Question

Simplify: ${\displaystyle 1\frac{1}{5}÷\{2\frac{1}{3}-(5+\overline{2-3})\}-3\frac{1}{2}}$

Answer 1

${\displaystyle 1\frac{1}{5}÷\{2\frac{1}{3}-(5+\overline{2-3})\}-3\frac{1}{2}}$

= ${\displaystyle \frac{6}{5}÷\{\frac{7}{3}-(5-1)\}-\frac{7}{2}}$

= ${\displaystyle \frac{6}{5}÷\{\frac{7}{3}-\frac{4}{1}\}-\frac{7}{2}}$

= ${\displaystyle \frac{6}{5}÷\left\{\frac{7-12}{3}\right\}-\frac{7}{2}}$

= ${\displaystyle \frac{6}{5}÷\frac{-5}{3}-\frac{7}{2}}$

= ${\displaystyle \frac{6}{5}\times \frac{3}{-5}-\frac{7}{2}}$

= ${\displaystyle -\frac{18}{25}-\frac{7}{2}}$

= ${\displaystyle \frac{-36-175}{50}=\frac{-211}{50}}$

= ${\displaystyle -4\frac{11}{50}}$