Quantity A

$\frac{\frac{1}{4}}{\frac{2}{3} - \frac{1-2}{\frac{1}{3}}$

$\frac{\frac{1}{4}}{\frac{2}{3} - \frac{-1}{\frac{1}{3}}$

$\frac{\frac{1}{4}}{\frac{2}{3} - \frac{-3}{1}$

$\frac{\frac{1}{4}}{\frac{2}{3} + \frac{3}{1}$

$\frac{\frac{1}{4}}{\frac{2}{3} + \frac{9}{3}$

$\frac{\frac{1}{4}}{\frac{2+9}{3}$

$\frac{\frac{1}{4}}{\frac{11}{3}$

$\frac{1}{4} \times \frac{3}{11}$

$\frac{3}{44}$

Quantity B

$\frac{\frac{1}{3}}{\frac{1}{4} - \frac{3-4}{\frac{2}{3}}$

$\frac{\frac{1}{3}}{\frac{1}{4} - \frac{-1}{\frac{2}{3}}$

$\frac{\frac{1}{3}}{\frac{1}{4} - \frac{-3}{2}$

$\frac{\frac{1}{3}}{\frac{1}{4} + \frac{3}{2}$

$\frac{\frac{1}{3}}{\frac{1}{4} + \frac{6}{4}$

$\frac{\frac{1}{3}}{\frac{1+6}{4}$

$\frac{\frac{1}{3}}{\frac{7}{4}$

$\frac{1}{3} \times \frac{4}{7}$

$\frac{4}{21}$

Quantity A: $\frac{3}{44}$ less than $\frac{1}{11}$ (somewhere around $\frac{1}{11}$)
Quantity B: $\frac{4}{21}$ greater than $\frac{1}{7}$ (somewhere around $\frac{1}{7}$)

Approx $\frac{1}{7}$ > Approx $\frac{1}{11}$

Quantity B is greater.