By Indeed Editorial Team
Updated May 18, 2022 | Published February 25, 2020
Updated May 18, 2022
Published February 25, 2020
Calculating percentages is an easy mathematical process to carry out. Sometimes, when there is the need to find the ratio or portion of a quantity as a part of another quantity, you will need to express it as a percentage.
In this article, we show you what percentages are and how to calculate them. We also provide examples of using percentages.
What are percentages?
Mathematically, percentages are either numbers or ratios that are expressed as fractions of 100. They are usually denoted as "%" or "percent." An example of a percentage is 65% or 65 percent. They may be further represented as simple fractions or decimal fractions.
The term "percentage" is formed from two words: per and cent. Cent is a word with Latin and French origins that means "hundred," and "percent" means "per hundred." For example, 50 percent, or 50%, means 50 out of 100 or half of a whole.
Calculating percentage meansfinding the share of a whole in terms of 100.It can be calculated manually or by using online calculators.
How to calculate percentages
Here are steps to manually calculate percentages:
1. Determine the initial format of the number to be converted to a percentage
The number to be converted to a percentage can either be in the decimal or fraction format. For example, a decimal number is 0.57 and a fraction is 3/20. The initial format will determine the next mathematical process to be carried out on the number.
2. Carry out a mathematical process on the number to be converted to a percentage
If the number to be converted to a percentage is a decimal number like 0.57, you may not need to do anything before you go to the next step. However, if it is a fraction like 3/20, divide the numerator (the top number 3) by the denominator (the bottom number 20) to get a decimal number.
3. Multiply the number by 100
If you are required to convert a decimal number like 0.57 to a percentage, you simply multiply it by 100. That is, 0.57 x 100 = 57. Therefore, 0.57 as a percentage equals 57%. Another example is 0.03 x 100 = 3%.
If you are required to convert a fraction, such as 3/20 to a percentage, you should divide 3 by 20 = 0.15. Then multiply 0.15 by 100 = 15%.
How to calculate percentages by working backward
Sometimes, you will be required to calculate percentages by working backward. This is also referred to as reverse percentages and is used when the percentage and the final number are given and the original number is to be calculated.
For example, if 40% of a number is 500, what is the number? The following are ways to calculate the percentage by working backward:
- Find the percentage of the original or real number. In this case, it's 500.
- Multiply the final number by 100. 500 x 100 = 50,000.
- Divide the result of the multiplication by the percentage. 50,000 divided by 40% = 1,250. Thus, 500 is 40% of 1,250. Therefore, the original number was 1,250.
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Examples of percentages
Here are several examples of percentages and how to calculate them:
Convert 3.25 to a percentage
To convert the decimal number 3.25 to a percentage, multiply it by 100. Therefore, 3.25 x 100 = 325%.
Convert 5/6 to a percentage
To convert the fraction 5/6 to a percentage, you should first convert 5/6 to a decimal by dividing the numerator 5 by the denominator 6. This implies that 5/6 = 0.833 to two decimal places. Then, multiply 0.83 by 100 = 83%.
Here are a few examples of calculating percentages in certain situations:
The price of a laptop was reduced by 30% to $120. What was the original price?
- Find the percentage of the original or real number. In this case, it's $120.
- Multiply the final number by 100. $120 x 100 = $12,000
- Divide the result of the multiplication by the percentage. $12,000 divided by 30% = $400.
- Thus, $120 is 30% of $400. Therefore, the original number was $400.
You can double-check your answer by dividing $400 by 100. 100 represents 10% of the total. $40 x 3 = $120.
Related: How To Calculate Percentage Decrease (With Examples)
Find the sale price if a 20% discount is allowed off the marked price of $30
- Convert the percentage to a decimal. 20 divided by 100 = .20
- Multiply the decimal by the original price to get the discount amount. 20 X $30 = $6
- The $30 price is discounted by $6 for a total of $24.
Two years ago, a football ticket was $20. This year, it has increased by 60%. What is the price of this year's ticket?
- Divide the percentage increase by 100 to determine its decimal form. 60% divided by 100 = 0.6
- Then, multiply the decimal by the original price. 0.6 x $20 = $12
- Add the price of the original ticket and the amount of increase to find the new ticket price. $20 + $12 = $32
- $32 is the cost of the new ticket.
Related: What Is the Percentage Increase Formula? With Examples