Question

Question 54

State whether the given statement is True or False.

If $\frac{p}{q}$ is a rational number and m is a non-zero integer, then $\frac{p\times m}{q\times m}$ is a rational number not equivalent to $\frac{p}{q}$ .

Answer 1

False

Let $m=1,2,3,\cdots$
When m = 1 then $\frac{p\times m}{q\times m}=\frac{p\times 1}{q\times 1}=\frac{p}{q}$
When m = 2 then $\frac{p\times m}{q\times m}=\frac{p\times 2}{q\times 2}=\frac{p}{q}$
For any non-zone value of m, $\frac{p\times m}{q\times m}$ is always equivalent to $\frac{p}{q}$