In terms of mathematical representation, fractions and rational numbers may appear to be extremely similar, but there is a significant difference between them. Let’s learn about the comparison and difference between fractions and rational numbers with examples.
Let’s begin:
Difference Between Fractions and Rational Numbers
Parts of a whole are defined as fractions. It can be thought of as a component, part, or section of a larger whole. A fraction is defined mathematically as the ratio of two whole numbers, with the denominator being a non-zero whole number.
For example, 1/2, 6/7, and so forth. There are six sorts of fractions in total:
- Proper fraction
- Improper fraction
- Mixed fraction
- Like fractions
- Unlike fractions
- Equivalent fractions
A rational number is a subset of real numbers that, in terms of mathematical representation, is extremely comparable to fractions. A rational number is defined mathematically as the ratio of two integers, with the denominator always being a non-zero integer. For example, – 2/3, 7/8, and so on.
Fractions and rational numbers are frequently thought to be mathematically equivalent. Let us now tabulate and compare them to observe how fractions and rational numbers compare and vary.
Take a look at the table below to learn about the Difference Between Fraction and Rational Numbers:
| Rational Number | Fraction |
| A rational number is defined as the ratio of two numbers, p, and q, and is written as p/q when q ≠ 0. For instance, 11/17, – 13/19. | A fraction is defined as the ratio of two whole numbers, x, and y, and is written as x/y when y ≠ 0. For instance, 16/21 and 14/23. |
| Every rational number cannot be a fraction since negative values, such as − 1/2, do not fit into the category of fractions. | Because fractions are always the ratio of positive integers, such as 4/5, they are all rational numbers. |
| A rational number might be positive or negative. For instance, 11/27, 13/15. | In nature, a fraction is always positive. For instance, 22/49. |
Similarities Between Fraction and Rational Number
Let us now look at the similarities between the two:
- Real numbers include both fractions and rational numbers.
- The ratio of numbers is the mathematical representation of both fractions and rational numbers.
- A non-zero denominator exists in both fractions and rational numbers.
Is Every Fraction a Rational Number?
Because fractions are defined as the ratio of two whole numbers with a non-zero denominator, every fraction is a rational number. As shown below, those whole numbers are a subset of integers.
- Whole numbers (W) = {0,1,2,3,4,…}
- Integers (Z) = {…, -3,-2,-1,0,1,2,3,…}
Whole numbers are defined as all positive integers plus 0. Thus, the ratio of two whole numbers can alternatively be thought of as the ratio of two positive integers. For example, 28/31 and 5/7 are both fractions and rational numbers. As a result, it is possible to deduce that every fraction is a rational number.
Is every Rational number a Fraction?
Since the ratio of integers is the definition of a rational number, it cannot be categorized as a fraction. Because a fraction can only be the ratio of two whole numbers, and all whole numbers are positive, if we divide a negative integer by a positive integer, for example, – 4/9, – 31/70, we do not receive a fraction.
The conclusion that no rational number may be a fraction follows from this.