# Concept of Percentages

Comparing fractions is not an easy task, especially when the two fractions have different denominators.

For example, you are asked which of the fractions and is greater than the other, i.e. we want to compare whether is greater than or less than .

Since the denominators of and are different, to compare these fraction, first we make their denominators the same.

Now, we have two fractions as , with the same denominator.

Since the numerator of is greater than the numerator of .

is greater than

But comparison becomes easier if the common denominator is 100.

**A fraction with the denominator 100 is called a percentage**, denoted by a % or a /100. The sign % is called percent.

For example, = 3%, = 5%

**The term percent is a short form of the Latin word “Per Centum” which means “Out of Hundred”**.

**Example:** On a math paper, out of a total score of 50 Waqas got 35, Usman got 43 and Shakeel got 32.7

Waqas got 35 out of 50 marks

i.e.

Usman got 43 out of 50

i.e.

Shakeel got 32 out of 50

i.e.

**Example:**

15% = (replace % by 1/100)

**Example:**

48% =

**Example:**

**Example:**

Express in decimals

(1)

(2)

(3)

__Changing a Fraction into a Percentage__

We can change a fraction into a percentage by multiplying the fraction by 100% and simplifying it, if possible.

__Examples__**:**

Express as percentages: