Simplify

$$\begin{gathered} b) 4\frac{1}{6} + \left[2\frac{1}{2} - \left\{3-\left(4 of 5\frac{1}{2}-\frac{1}{2}-13\frac{1}{2}\right)\right\}\right] \\ d) 11\frac{1}{2}- \left[12\frac{1}{5}-\left\{8\frac{1}{2}-\left(6\frac{1}{2} of 5\frac{1}{3} - 34\frac{2}{3}\right)\right\}\right] \end{gathered}$$

Dear Student,

Please find below the solution to the asked query:

b ) We have : $4\frac{1}{6} + \left[2\frac{1}{2} -\left\{ 3 - \left( 4 \mathrm{of} 5 \frac{1}{2} - \frac{1}{2} - 13 \frac{1}{2}\right)\right\}\right]$ , By using BODMAS :

$$\begin{gathered} \Rightarrow \frac{24 + 1}{6} + \left[\frac{4 + 1}{2} -\left\{ 3 - \left( 4 \mathrm{of} \frac{10 +1}{2} - \frac{1}{2} - \frac{26 + 1}{2}\right)\right\}\right] \\ \Rightarrow \frac{25}{6} + \left[\frac{5}{2} -\left\{ 3 - \left( 4 \mathrm{of} \frac{11}{2} - \frac{1}{2} - \frac{27}{2}\right)\right\}\right] \\ \Rightarrow \frac{25}{6} + \left[\frac{5}{2} -\left\{ 3 - \left( 4 \times \frac{11}{2} - \frac{1}{2} - \frac{27}{2}\right)\right\}\right] \\ \Rightarrow \frac{25}{6} + \left[\frac{5}{2} -\left\{ 3 - \left( 22 - \frac{1}{2} - \frac{27}{2}\right)\right\}\right] \\ \Rightarrow \frac{25}{6} + \left[\frac{5}{2} -\left\{ 3 - \left( \frac{44 -1 - 27}{2}\right)\right\}\right] \\ \Rightarrow \frac{25}{6} + \left[\frac{5}{2} -\left\{ 3 - \left( \frac{16}{2}\right)\right\}\right] \\ \Rightarrow \frac{25}{6} + \left[\frac{5}{2} -\left\{ 3 - 8 \right\}\right] \\ \Rightarrow \frac{25}{6} + \left[\frac{5}{2} + 5\right] \\ \Rightarrow \frac{25}{6} + \left[\frac{5 + 10}{2}\right] \\ \Rightarrow \frac{25}{6} + \frac{15}{2} \\ \Rightarrow \frac{25 + 45}{6} \\ \Rightarrow \frac{70}{6} \\ \mathbf{\Rightarrow }\frac{\mathbf{35}}{\mathbf{3}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$

d ) We have : $11\frac{1}{2} - \left[12\frac{1}{5} -\left\{8\frac{1}{2}- \left( 6\frac{1}{2} \mathrm{of} 5 \frac{1}{3} -34 \frac{2}{3}\right)\right\}\right]$ , By using BODMAS :

$$\begin{gathered} \Rightarrow \frac{22 + 1}{2} - \left[\frac{60 + 1}{5} -\left\{ \frac{16 + 1}{2} - \left( \frac{12 + 1}{2} \mathrm{of} \frac{15 +1}{3} - \frac{102 + 2}{2} \right)\right\}\right] \\ \Rightarrow \frac{23}{2} - \left[\frac{61}{5} -\left\{ \frac{17}{2} - \left( \frac{13}{2} \mathrm{of} \frac{16}{3} - \frac{104}{2} \right)\right\}\right] \\ \Rightarrow \frac{23}{2} - \left[\frac{61}{5} -\left\{ \frac{17}{2} - \left( \frac{13}{2} \times \frac{16}{3} - \frac{104}{2} \right)\right\}\right] \\ \Rightarrow \frac{23}{2} - \left[\frac{61}{5} -\left\{ \frac{17}{2} - \left( \frac{104}{3}- \frac{104}{2} \right)\right\}\right] \\ \Rightarrow \frac{23}{2} - \left[\frac{61}{5} -\left\{ \frac{17}{2} - \left( \frac{208 - 314}{6} \right)\right\}\right] \\ \Rightarrow \frac{23}{2} - \left[\frac{61}{5} -\left\{ \frac{17}{2} - \left( -\frac{104}{6} \right)\right\}\right] \\ \Rightarrow \frac{23}{2} - \left[\frac{61}{5} -\left\{ \frac{17}{2} +\frac{104}{6} \right\}\right] \\ \Rightarrow \frac{23}{2} - \left[\frac{61}{5} -\left\{ \frac{51 + 104}{6} \right\}\right] \\ \Rightarrow \frac{23}{2} - \left[\frac{61}{5} - \frac{155}{6} \right] \\ \Rightarrow \frac{23}{2} - \left[\frac{366 - 775}{30} \right] \\ \Rightarrow \frac{23}{2} - \left[-\frac{409}{30} \right] \\ \Rightarrow \frac{23}{2} +\frac{409}{30} \\ \Rightarrow \frac{345 + 409}{30} \\ \Rightarrow \frac{754}{30} \\ \mathbf{\Rightarrow }\frac{\mathbf{377}}{\mathbf{15}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$
Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards