The Fundamental Difference between Fraction and Rational Numbers
When it comes to numbers, there are a variety of different types and classifications to be aware of. Among these classifications are fractions and rational numbers. While they may seem similar in some regards, there are some significant differences that set them apart. In this article, we will explore the fundamental difference between fraction and rational numbers.
Fractions vs. Rational Numbers: What’s the Difference?
Let’s start by defining what each of these terms actually means. A fraction is a numerical quantity that represents a part or a fraction of a whole. It is usually represented as a numerator over a denominator, with a line separating the two numbers. For example, 1/2 is a fraction that represents one half of a whole.
A rational number, on the other hand, is any number that can be expressed as a ratio of two integers. This includes not only fractions but also integers and decimals that repeat or terminate. For example, 1.5 is a rational number because it can be expressed as a fraction (3/2).
Why the Difference Matters
So, what’s the big deal about the difference between fractions and rational numbers? The answer lies in the fact that not all fractions are rational numbers. For instance, the fraction 1/3 cannot be expressed as a ratio of two integers because the decimal equivalent of 0.33333… goes on indefinitely without repeating. Therefore, 1/3 is considered to be an irrational number.
Understanding the difference between these two terms is critical for a variety of reasons. For one thing, it is essential for simplifying and manipulating expressions in algebraic equations. Additionally, it is useful for interpreting data in fields like statistics, where fractions and rational numbers can be used to represent proportions and probabilities.
In Conclusion
In conclusion, fractions and rational numbers may seem similar at first glance, but they are not the same thing. While a fraction is a representation of a part of a whole, a rational number is any number that can be expressed as a ratio of two integers. Knowing the differences between these two types of numbers is essential for understanding mathematical concepts and applying them in real-world scenarios.
Table difference between fraction and rational number
| Features | Fraction | Rational Number |
|---|---|---|
| Definition | A fraction is a number that represents a part of a whole. It usually consists of a numerator, a denominator, and a fraction bar between them. | A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers. |
| Representation | Fractions are usually represented in the form of a/b, where a is the numerator and b is the denominator. They can also be represented as decimals or percentages. | Rational numbers can be represented in the form of a/b, where a is the numerator and b is the denominator. They can also be represented as decimals or percentages. |
| Examples | 1/2, 3/4, 5/6 | 1/3, -3/5, 7/2 |
| Type of Number | Fractions are a type of rational number. | Rational numbers are a type of real number. |
| Operations | Fractions can be added, subtracted, multiplied or divided by following certain rules and procedures. | Rational numbers can be added, subtracted, multiplied or divided by following certain rules and procedures. |