Fraction and its representation.

We have read in our text books that "fraction represents a part of a whole" or "“a fraction describes how many parts of a certain size there are” and it can be represent as

 (Z is the set of integers)

Some define as

(W is the set of whole numbers)

Which of these representation is correct?
As per the definitions (above), Ö2/2, p/2 can not be fractions. But these represents part of a whole. 

Let us discuss on the representation of the fraction

1. Common, vulgar, or simple fractions

A common fraction (also known as a vulgar fraction or simple fraction) is a rational number written as 

where the integers a and b are called the numerator and the denominator respectively. The numerator represents a number of equal parts and the denominator, which cannot be zero, indicates how many of those parts make up a unit or a whole.


Examples: 1/2, 7/4, 15/8, 1/8 are common fractions.

2. Algebraic Fraction:

An algebraic fraction is the indicated quotient of two algebraic expressions. 
Two examples of algebraic fractions are
                            

2.1. RATIONAL FRACTION:

If the numerator and the denominator are polynomials, as in 3x / ( x²+2x-3) , the algebraic fraction is called a rational fraction (or rational expression).

Examples: 

So, Ö2/2 is a rational fraction.

2.2. IRRATIONAL FRACTION:

An irrational fraction is one that contains the variable under a fractional exponent, as in

Example: 
         

From these examples it is clear that 1/2, 7/3, Ö2/2, p/2 are fractions (1/2 & 7/3 are common fractions where as Ö2/2 & p/2 are algebraic fractions).

So, to represent a fraction, the types of number used in numerator and denominator have no impact (it can be any number, symbol). But the fraction bar plays an important role.

Can we define…….

A symbol is a fraction if it has a fraction bar/forward slashes.

Example: 7/3, Ö2/3, p/2, x²/2, e/2, ………..