Difference Between Fraction and Rational Number

The concept of “fractional number” and “rational numbers” are closely related but are different in various aspects. It should be noted that "a fractional number is always a rational number but a rational number may or may not be a fractional number".

Fraction and Rational Number Differences:

The difference in Definition: A fraction is any number of the form a/b where both “a” and “b” are whole numbers and b≠0. On the other hand, a rational number is a number which is in the form of p/q where both “p” and “q” are integers and q≠0.

Thus, a fraction is written in the form of a/b, where n is not 0 and m & n are whole (or natural numbers). For example, 12/23, 10/32, 12/10, 4/21. A rational number can also be written in the form of a/b, where b is not 0 and a & b are integers. For example, 15/7, -18/13, 3/-7, -6/-12. In general, rational numbers are denoted as p/q.

Why Every Fraction is a Rational Number but not Vice Versa?

All fractions can be termed as rational numbers, however, all rational numbers cannot be termed as fractions. Only those rational numbers in which ‘p’ and ‘q’ are positive integers are termed as fractions. Let a/b be any fraction. Now, a and b are natural numbers. Since all natural numbers are also integers, a and b are also integers. Thus, the fraction a/b is the quotient of 2 integers such that m ≠ 0. Hence, a/b is a rational number. One of the examples in which a number is a rational number but not a fraction is:

  • Consider the fraction 12/-32. It is a rational number but not a fraction because its denominator (n) is not a natural number.