4 1/4 ÷ 3/4 is the same as 4 1/4 x 4/3
To solve this, first you have to transform the mixed number into a fraction, as follows:
[tex]4\frac{1}{4}=\frac{4\cdot4+1}{4}=\frac{17}{4}[/tex]then:
[tex]4\frac{1}{4}\cdot\frac{4}{3}=\frac{17}{4}\cdot\frac{4}{3}=\frac{17}{3}=\frac{15+2}{3}=\frac{15}{3}+\frac{2}{3}=5\frac{2}{3}[/tex]