Percentages are used everywhere in daily life—whether it’s scoring in a test, calculating discounts, or understanding data. A percentage tells us “out of 100,” making it easy to compare values across different contexts. This page will help you understand how to calculate percentages step by step and show where they’re useful in real life.
Finding Percentage of a Number
Percentage of a Number=$\frac{Percentage}{100}$×Number
Method 1:
- Convert the percentage to a decimal by dividing it by 100.
- Multiply the decimal by the number you’re finding the percentage of.
To find 30% of 150, convert 30% into a decimal.
$\frac{30}{100}$ = 0.3
Multiply by 150.
0.3 x 150 = 45
So, 30% of 150 is 45.
Method 2:
- Multiply the percentage by the number you want to find the percentage of. Divide the result by 100.
Percentage of a Number=$\frac{Percentage X Number}{100}$
- Simplify by cancelling out the common factors. Look for common factors in the numerator (percentage multiplied by the number) and the denominator (100). Cancel out these common factors and then do the final division.
Example 1: Let’s find 25% of 160 using this method.
25% of 160 = $\frac{25}{100}$x160
25 and 100 have 25 as the common factor. On simplifying,
$\frac{25}{100}$ = $\frac{1}{4}$
25% of 160 = $\frac{25}{100}$x160 = $\frac{1}{4}$x160 = 40
Example 2: Let’s find 32% of 50.
32% of 50 = $\frac{32}{100}$50
50 and 100 have a common factor 50. Canceling it out,
32% of 50 = $\frac{32}{100}$ x 50 = $\frac{32}{2}$ = 16
Here’s a quick way of solving the above problem. 32% indicates 32 for every 100. So, for 50, it would be half of that. Half of 32 is 16.
How to Calculate Percentage of a Whole
To find what percentage a number is of the whole:
- Divide the part by the whole.
- Multiply the result by 100.
- Add the % symbol.
Percentage=$\frac{Part}{Whole}$×100
Example: Imagine you scored 18 out of 20 on a test. To find your score as a percentage:
Percentage=$\frac{18}{20}$×100 = 90%
So, you scored 90% on your test!
What Percentage is one Number of another?
To find what percentage one number is of another, we can divide the “part” (the first number) by the “whole” (the second number) and then multiply by 100. This calculation tells us what fraction of the whole the part represents in percentage terms.
For example, to find what percentage 30 is of 150, we would divide 30 by 150, resulting in 0.2. Then, multiply by 100 to get 20%. So, 30 is 20% of 150.
This method is useful in various real-life situations, such as determining what percentage of total savings has been spent or what percentage of a group has achieved a particular score.
Example: What % is 45 of 60?
Percentage=$\frac{Part}{Whole}$×100 = $\frac{45}{60}$×100 = 75%
Percentage Increase and Decrease
Sometimes, we need to find the percentage change, which could be an increase or a decrease.
Percentage Increase: When the new value is greater than the original, the percentage increase formula is:
Percentage Increase = $\frac{(New Value – Original Value}{Original Value}$×100
Example: Imagine a bike was originally priced at ₹8,000, and the price increased to ₹9,500. What is the percentage increase?
Percentage Increase = $\frac{(9500 – 8000}{8000}$×100 = $\frac{(1500}{8000}$×100 = 18.75%
- Percentage Decrease: When the new value is less than the original, the percentage decrease formula is:
Percentage Decrease = $\frac{(Original Value – New Value}{Original Value}$×100
Example: If a mobile phone’s price drops from ₹20,000 to ₹15,000:
Percentage Decrease = $\frac{(20000 – 15000}{20000}$×100 = 25%
Practice Problems
- What is 20% of 150?
- If a laptop’s price increases from ₹40,000 to ₹45,000, what is the percentage increase?
- Convert 0.6 to a percentage.
- If you scored 45 out of 50 on an assignment, what is your score as a percentage?