All numbers, including whole numbers, integers, fractions and decimal numbers, can be written in the numerator-denominator form. A rational number is a number that can be written in the form p/q, where p and q are integers and q ≠ 0. . The denominator of a rational number can never be zero. A rational number is positive if its numerator and denominator are both either positive integers or negative integers. . If either the numerator or the denominator of a rational number is a negative integer, then the rational number is called a negative rational number.
The rational number zero is neither negative nor positive.
On the number line:
- Positive rational numbers are represented to the right of 0.
- Negative rational numbers are represented to the left of 0.
By multiplying or dividing both the numerator and the denominator of a rational number by the same non-zero integer, we can get another rational number that is equivalent to the given rational number.
A rational number is said to be in its standard form if its numerator and denominator have no common factor other than 1, and its denominator is a positive integer.
To reduce a rational number to its standard form, divide its numerator and denominator by their Highest Common Factor (HCF). To find the standard form of a rational number with a negative integer as the denominator, divide its numerator and denominator by their HCF with a minus sign.