How To Calculate Percentage Of A Number With Formula and Solved Examples
The topic ‘Percentage’ is a very important concept because students use it regularly in various mathematical activities and day-to-day activities. So, it is essential to build the concept of percentage as future Maths concepts build upon prior knowledge. Learning the concept of percentage starts in third grade. It plays a crucial role throughout your life while solving mathematical problems.
So, in this article, we will discuss the definition of percentage, examples of percentage, and how to calculate it.
Let’s start with the definition of percentage.
What is Percentage?
A percentage in Mathematics is a number or ratio that is represented as a fraction of 100. The word ‘percent’ is derived from the Latin word ‘per centum’ which means “by a hundred”. Percentage is denoted by the symbol ‘%’. It is a dimensionless number and has no units.
Examples of Percentages
Percentage basically means a part per hundred. It can be expressed in fraction form as well as decimal form.
For example, if we say 25%, it means 25 out of 100. So, 25% is equivalent to the fraction 25/100 or 0.4 in decimal form.
Here are some examples of percentages.
10% is equivalent to 10/100 or 0.1
20% is equivalent to 20/100 or 0.2
25% is equivalent to 25/100 or 0.25
50% is equivalent to 50/100 or 0.5
75% is equivalent to 75/100 or 0.75
90% is equivalent to 90/100 or 0.9
100% is equivalent to 100/100 or 1
Examples of Percentage
Percentage Formula
To find out the share of a whole in terms of 100, we use the percentage formula. You can express a number as a fraction of 100 by using the percentage formula.
First, divide the value by the total value and then multiply it by 100 to get the percentage.
Percentage formula = (Value/Total value) × 100
For example, 4/5 × 100 = 0.8 × 100 = 80%
How to Calculate Percentage?
Follow the below steps to calculate the percentage of a number.
To find out the percentage of a number if the given number is in the decimal form, you have to multiply the decimal number by 100.
For example, to convert 0.6 to a percentage, you need to multiply 0.6 by 100. So, we will get 0.6 × 100 = 60%.
To find out the percentage of a number if the given number is in fractional form, first, you have to convert it to a decimal form and then multiply it by 100.
For example, to convert 1/4 to percentage, first you need to convert 1/4 to the decimal form that is 0.25 and then multiply 0.25 by 100. So, we get 0.25 × 100 = 25%.
Solved Examples
1. Convert 0.32 to percentage.
Solution: Multiplying 0.32 by 100, we get 0.32 × 100 = 32% as the answer.
2. Convert the fraction 23/25 to percentage.
Solution: Converting 23/25 to a decimal value, we get 0.92.
So, 0.92 × 100 = 92% is the answer.
3. Convert 75% to a decimal value.
Solution: 75% means 75 out of 100. So, we can write it as 75/100.
By simplifying this fraction, we get 3/4.
Then, converting 3/4 to a decimal value, we get 0.75.
4. Convert 2.5% to fractional form.
Solution: 2.5% means 2.5 out of 100. So, we can write it in the fraction form as
2.5/100.
By simplifying the fraction, we get 1/40.
5. Find the value: 7.5% of 500.
Solution:
=(7.5/100) × 500
= (3750)/100
= 37.5
6. The number 450 is what percentage of 1200?
Solution:
=(450/1200) × 100
By simplifying the fraction, we get
= (3/8) × 100
= 0.375 × 100
= 37.5%
So, the number 450 is 37.5% of 1200.
Conclusion
Possessing knowledge of how to calculate percentages is not only helpful for you to excel in Mathematics but also to apply outside the class and solve practical problems involving percentages. This article provides a step-by-step guide on how to calculate percentages with examples.
FAQs on Percentage Of A Number Explained With Formula and Steps
1. What is percentage of a number?
The percentage of a number is a fraction of that number expressed per hundred and calculated by multiplying the number by the given percent divided by 100.
Formula:
Percentage of a number = (Percent × Number) ÷ 100
Example:
To find 20% of 150:
20 × 150 ÷ 100 = 30
This concept is commonly used in discounts, profit and loss, interest, and exam scores.
2. How do you calculate a percentage of a number?
To calculate a percentage of a number, multiply the number by the percent and divide by 100.
Steps:
- Write the percentage as a number over 100.
- Multiply it by the given number.
- Simplify to get the final result.
Example: Find 35% of 80.
35 × 80 ÷ 100 = 28
3. What is the formula for percentage of a number?
The formula for finding the percentage of a number is (P × N) ÷ 100, where P is the percent and N is the number.
Example:
Find 12% of 250.
(12 × 250) ÷ 100 = 3000 ÷ 100 = 30
This formula works for all percentage calculations involving finding a part of a whole.
4. How do you find 10%, 20%, or 50% of a number quickly?
You can find 10%, 20%, or 50% of a number quickly using mental math shortcuts.
- 10%: Divide the number by 10.
- 20%: Find 10% and multiply by 2.
- 50%: Divide the number by 2.
Example for 200:
10% = 20
20% = 40
50% = 100
5. How do you find what percent one number is of another?
To find what percent one number is of another, divide the part by the whole and multiply by 100.
Formula:
(Part ÷ Whole) × 100
Example: What percent is 25 of 200?
(25 ÷ 200) × 100 = 0.125 × 100 = 12.5%
This method is widely used in exam score analysis and data comparison.
6. How do you convert a percentage to a decimal to find a percentage of a number?
To convert a percentage to a decimal, divide it by 100 and then multiply by the number.
Steps:
- Divide the percent by 100.
- Multiply the decimal by the given number.
Example: 15% of 60
15% = 0.15
0.15 × 60 = 9
This method simplifies percentage calculations in algebra and real-life problems.
7. What is an example of finding a percentage of a number?
An example of finding a percentage of a number is calculating 25% of 120.
Using the formula:
(25 × 120) ÷ 100 = 3000 ÷ 100 = 30
This means 25% of 120 equals 30, which is commonly used in discount and tax calculations.
8. How is percentage of a number used in real life?
The percentage of a number is used in real life to calculate discounts, taxes, interest, profit, and exam scores.
Examples:
- 20% discount on $50 → 20% of 50 = 10
- 5% interest on $1000 → 5% of 1000 = 50
- 80% score out of 200 → 160 marks
Percentages help compare quantities and understand proportional relationships.
9. What is the difference between percentage and percent of a number?
A percentage is a value out of 100, while percent of a number is the actual part obtained after calculation.
For example:
40% is a percentage.
40% of 90 = (40 × 90) ÷ 100 = 36
So, the percentage is the rate, and the percent of a number is the resulting value.
10. What are common mistakes when finding a percentage of a number?
Common mistakes when finding a percentage of a number include forgetting to divide by 100 and confusing part with whole.
- Not dividing the percent by 100.
- Using the wrong base number.
- Misplacing decimal points.
Example mistake:
Calculating 30% of 80 as 30 × 80 = 2400 (incorrect).
Correct method: (30 × 80) ÷ 100 = 24
