Chapter 3 - Adding and Subtracting Fractions - 3.5 Order Relation and the Order of Operations - 3.5 Exercises - Page 245: 63

$\frac{5}{16}$

$(\frac{3}{4})^2 - (\frac{1}{2} - \frac{1}{6}) \div \frac{4}{3}$ = $(\frac{3}{4})^2 - (\frac{3}{6} - \frac{1}{6}) \div \frac{4}{3}$ = $(\frac{3}{4})^2 - \frac{2}{6} \div \frac{4}{3}$ = $\frac{9}{16} - \frac{2}{6} \div \frac{4}{3}$ = $\frac{9}{16} - \frac{2}{6} \div \frac{4}{3}$ = $\frac{9}{16} - \frac{2}{6} \times \frac{3}{4}$ = $\frac{9}{16} - \frac{6}{24}$ = $\frac{9}{16} - \frac{1}{4}$ = $\frac{9}{16} - \frac{4}{16}$ = $\frac{5}{16}$