Question

Why is every rational no. not a fraction even though every fraction is a rational number

Answer 1

Every fraction is a rational number but a rational number need not be a fraction.

Let a/b be any fraction. Then, a and b are natural numbers. Since every natural number is an integer. Therefore, a and b are integers. Thus, the fraction a/b is the quotient of two integers such that b ≠ 0.

Hence, a/b is a rational number.

We know that 2/-3 is a rational number but it is not a fraction because its denominator is not a natural number.

Since every mixed fraction consisting of an integer part and a fractional part can be expressed as an improper fraction, which is quotient of two integers.

Thus, every mixed fraction is also a rational number.

Hence, every fraction is also a rational number.