Question

$( \frac{5}{2} -3) <strong>:</strong> (1 \frac{1}{2} -\frac{2}{3})$

Answer 1

$\ \ \ ( \frac{5}{2} -3) \div (1 \frac{1}{2} -\frac{2}{3})\\ \\=( \frac{5}{2} -\frac{6}{2}) \div (\frac{2\cdot1+1}{2} -\frac{2}{3})\\ \\=( \frac{5-6}{2}) \div (\frac{3}{2} -\frac{2}{3})\\ \\=(-\frac{1}{2}) \div (\frac{9}{6} -\frac{4}{6})\\ \\=-\frac{1}{2} \div (\frac{9-4}{6})\\ \\=-\frac{1}{2} \div \frac{5}{6}\\ \\=-\frac{1}{2} \cdot \frac{6}{5}\\ \\=-\frac{6^{:2}}{10_{:2}}\\ \\= -\frac{3}{5}$