Is Every Rational Number Is a natural Number

Every natural number is a rational number but a rational number need not to be a natural number.

We know that

1/1 = 1,

2 = 2/1,

3 = 3/1,

4 = 4/1 and so on…..

In other words we can say that every natural number can be written as n = n/1, which is the quotient of two integers.

Thus, every natural number is a rational number.

3/2, 4/5, 25/20, 5/4, etc. are rational numbers but these are not 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 are not.

(i) 9/3

9/3 is a natural number, if we simplify 9/3 to its lowest form we get 9/3 = 3, which is a natural number.

(ii) -10/2

-10/2 is not a natural number because if we simplify -10/2 to its lowest form we get, -5/1 = -5 which is not a natural number.

(iii) -8/-2

if we simplify -8/-2 to its lowest form we get, -8/-2 = 4, which is a natural number.

(iv) -8/2

8/-2 is not a natural number because if we simplify 8/-2 to its lowest form we get, 8/-2 = -4 which is not a natural number.

(v) 0/1

0/1 = 0 which is not a natural number.

(vi) 0/8

0/8 = 0 which is not a natural number.

(vii) 21/35

21/35 is not a natural number because if we simplify 21/35 to its lowest form we get,

21/35 = 3/5, which is a rational number but not a natural number.

(viii) 24/12

if we simplify 24/12 to its lowest form we get, 24/12 = 2, which is a natural number.

Therefore, 24/12 is a natural number.