What are the terminologies and properties of fraction

Answer :

We know 

Proper fraction : An proper fraction has a numerator smaller than denominator. 
Example :

$\frac{1}{2} or \frac{2}{3} ...$

Improper fraction  : An Improper fraction has a numerator larger than denominator. 
Example : 
$\frac{3}{2} or \frac{5}{3} ...$

Mixed fraction : A Mixed Fraction is a whole number and a proper fraction combined. 
Example :
$2\frac{3}{8} or 7\frac{1}{4} ...$

And

Properties of fractions :

$$\begin{gathered} 1 ) \mathrm{Commutative} \mathrm{Property} \mathrm{for} \mathrm{Fraction} \mathrm{Addition} \frac{\mathrm{a}}{\mathrm{b}} + \frac{\mathrm{p}}{\mathrm{q}} = \frac{\mathrm{p}}{\mathrm{q}} +\frac{\mathrm{a}}{\mathrm{b}} , \mathrm{for} \mathrm{Fraction} \mathrm{multiplication} \frac{\mathrm{a}}{\mathrm{b}} \times \frac{\mathrm{p}}{\mathrm{q}} = \frac{\mathrm{p}}{\mathrm{q}} \times \frac{\mathrm{a}}{\mathrm{b}} \\ 2 ) \mathrm{Associative} \mathrm{Property} \mathrm{for} \mathrm{Fraction} \mathrm{Addition} \left(\frac{\mathrm{a}}{\mathrm{b}} + \frac{\mathrm{p}}{\mathrm{q}}\right) + \frac{\mathrm{x}}{\mathrm{y}} = \frac{\mathrm{a}}{\mathrm{b}} + \left(\frac{\mathrm{p}}{\mathrm{q}} + \frac{\mathrm{x}}{\mathrm{y}}\right) , \mathrm{for} \mathrm{Fraction} \mathrm{multiplication} \left(\frac{\mathrm{a}}{\mathrm{b}} \times \frac{\mathrm{p}}{\mathrm{q}}\right) \times \frac{\mathrm{x}}{\mathrm{y}} = \frac{\mathrm{a}}{\mathrm{b}} \times \left(\frac{\mathrm{p}}{\mathrm{q}} \times \frac{\mathrm{x}}{\mathrm{y}}\right) \\ 2 ) \mathrm{Distributive} \mathrm{Property} \mathrm{for} \mathrm{Fraction} \left(\frac{\mathrm{a}}{\mathrm{b}} + \frac{\mathrm{p}}{\mathrm{q}}\right) \times \frac{\mathrm{x}}{\mathrm{y}} = \left(\frac{\mathrm{a}}{\mathrm{b}}\times \frac{\mathrm{x}}{\mathrm{y}}\right) + \left(\frac{\mathrm{p}}{\mathrm{q}} \times \frac{\mathrm{x}}{\mathrm{y}}\right) \end{gathered}$$