Difference Between Fraction and Rational Number


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Difference Between Fraction and Rational Number

There is a massive difference between a fraction and a rational number. The concept of “fractional numbers” 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”.

Definition of Fraction and Rational Numbers

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 m/n, 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.

What is the Difference Between Fraction and Rational Number?

S.No. Fraction Rational Numbers
1. Written in the form of a/b, where a and b are whole numbers, and b≠0 Written in the form of p/q, where p and q are integers, and q≠0
2.  All fractional numbers are rational All rational numbers are not fractions.
3.  ⅓, ¼, ⅛, etc. 11/2, 3/-4, etc.
4 Note: Both are real numbers

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 b ≠ 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.

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Frequently Asked Questions – FAQs

Is fraction also a rational number?

All fractions are rational numbers but it is not necessary that all rational numbers are fractions.

What is the difference between a fractional number and a rational number?

A fraction is expressed in the form of the ratio of whole numbers, a/b and b≠0.
A rational number is also expressed in the form of a ratio, p/q, where numerator and denominator are integers and q≠0.

What are the examples of rational numbers and fraction?

The examples of rational numbers are 1/4, 9/-2, 12/-8, etc.
The examples of fractions are 1/2, 1/8, 6/4, etc.

Give examples of proper fraction and improper fraction.

Proper fractions are the one which has denominator greater than the numerator. For example 1/2, 1/3, 1/4, 2/3, 3/4, etc. An improper fraction is the one which has numerator greater than the denominator, for example, 3/2, 5/4, 7/6, etc.