In this chapter we will try to answer the question, “ if fraction can be a rational number ? “
If yes, then the next question arises ” is every fraction a rational number ? “.
To understand the explanation, you should have basic understanding of the concept of fractions and rational numbers.
Let us first review the both the above concepts.
What are fractions ?
The number which have both numerators and denominators are called fraction.
The fraction represents the part of whole number.
The numbers \mathtt{\frac{1}{5} ,\ \frac{2}{10} ,\ \frac{3}{2}} are all examples of fractions.
Note that fractions do not involve negative numbers.
If you want to learn about fractions in detail, click the red link.
What are Rational Numbers ?
The numbers which can be expressed in the form of P / Q are called rational numbers.
Here both P & Q are integers.
Numbers like \mathtt{\frac{3}{2} ,\ \frac{15}{17} ,\ 6.78,\ 7.13} are examples of rational numbers.
If you want to study about rational numbers in detail, click the red link.
Can a fraction be a rational number ?
The answer is YES !!!
In fact all the possible fractions are part of rational numbers.
Since the fractions are already arranged in the form of P / Q, it’s identification as a rational number is a no brainer.
For example;
Consider the fraction \mathtt{\frac{7}{11}}
Since the fraction 7 / 11 is in form of P/Q, it is a rational number.
But the opposite is not the case.
Not every rational number is a fraction.
For example;
Consider the rational number \mathtt{\frac{-3}{5}}
Here the number \mathtt{\frac{-3}{5}} is not a fraction since it contains negative number in numerator.
Example 02
Consider the rational number 6
The number 6 is not a fraction as it doesn’t have numerator and denominator.
Conclusion
All fractions are rational number. But not all rational numbers are fraction.