No. Not all the time.
Example:
[tex]\text{ }\frac{1}{2}x\text{ }=\text{ }\frac{3}{2}[/tex][tex]\text{ }x\text{ }=\text{ }\frac{3}{2}\text{ x }\frac{2}{1}\text{ = }\frac{6}{2}\text{ = 3}[/tex]Therefore, x = 3
Thus, an equation containing a fraction doesn't always have a solution that is a fraction.
