Question

By using appropriate PROPERTIES find the value of 4/5 × -3/4 -2/5 + 4/5 × 5/6

Answer 1

We have to find   $\displaystyle\sf{(\frac{4}{5}\times\frac{-3}{4})-(\frac{2}{5})+(\frac{4}{5}\times\frac{5}{6})$

$\displaystyle\sf{(\frac{4}{5}\times\frac{-3}{4})-(\frac{2}{5})+(\frac{4}{5}\times\frac{5}{6})$

$\displaystyle\sf{= \frac{-12}{20}-\frac{2}{5}+\frac{20}{30}$

Here the LCM is 60.

So we have to get a common denominator as 60,

$=\displaystyle\sf{\frac{-12\times3}{20\times3}-\frac{2\times12}{5\times12}+\frac{20\times2}{30\times2}$

$=\displaystyle\sf{\frac{-36}{60}-\frac{24}{60}+\frac{40}{60}$

$=\displaystyle\sf{\frac{-36-24+40}{60}}$

$=\displaystyle\sf{\frac{-20}{60}$

$=\displaystyle\sf{\frac{-1}{3}}$

$\boxed{\displaystyle\sf{(\frac{4}{5}\times\frac{-3}{4})-(\frac{2}{5})+(\frac{4}{5}\times\frac{5}{6})=\frac{-1}{3}}}$