# Solve the following:$3 \frac{2}{5} \div \frac{4}{5} of \frac{1}{5} + \frac{2}{3} of \frac{3}{4} - 1 \frac{35}{72}$.

Given :

The given expression is $3 \frac{2}{5} \div \frac{4}{5} of \frac{1}{5} + \frac{2}{3} of \frac{3}{4} - 1 \frac{35}{72}$.

To do:

We have to solve the given expression.

Solution :

We have to use BODMAS in these types of problems.

In the Bodmas method, we have to solve in the following order: Brackets first, then of, then division, multiplication, and at last addition and subtraction.

$3 \frac{2}{5} \div \frac{4}{5} of \frac{1}{5} + \frac{2}{3} of \frac{3}{4} - 1 \frac{35}{72} = \frac{(3\times 5+2)}{5} \div (\frac{4}{5} \times \frac{1}{5}) + (\frac{2}{3} \times \frac{3}{4}) - \frac{(72\times 1+35)}{72}$

$= \frac{17}{5} \div \frac{4}{25} + \frac{1}{2} - \frac{107}{72}$

$= \frac{17}{5} \times \frac{25}{4} + \frac{1}{2} - \frac{107}{72}$

$=\frac{(17\times 5)}{4} +\frac{1}{2} - \frac{107}{72}$

$= \frac{85}{4} +\frac{1}{2} - \frac{107}{72}$

$= \frac{(18\times 85+36\times 1-107)}{72}$

$= \frac{(1530+36-107)}{72}$

$= \frac{1459}{72}$.

Therefore, the value of  $3 \frac{2}{5} \div \frac{4}{5} of \frac{1}{5} + \frac{2}{3} of \frac{3}{4} - 1 \frac{35}{72}$ is  $\frac{1459}{72}$.

Updated on: 10-Oct-2022

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