let's firstly convert the mixed fraction to improper fraction and then divide.
namely how many times does 1/4 go into 2 and 2/4.
[tex]\bf \stackrel{mixed}{2\frac{2}{4}}\implies \cfrac{2\cdot 4+2}{4}\implies \stackrel{improper}{\cfrac{10}{4}}\implies \cfrac{5}{2} \\\\\\ \cfrac{5}{2}\div \cfrac{1}{4}\implies \cfrac{5}{2}\cdot \cfrac{4}{1}\implies \cfrac{5}{1}\cdot \cfrac{4}{2}\implies 5\cdot 2\implies 10[/tex]
