Question

Is \[\dfrac{3}{5}\] a rational number?

Answer 1

Hint: In the question we have to check whether \[\dfrac{3}{5}\] is a rational number or not. A rational number is a real number, which can be written in the form of \[\dfrac{p}{q}\] where \[p\] and \[q\] are integers and \[q\] is not equal to zero and \[p\] and \[q\] are co-primes. In order to solve this question, we will use the definition of the rational numbers and check whether \[\dfrac{3}{5}\] satisfies the conditions of a rational number or not. Hence, we get the required result.

Complete step by step solution:
We know that a number which can be expressed in the form of \[\dfrac{p}{q}\] where \[p\] and \[q\] are integers and \[q\] is not equal to zero and \[p\] and \[q\] are co-primes is known as a rational number. For examples: \[\dfrac{1}{2},\dfrac{7}{9},\dfrac{8}{5},.....\]etc.
In the question, we have to check whether \[\dfrac{3}{5}\] is a rational number or not
So, basically when we have to check whether a number is a rational number or not, we need to check three conditions:
1) it is represented in the form of \[\dfrac{p}{q}\]
2) \[p\] and \[q\] are integers and \[q\] is not equal to zero
3) \[p\] and \[q\] are co-primes
Here, the given number is \[\dfrac{3}{5}\]
So, let’s check the conditions one by one:
Here, we can see that \[\dfrac{3}{5}\] is in the form of \[\dfrac{p}{q}\]
Hence, the first condition is satisfied.
Now, \[3\] and \[5\] both are integers and \[q = 5 \ne 0\] which means the second condition is also satisfied.
Now if we see, only $1$ is the common factor between \[3\] and \[5\] which implies that they are co-primes. Hence, the third condition is also satisfied.
Thus, all the conditions are satisfied to be a rational number.
Hence, \[\dfrac{3}{5}\] is a rational number.

Note:
Students should note that sometimes there are rational numbers in which \[p\] and \[q\] are not co-primes. Therefore, don’t think that these are not rational numbers. They are also rational numbers because we can convert them into the standard form of rational numbers.
For example, \[\dfrac{{12}}{{24}}\]
Here, many think \[12\] and \[24\] are not co-primes, so it is not a rational number. But it’s not like that. It is also a rational number because it can be written as \[\dfrac{{12}}{{24}} = \dfrac{1}{2}\] ; and \[1\] and \[2\] are co-primes which satisfy the condition to be a rational number.