Types of Rational Numbers

A number is rational if we can write it as a fraction, where both denominator and numerator are integers and the denominator is a non-zero number.

The below diagram helps us to understand more about the number sets.

• Real numbers (R) include all the rational numbers (Q).
• Real numbers include the integers (Z).
• Integers involve natural numbers(N).
• Every whole number is a rational number because every whole number can be expressed as a fraction.

Standard Form of Rational Numbers

The standard form of a rational number can be defined if it’s no common factors aside from one between the dividend and divisor and therefore the divisor is positive.

For example, 12/36 is a rational number. But it can be simplified as 1/3; common factors between the divisor and dividend is only one. So we can say that rational number ⅓ is in standard form.

Positive and Negative Rational Numbers

As we know that the rational number is in the form of p/q, where p and q are integers. Also, q should be a non-zero integer. The rational number can be either positive or negative. If the rational number is positive, both p and q are positive integers. If the rational number takes the form -(p/q), then either p or q takes the negative value. It means that

-(p/q) = (-p)/q = p/(-q).

Now, let’s discuss some of the examples of positive and negative rational numbers.