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, how to calculate them and everyday examples of their use.

What are percentages?

Mathematically, percentages are either numbers or ratios that are expressed as fractions of 100. They are usually denoted as "%" or simply "percent." They may be further represented as simple fractions or as decimal fractions. An example of a percentage is 65% or 65 percent.

The term percentage was formed from two words, “per” and “cent.” Cent is a word with Latin and French origin that means "hundred," and "percent" means "per hundred." For example, 90 percent (or 90%) means 90 out of 100 while 50 percent (or 50%) means 50 out of 100 or half of a whole.

How to calculate percentages

There are many online calculators to find percentages, but percentages can be calculated manually by following these steps:

Determine the initial format of the number to be converted to a percentage

Carry out a mathematical process on the number to be converted to a percentage

Multiply the result of the mathematical process by 100

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. A good example of a decimal number is 0.57, which may be the calculated ratio of the values you are comparing, while an example of 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 to it before you go to the next step. However, if it is a fraction like 3/20, you should first divide the numerator (3 in this case) by the denominator (20 in this case) to get a decimal number.

3. Multiply the result of the mathematical process by 100

If you are required to convert a decimal number like 0.57 to a percentage, you are to simply multiply it by 100. That is, 0.57 x 100 = 57. Therefore, 0.57 as a percentage = 57% or 57 percent. Another example of converting a decimal to a percentage is 0.03 x 100 = 3% or 3 percent.

However, if you are required to convert 3/20 to a percentage, you should divide 3 by 20 = 0.15. Then multiply 0.15 by 100 = 15% or 15 percent.

Another example is if you are to convert 5/10 to a percentage, you should divide 5 by 10 = 0.5. Then, multiply 0.5 by 100. Therefore, 0.5 x 100 = 50% or 50 percent.

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 it 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

Multiply the final number by 100

Divide the result of the multiplication by the percentage

1. Find the percentage of the original or real number

The percentage of the original number as given in the math problem is 40%.

2. Multiply the final number by 100

You should multiply the final number as given in the math problem by 100. This implies that, 500 x 100 = 50,000.

3. Divide the result of the multiplication by the percentage

The next and final step is to divide the result of the multiplication carried out under step two by the percentage number given in the question. This implies that 50000/40 = 1,250. Therefore, the original number was 1,250.

Examples of percentages

Here are several examples of percentages and how to calculate them:

Convert the decimal number 3.25 to a percentage.

Convert the decimal number 0.65 to a percentage.

Convert the fraction 5/6 to a percentage.

Convert the fraction 60/100 to a percentage.

The price of a laptop was reduced by 30% to $120. What was the original price?

Find the sale price if a 20% discount is allowed off the marked price of $30.

Two years ago, a ticket to the football match was $20. This year, the price has been increased by 60%. What is the price of a ticket this year?

Convert the decimal number, 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 the decimal number 0.65 to a percentage

To convert the decimal number 0.65 to a percentage, multiply 0.65 by 100. Therefore, 0.65 x 100 = 65%.

Convert the fraction 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%.

Convert the fraction 60/100 to a percentage

To convert the fraction 60/100 to a percentage, you should first convert 60/100 to a decimal by dividing the numerator 60 by the denominator 100. This implies that 60/100 = 0.6. Then, multiply 0.6 by 100 = 60%.

The price of a laptop was reduced by 30% to $120. What was the original price?

To determine the original price, determine the percentage of the original price by subtracting 30% from 100. Next, multiply the final price by 100. That is, 120 x 100 = 12, 000. Finally, divide the result by the percentage calculated in step 1 above. This implies that, 12000/70 = $171.43. The original price is, therefore, $171.43 to two decimal places.

Find the sale price if a 20% discount is allowed off the marked price of $30.00

Convert the percentage to a decimal = 20/100=.20 and multiply the decimal by the original price to get the discount amount = .20 X $30=$6. The sale price = full price - discount = $30.00 - $6.00 = $24.00. Therefore, the sale price is $24.00

Two years ago, a ticket to the football match was $20.00. This year, the price has been increased by 60%. What is the price of a ticket this year?

Take the percentage increase 60%, divide it by 100 to determine the decimal form and multiply it by the original price = 60% of $20.00 = $12.00. Therefore, the price of the ticket this year = the initial price + the increase in the cost of the ticket = $20.00 + $12.00 = $32.00