Question

Simplify:
$1\frac{5}{6}+\left[2\frac{2}{3}-\left\{3\frac{3}{4}\left(3\frac{4}{5}÷9\frac{1}{2}\right)\right\}\right]$

Answer 1

Given expression:
$$\begin{gathered} =1\frac{5}{6}+\left[2\frac{2}{3}-\left\{3\frac{3}{4}\left(3\frac{4}{5}÷9\frac{1}{2}\right)\right\}\right] \\ =\frac{11}{6}+\left[\frac{8}{3}-\left\{\frac{15}{4}\left(\frac{19}{5}÷\frac{19}{2}\right)\right\}\right] \\ =\frac{11}{6}+\left[\frac{8}{3}-\left\{\frac{15}{4}\left(\frac{19}{5}\times \frac{2}{19}\right)\right\}\right] \\ =\frac{11}{6}+\left[\frac{8}{3}-\left\{\frac{15}{4}\times \frac{2}{5}\right\}\right]\left(\mathrm{Removing}\mathrm{parentheses}\right) \\ =\frac{11}{6}+\left[\frac{8}{3}-\frac{3}{2}\right]\left(\mathrm{Removing}\mathrm{braces}\right) \\ =\frac{11}{6}+\left[\frac{16-9}{6}\right] \\ =\frac{11}{6}+\frac{7}{6}(\mathrm{Removing}\mathrm{square}\mathrm{brackets}) \\ =\frac{18}{6}=3 \end{gathered}$$