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How to Find Percentage

In arithmetic, the percentage is the most important topic. It is very easy to calculate the percentage if you have knowledge about multiplication, division, and decimal. It helps us to calculate interest rates, discounts on sale, measuring quantity, etc. In this section, we will learn how to find a percentage. Before moving to the calculation of percentage, we first understand what a percentage is.

Percentage

The word percentage originated from the word percent. When we split the word percent, we get two words one is Per, and the other is Cent. The Cent is a French word, which means Hundred. Hence, the word percent means per hundred or for each hundred.

In mathematics, it is a number or ratio represented as a fraction of 100. In other words, the percentage is defined as parts per hundred or out of a hundred. It is denoted by the symbol %. It is a quick method to represent a fraction with a denominator of 100.

Suppose that in a class there is a total of 100 students, and only 40 is present. Then we can say that 40% of students are present and 60% of students are absent.

It is easier to calculate percentage in decimal format or convert from percentage. The number that we want to convert into percentage may be in two different formats, decimal and fraction.

Consider the following image. We see that a glass of water is half full and half empty. So, we can represent it in three different forms percentage, decimal, and fraction.

In percentage, it is: 50% full or 50% empty

In decimal, it is: 0.5 full or 0.5 empty

In fraction, it is: ½ full or ½ empty

• To convert a fraction or decimal number to a percentage, multiply it by 100. We can represent a decimal number into a percentage by moving the decimal point two places to the right. For example:
  0.76×100=76%
• To convert a percent into a fraction, divide the percent by 100 and simplify it, if required. For example:
  

Percentage Problems

There are basically three types of percentage problems. If X and Y are the numbers and P is a percentage, then the problem may have any of the following forms:

• Find P percent of X.
• What % (percent) of X is Y?
• Find X if P percent of it is Y.

Let’s see the above forms of the problem through examples.

Find P percent of X

For solving this type of problem, we use the following formula:

Example: What is 20% of 250?

Solution:

In this question, P is 20% and X is 250. Putting these values in the above formula, we get:

20%*250=Y

Now, convert 20% into a decimal. We will remove % sign and divide 20 by 100, we get:

0.20 is the substitute value of 20%. So, we will put the decimal value in the formula.

Hence, 20% of 250 is 50.

What % (percent) of X is Y?

For solving this type of problem, we use the following formula:

Example: Find out what percent of 90 is 23?

Solution:

In this question, X is 90 and Y is 23. Putting these values in the above formula, we get:

On simplifying the fraction, we get:

0.25=P%

Remember that the result will always in the decimal form, not in percentage form. To get the result in the percent, we need to multiply the result by 100.

0.25×100=25%

Hence, 25% of 90 is 23.

Find X if P percent of it is Y

For solving this type of problem, we use the following formula:

Example: 20% of what number is 95?

Solution:

In this question, P is 20% and Y is 95. Putting these values in the above formula, we get:

Now, convert 20% into a decimal. We will remove % sign and divide 20 by 100, we get:

0.20 is the substitute value of 20%. So, we will put the decimal value in the formula.

On solving the above fraction, we get:

Hence, 95 is 20% of 475.

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