after conversion
After converting a number to percentage students may forget to add the percentage symbol(%). So it is very important to add the percentage symbol in the final answer. That is 5 out of 25 in percentage is 5/25 × 100 =20%
Mistake 5
Using the wrong base
When calculating the percentage increased or decreased, students tend to use the wrong base which is the denominator. Suppose the price of a product is increased from $80 to $100, calculate the percentage increase. Here the base value is 80 and in the numerator, the part is the difference between the new value and the old value.
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Percentage Examples
Problem 1
A store sells a shirt for $80. If there is a 25% discount, how much will the shirt cost after the discount?
After the discount, the price of the shirt is $60
Explanation
To find the discount on the cost of the shirt, we find the discount rate.
Finding 25% of $80, that is (25 / 100) × 80 = 20
So, the price discount is $20
The price after discount = $80 — $20 = $60
Problem 2
A car was valued at $25000, but its value depreciated by 10%. What is its new value?
The value of the car after the depreciation is $22,500
Explanation
10% of $25000 is (10/100) × 25000 = 2500
So, the price of the car after deducting depreciation is $25000 - $2500 = $22,500
Problem 3
30% of the number is 60. What is the original number?
The number is 200
Explanation
To find the number, let’s consider it as X
The 30% of the number is 60, that means (30 / 100) × X = 60
X = 60 × 100 / 30 = 200
So, the number is 200
Problem 4
In a class of 40 students, 10 students chose football. What is the percentage of the class who select football?
25% of students choose football
Explanation
To find the percentage, we use the formula, Part/Total ×100
Here the part is 10
Total is 40
That is 1040 × 100 = 25
That means, 25% of students select football.
Problem 5
A test has 80 questions. If a student answers 64 correctly, what is their percentage score?
The percentage the student scored is 80%
Explanation
The percentage the student scored = Part/Total × 100
That is, (64 / 80) × 100 = 80%
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FAQs on Percentage
1.What is a percentage?
2.How do you calculate the percentage?
3.What is 2% out of 100?
4.How are percentages used in real life?
5.What is 20% out of 45?
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Dr. Sarita Ghanshyam Tiwari
About the Author
Dr. Sarita Tiwari is a passionate educator specializing in Commercial Math, Vedic Math, and Abacus, with a mission to make numbers magical for young learners. With 8+ years of teaching experience and a Ph.D. in Business Economics, she blends academic rigo
Fun Fact
: She believes math is like music—once you understand the rhythm, everything just flows!
