Introduction

In our day to day life, many a time we compare two quantities. We generally use fractions and percent for the comparison. The fraction refers to how many parts of a given whole quantity. While, percentage or percent refers to how many parts out of 100 quantities.

What is Fraction?

The term fraction represents how many parts of a given whole quantity or, in general, it describes how many parts of a certain size divided by the whole quantity.

Fraction consists of Numerator which is written above the line and Denominator which is written below the line.

The numerator indicates a number of equal parts, and the denominator indicates how many of those parts make up a whole. The denominator of a fraction can never be zero because zero parts can never make up a whole.

For example, In the simple fraction \[\frac{1}{2}\], the numerator ‘1’ indicates that the fraction represents 1 equal part, and the denominator ‘2’ indicates that 2 parts make up a whole.

What is Percent?

The term percent represents how many parts out of 100 quantities. In other words, Percentages are the numerators of the fractions with denominator 100.

The word ‘Percent’ has been derived from Latin word ‘per centum’ which means ‘per hundred’.

The percentage is a dimensionless pure number.

The percent is denoted using the sign % meaning hundredths.

For example, 5% means 5 out of one hundred or Five hundredth.

It can be written as: \[5\% = \frac{5}{{100}} = 0.05\]

Percentage Formula

Percentage formula is used to find the share or amount of something in terms of 100.

The Percentage Formula is given by:

Percentage =\[\frac{{{\text{Given value}}}}{{{\text{Total value}}}} \times \] 100

How Fractions and Percentages are Used for Comparing Two Quantities?

To understand this let us consider an example, In the annual exam reports of two friends Henna and Mona, Henna got 320 marks out of 400 i.e. \[\frac{{320}}{{400}}\]and her friend Mona got 350 marks out of 500 i.e. \[\frac{{350}}{{500}}\]. If we compare the marks obtained by them then Mona has secured more marks than Henna. But, only by seeing their obtained marks, we cannot decide who has performed better in their annual exam because the maximum marks out of which they got the marks are not the same. For this, we have to convert their obtained marks given in fraction to their equivalent percentage.

How to Convert Fraction to Percent?

The following steps are followed to convert fraction to percent:

Step 1: Convert the given fraction into its equivalent decimal number (refer Note).

Step 2: The obtained decimal number is multiplied by 100, to get the required percent value.

Note: Fractions are converted to their equivalent decimal number using the following steps:

Step 1: The numerator of fraction is divided by its denominator.

Step 2: The quotient obtained after division is the decimal equivalent of a given fraction.

Solved Examples

Q.1. Convert the fraction \[\frac{2}{5}\] to a percent.

Solution:

Step 1: Convert the given fraction\[\frac{2}{5}\] into its equivalent decimal number. i.e.

⇒ \[\frac{2}{5}\]= 0.4

Step 2: Multiply the obtained decimal by 100. i.e.

⇒ 0.4 \[ \times \]100 = 40%

Therefore, the required percent value of fraction \[\frac{2}{5}\] is 40%

Q.2. Out of 40 students in a class, 8 are absent. What percent of the students are absent?

Solution: Given, total number of students in class = 40. And, Number of absent students = 8.

Therefore, percentage of absent students in the class = \[\frac{8}{{40}}\]\[ \times \]100 = 20%

Q.3. In the annual exam reports of two friends Henna and Mona, Henna got 320 marks out of 400 and her friend Mona got 350 marks out of 500. Who has performed better?

Solution: First we will convert their obtained marks into its percentage equivalent.

Therefore, percentage of marks obtained by Henna = \[\frac{{320}}{{400}} \times \]100 = 80%

And percentage of marks obtained by Mona = \[\frac{{350}}{{500}} \times \] 100 = 70%

On comparing their percentage of marks obtained, Henna has performed better than Mona.

Q.4. An alloy contains 33% aluminium. What quantity of alloy is required to get 132 g of aluminium?

Solution:

Let the quantity of alloy required be x g

Then 33 % of x = 132 g

⇒ \[\frac{{33}}{{100}} \times X = 132g\]

⇒ \[X = \frac{{132 \times 100}}{{33}}g\]

⇒ x = 400 g

Therefore, the amount of alloy required to get 132 g of aluminium is 400 g.