When you divide a number by four you are dividing it in four equal parts. A fraction is created by dividing something in a certain number of parts aswel, if the denominator of the fraction is four, then this number was divided by four equal parts. If we divide by four and multiply by 1/4 we are executing the same operation, therefore the results will be equal.
Example:
[tex]\begin{gathered} 100\colon4\text{ = 25} \\ 100\cdot\frac{1}{4}\text{ = 25} \end{gathered}[/tex]
