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, and 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 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.
Learn More:
| Difference Between Percentage And Percentile | Difference Between Natural And Whole Numbers |
| Difference Between Relation And Function | Difference Between Rational And Irrational Numbers |
Frequently Asked Questions – FAQs
Is fraction also a rational number?
What is the difference between a fractional number and a rational number?
A rational number is also expressed in the form of a ratio, p/q, where the numerator and denominator are integers and q≠0.
What are the examples of rational numbers and fraction?
The examples of fractions are 1/2, 1/8, 6/4, etc.
Sir, is 0 a fraction or not
Yes, 0 is a fraction, because we can write 0 in the form of p/q (where q is not equal to 0).
Yes, 0 can be represented as a fraction.
For ex: 0/10
Structure of a fractional number:a/b, where ‘a’ and ‘b’ represents a variable in whole number. And ‘b’ is not equal to 0.
Fraction is a number in the form of p/q where ‘p’ and ‘q’ are positive integers and q != 0
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