Difference Between Fraction And Rational Number - Cuemath

Difference between Fraction and Rational Number

Fractions and rational numbers might look very similar in terms of mathematical representation but there is a huge difference between fractions and rational numbers. In this article, we will be learning about the comparison and difference between fraction and rational number with examples.

1.	What is the Difference between Fraction and Rational Number?
2.	Examples on Difference between Fraction and Rational Number
3.	FAQs on Difference between Fraction and Rational Number

What is the Difference between Fraction and Rational Number?

A fraction is defined as parts of a whole. It can be considered as a portion, part, or section of a complete whole. Mathematically, a fraction is defined as the ratio of two whole numbers and the denominator will be a non-zero whole number. For example, 1/2, 6/7, etc.

A rational number is a subset of real numbers and very similar to fractions in terms of mathematical representation. Mathematically, a rational number is defined as the ratio of two integers and the denominator will always be a non-zero integer. For example, - 2/3, 7/8, etc.

We often consider the fractions and rational numbers to be mathematically similar. Let us now tabulate and compare them and see the similarities and differences between fraction and rational number.

Difference between Fraction and Rational Number

Let us look at the tabular difference between fraction and rational number given below:

Rational Number	Fraction
A rational number is defined as the ratio of two integers p and q and is represented in the form of p/q where q ≠ 0. For example: 11/17, - 13/19.	A fraction is defined as the ratio of two whole numbers x and y and is represented in the form of x/y where y ≠ 0. For example, 16/21, 14/23.
Every rational number cannot be a fraction because when there are negative numbers, they do not fall in the category of fractions such as - 1/2.	Every fraction is a rational number because fractions are always the ratio of positive integers such as 4/5.
A rational number can be both negative and positive. For example, - 11/27, 13/15.	A fraction is always positive in nature. For example, 22/49.

Similarities between Fraction and Rational Number

We have discussed the differences between a rational number and fraction in the previous section. Let's now discuss the similarities seen in the two.

• Both fractions and rational numbers fall in the set of real numbers.
• The mathematical representation of both fractions and rational numbers are in the form of ratio of numbers.
• Both fractions and rational numbers have a non-zero denominator.

Is every Fraction a Rational Number?

Every fraction can be considered as a rational number because fractions are defined as the ratio of two whole numbers with a non-zero denominator. We know that whole numbers is a subset of integers as shown below.

Whole numbers (W) = {0, 1, 2, 3,...} Integers (Z) = {..., 2, - 1, 0, 1, 2,...}

Whole numbers can be defined as all the positive integers along with 0. Thus, ratio of two whole numbers, in other words, can also be considered as ratio of two positive integers. For example, 28/31, 5/7 are fractions as well as rational numbers. Therefore, it can be concluded that every fraction is a rational number.

Is every Rational number a Fraction?

Every rational number cannot be considered as a fraction because a rational number is defined as the ratio of integers. Hence, if we take the ratio of a negative integer with a positive integer such as - 4/9, - 31/70, we do not get a fraction as fraction can only be the ratio of two whole numbers and all whole numbers are positive in nature. Thus, it can be concluded that every rational number cannot be a fraction.

Related Articles

Check these articles related to the concept of the difference between a fraction and a rational number.

• Rational Number
• Fractions
• Integers