Yesterday, I went out with two of my friends. We bought a pizza for ourselves and shared it. The pizza was cut into six slices. So, obviously, each of us got 2 slices to our share.

Now, if you ask me how much of the pizza did I eat and how much I shared, I would have to refer to fractions, in this case. .

A fraction expresses the ratio of two numbers as a comparison between parts and a whole. Thus, one way to show parts of a whole is, through fraction.

The word **fraction** is taken from the Latin word **“fractus”** meaning **broken**.

In the ancient times fraction was the reciprocal of integers where ancient symbols were used to show parts of a whole, like, one part of two, one part of three etc.

Much later **common or vulgar fraction** came into picture. These fractions are used today.

**Example****,** 2/3, 5/6 etc., where the number at the top denotes the number of equal parts and the number at the bottom denotes the whole.

A fraction is represented by a pair of numbers divided by a line in between. The number at the top is called the **numerator** and that at the bottom is called the **denominator** of the fraction

It can be written in two ways:

With a forward slash, like, 1/2 , where 1 is the numerator and 2 is the denominator.

With a forward slash, like, 1/2 , where 1 is the numerator and 2 is the denominator.

Also called common or simple fraction, it is the ratio of two rational numbers, namely, the numerator and the denominator, where the denominator is a non-zero.

**Example, ** **, ** ** **1

A ** **

is one where the numerator is smaller than the denominator.

**Example, ** **, ** ** **

An** **

is one where the numerator is greater than the denominator. So, this fraction is also called “top heavy”.

**Example,****, ** ** **

Two or more fractions, having the same denominator are called **like fractions**.

**Example, ** ** and ** ** are like fractions.**

Two or more fractions, having different denominators are called **unlike fractions**.

**Example, ** ** and ** ** are unlike fractions**

A** mixed number **is the sum of a whole number and a proper fraction

**Example , 5 + **

If we multiply the numerator and the denominator of a fraction with the same number (non-zero),the new fraction formed as a result is said to be equivalent to the original fraction.

**Example, ** ** ** ** ( ** **)**** ( ** ** ) **are equivalent fractions.

*A fraction is said to be in its lowest terms when, the numerator and the denominator have no common factor between them. *

A fraction is reduced to its lowest terms by dividing the numerator and the denominator by their common factor until they don’t have any more common factor between them

**Example, **Consider the fraction** ** **.** The common factor is 2. So, we divide both 12 and 24 by 2, we get, , which can still be reduced to and further to **.**

A reciprocal fraction is just the reverse of the original fraction.

The numerator of the original fraction becomes the denominator of the new fraction and similarly the denominator becomes the numerator of the new fraction.

**Example, ** ** is the reciprocal fraction of ** ** **

Also called a compound fraction, it is a fraction whose numerator or denominator is a fraction**.**

**Example****, ** ** ****etc.**

To simplify a complex fraction, we need to divide the numerator of the fraction by its denominator.

**Example**** **can be simplified as** ** ** ****÷ 3**** ****=**** ** ** ****x**** ** ** ****= ** ** **

**How to convert a mixed number into an improper fraction and vice-versa**

**To convert a mixed number into an improper fraction we need to:**

- Multiply the whole number by the denominator of the fractional part of the mixed numbe
- Add the numerator of the fractional part to the product.
- The resulting sum is the numerator of the new fraction and the new denominator is the same as the denominator of the fractional part of the mixed number

**Example,** 5 2/3 = ((5 x 3)+2)/3 = 17/3

**To convert an improper fraction into a mixed number we need to**

- Divide the numerator of the fraction by the denominator.
- The quotient becomes the whole number of the mixed number while the remainder becomes its numerator of the fractional part.
- The new denominator is the same as the denominator of the original improper fraction.

**Example, ** ** ****=**** 7**

**Uses**

By now you must have realized the vastness of fraction, how it can be used in any context referring to parts of a whole, be it the part of a pizza or time.