Answer:
see the explanation
Step-by-step explanation:
we know that
A Rational Number is a number that can be made by dividing two integers
we have
[tex]\frac{\sqrt{2}}{8}[/tex]
[tex]\sqrt{2}[/tex] ----> is not a integer
so
The given number cannot be rewritten as the quotient of two integers
therefore
The given number is irrational
Student A is incorrect because is a irrational number and not all fractions are rational
Student B reasoning is incorrect, because there are fractions that have as numerator an irrational number and can be rational numbers
example
[tex]\frac{\sqrt{2}}{3\sqrt{2}}=\frac{1}{3}[/tex] ----> is a rational number and the numerator is a irrational number
