What is Percentage?

The word Percentage is made up of ‘per’ and ‘cent’. Per means divided by and cent means 100. So if we are calculating the percentage of any number, mathematically, we are dividing it by 100. Percentage is denoted by the symbol ‘%’. For example, when we write 25%, it actually means 25 divided by 100, i.e. 25 /100. The concept of percentage is most commonly used in classrooms, when we have to compare percentage of marks scored by two or more students.

For instance, lets us assume the marks of any two students in two different subjects as 7/10 and 18/25. To find the better scorer of the two, we will have to find out the ‘percentage’ of their marks. Percentage means division by 100, in order to do so we will convert the denominators of both fractions (7/10 and 18/25) into 100.

7/10 = 7 x 10/ 10 x 10 = 70/100
18/25 = 18 x 4/ 25 x 4 = 72/100

70/100 can be written as 70% whereas 72/100 can be written as 72%. Therefore, the student with 72% marks is a better scorer.

Conversion of Fractions into Percentage
To write a fraction as a percent, we have to convert it to an equivalent fraction with a denominator of 100. We then multiply the numerator by the same number. The resultant numerator is the required percentage.

For example,

¼ = 1 x 25/ 4 x 25
=> 25/100
=> 25%

2/5 = 2 x 20/ 5 x 20
=> 40/ 100
=> 40%

3/8 = 3 x 12.5/ 8 x 12.5
=> 37.5/100
=> 37.5%

Another way to write a fraction as a percent is to divide its numerator by its denominator, and multiply the resulting decimal by 100.

For example,

¼ = ¼ x 100
=> 0.25
=> 0.25 x 100 = 25%

2/5 = 2/5 x 100
=> 0.4
=> 0.4 x 100
=> 40%

3/8 = 3/8 x 100
=> 0.375
=> 0.375 x 100
=> 37.5%

Conversion of Percentage into Fractions
The word percentage means division by 100, thus to convert a percentage back to a fraction, we simply write the percentage as the percent divided by 100. We then simplify (or reduce) the fraction if required.

For example, to convert 20% to a fraction, we will divide 20 by 100:

20% = 20/100

We will further simply it to get the lowest possible fraction.

20/100 = 1/5

Thus, 20% = 1/5

Similarly,
40% = 40/100 = 2/5

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