Simpify the following :
$(\frac{16}{17} of 6 \frac{4}{5}) -4 \frac{1}{5}-[1 \frac{1}{14} \div(\frac{1}{2}+\frac{1}{7})] $

Given :

The given expression is $(\frac{16}{17} of 6 \frac{4}{5}) -4 \frac{1}{5}-[1 \frac{1}{14} \div(\frac{1}{2}+\frac{1}{7})] $

To do :

We have to simplify the given expression.

Solution :

We have to use BODMAS method in these type of problems.

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

$= (\frac{16}{17} \times \frac{34}{5})- \frac{21}{5} - [\frac{15}{14} \div (\frac{7\times1+1\times2}{14})]$

$= (\frac{16}{1} \times \frac{2}{5}) - \frac{21}{5} - \frac{15}{14} \div \frac{9}{14}$

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

$= \frac{32}{5} - \frac{21}{5} - \frac{15}{9}$

$ = \frac{32-21}{5} - \frac{15}{9}$

$=\frac{11}{5} - \frac{15}{9}$

$= \frac{11\times 9-15\times 5}{45}$

$= \frac{(99-75)}{45}$

$= \frac{24}{45}$

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

The value of $(\frac{16}{17} of 6 \frac{4}{5}) -4 \frac{1}{5}-[1 \frac{1}{14} \div(\frac{1}{2}+\frac{1}{7})] $ is $\frac{8}{15}$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

62 Views

Kickstart Your Career

Get certified by completing the course

Get Started