Every Natural Number is a Rational Number but it’s not the same in the case of Rational Numbers. There is no such thing when it comes to a Rational Number it may or may not be a Natural Number.
We know that 1 = 1/1, 2 = 2/1, ….
In fact, we can say a natural number n can be expressed as n = n/1 which is nothing but the quotient of two integers. Therefore, every natural number is a Rational Number.
On the other hand, 5/2, 3/5, 2/7, 4/20, etc. are all Rational Numbers but aren’t natural numbers.
Therefore, every natural number is a Rational Number but a Rational Number need not be a Natural Number.
Determine Whether the Following Rational Numbers are Natural Numbers or Not
(i) 5/2
5/ 2 is not a natural number.
(ii) 8/2
8/2 is a natural number as on simplifying it we get the result as 4 which is a natural number.
(iii) -20/5
-20/5 isn’t a natural number as on further simplifying we get the result -4 which is an integer but not a natural number.
(iv) -6/-3
-6/-3 is a natural number as we will get the result 2 on simplification which is a natural number.
(v) 1/5
1/5 is not a natural number.
(vi) 0/3
0/3 is not a natural number since 0/3 =0 and 0 is not a natural number.
(vii) 5/5
5/5 is a natural number on simplifying to its lowest term we get 1/1 = 1 and 1 is a natural number.
(viii) 27/45
27/45 is not a natural number as we get 3/5 on reducing to its lowest term which is a rational number but not a natural number.
Thus, by looking after the instances above we can state that Not every Rational Number is a Natural Number.