Rational Numbers

A Number which can be represented in the form of ${\frac {p}{q}}$ where p & q are integers and q$\neq$0 is a Rational Number. When the rational number is divided the result will be in decimal form.

Examples:

p	q	${\frac {p}{q}}$
10	2	${\frac {10}{2}}=5$
1	1000	${\frac {1}{1000}}=0.001$
7	1	${\frac {7}{1}}=7$

Positive Rational Number

A Number which can be represented in the form of ${\frac {p}{q}}$ where q$\neq$0 and p & q are both positive integers is called as Positive Rational Number.

Example : ${\frac {1}{3}},{\frac {17}{3}},{\frac {3}{17}}$

Negative Rational Number

A Number which can be represented in the form of ${\frac {p}{q}}$ where q$\neq$0 and either p or q is a negative integer is called as Negative Rational Number.

Example : ${\frac {1}{-3}},{\frac {-17}{3}},{\frac {3}{-17}}$

Properties of a Rational Number

1. If we add zero to a rational number then we will get the same rational number Example : ${\frac {2}{3}}+0={\frac {2}{3}}$
2. A rational number remains the same if we multiply or divide both the numerator and denominator with the same factor . Example : ${\frac {2}{3}}={\frac {2X3}{3X3}}={\frac {2}{3}}$
3. If we add , subtract or multiply any two rational numbers the results are always a rational number. Example : ${\frac {2}{3}}+{\frac {2}{3}}={\frac {4}{3}}$