Can a fraction be a rational number ?

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.

All fractions are rational number. But not all rational numbers are fraction.

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