Simplify the following:

$\left(\frac{16}{17} \ \times \ 6\frac{4}{5}\right) \ -\ 4\frac{1}{5} \ -\ \left\{1\frac{1}{14} \ \div \ \left[\frac{1}{2} \ +\ \frac{1}{7}\right]\right\}$

Given: $\left(\frac{16}{17} \ \times \ 6\frac{4}{5}\right) \ -\ 4\frac{1}{5} \ -\ \left\{1\frac{1}{14} \ \div \ \left[\frac{1}{2} \ +\ \frac{1}{7}\right]\right\}$

To find: Here we have to find the value of the given expression $\left(\frac{16}{17} \ \times \ 6\frac{4}{5}\right) \ -\ 4\frac{1}{5} \ -\ \left\{1\frac{1}{14} \ \div \ \left[\frac{1}{2} \ +\ \frac{1}{7}\right]\right\}$.

Solution:

$\left(\frac{16}{17} \ \times \ 6\frac{4}{5}\right) \ -\ 4\frac{1}{5} \ -\ \left\{1\frac{1}{14} \ \div \ \left[\frac{1}{2} \ +\ \frac{1}{7}\right]\right\}$

$=\ \left(\frac{16}{17} \ \times \ \frac{34}{5}\right) \ -\ \frac{21}{5} \ -\ \left\{\frac{15}{14} \ \div \ \left[\frac{7+2}{14}\right]\right\}$

$=\ \left(\frac{32}{5}\right) \ -\ \frac{21}{5} \ -\ \left\{\frac{15}{14} \ \div \ \frac{9}{14}\right\}$

$=\ \frac{32}{5} \ -\ \frac{21}{5} \ -\ \left\{\frac{15}{14} \ \times \ \frac{14}{9}\right\}$

$=\ \frac{32}{5} \ -\ \frac{21}{5} \ -\ \frac{5}{3}$

$=\ \frac{11}{5} \ -\ \frac{5}{3}$

$=\ \frac{33\ -\ 25}{15}$

$=\ \mathbf{\frac{8}{15}}$

So, value of the given expression is $\frac{8}{15}$.

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Updated on: 10-Oct-2022

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