# Find the value of $\frac{3}{5} \times\left(\frac{-5}{6}\right)-\frac{1}{8} \times \frac{4}{5}+\frac{1}{12} \times \frac{3}{5}$

Given : $\frac{3}{5}\left(\frac{-5}{6}\right)-\frac{1}{8} \times \frac{4}{5}+\frac{1}{12} \times \frac{3}{5}$

We have to simplify the fractions and add them

$=\frac{3}{5} \times \frac{-5}{6}-\frac{1}{8} \times \frac{4}{5}+\frac{1}{12} \times \frac{3}{5}$

First term: $\frac{3}{5} \times \frac{-5}{6}=-\frac{1}{2}$

$=-\frac{1}{2}-\frac{1}{8} \times \frac{4}{5}+\frac{3}{5} \times \frac{1}{12}$

Second term:$\frac{1}{8} \times \frac{4}{5}=\frac{1}{10}$

Third Term:$\frac{1}{12} \times \frac{3}{5}=\frac{1}{20}$

$=-\frac{1}{2}-\frac{1}{10}+\frac{1}{20}$

Least Common Multiple of $2,10,20: \quad 20$

Adjust Fractions based on the LCM

$=-\frac{10}{20}-\frac{2}{20}+\frac{1}{20}$

since the denominators are equal, combine the fractions:

$=\frac{-10-2+1}{20}$

$=\frac{-11}{20}$

$=-\frac{11}{20}$

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Updated on: 10-Oct-2022

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