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.
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FAQs on Difference between Fraction and Rational Number
Is there a Difference between a Fraction and a Rational Number?
Yes, there is a difference between a fraction and a rational number. A fraction is defined as the ratio of two whole numbers with a non-zero denominator and a rational number is defined as the ratio of two integers with a non-zero remainder.
What is the Difference between Fraction and Rational Numbers?
Both numerator and denominator of a fraction are whole numbers with a non-zero denominator such as 1/3 and the numerator and denominator of a rational number are integers with a non-zero denominator such as - 3/5.
Are Fractions and Rational Numbers the same?
Fractions and rational numbers are not the same. Fractions are the ratio of two whole numbers whereas rational numbers are the ratio of two integers with a non-zero denominator. For example, 18/23 is a fraction whereas - 12/23 is a rational number. Here it is also important to note that all fractions are rational numbers, but all rational numbers are not fractions.
How are Rational Numbers Different from Fractions?
Rational numbers can be negative in nature whereas a fraction is always positive in nature. This is because a rational number is the ratio of integers that includes negative numbers whereas a fraction is the ratio of whole numbers which are always positive.
Are Rational Numbers always Fractions?
Rational numbers are not always fractions because a rational number might have negative integers in the numerator or denominator which makes it negative. But these rational numbers cannot be considered as a fraction as a fraction can only have positive numbers as they are the ratio of whole numbers. For example, - 9/10 is a rational number but not a fraction.
How Every Fraction is a Rational Number?
Every fraction is a rational number because fractions are ratios of whole numbers and rational numbers are ratios of integers and whole numbers are subsets of integers and therefore the ratio of any two whole numbers is by default the ratio of two integers. For example, 67/90 is a fraction as well as a rational number.