Verify:$\frac{-2}{5} + [\frac{3}{5} + \frac{1}{2}] = [\frac{-2}{5} + \frac{3}{5}] + \frac{1}{2}$

Given :

The given expression is $\frac{-2}{5} + [\frac{3}{5} + \frac{1}{2}] = [\frac{-2}{5} + \frac{3}{5}] + \frac{1}{2}$.

To do :

We have to verify the given expression using a suitable property.

Solution :

Associative Property of Addition:

The addition follows associative property. Associative property of addition states that

$(a+b)+c = a+(b+c)$

LHS

$\frac{-2}{5} + [\frac{3}{5} + \frac{1}{2}]=\frac{-2}{5}+[ \frac{(3\times2+1\times5)}{10}]$

$= \frac{-2}{5} + \frac{11}{10}$

$= \frac{(-2\times 2+11)}{10}$

$= \frac{(-4+11)}{10}$

$= \frac{7}{10}$.

RHS

$[\frac{-2}{5} + \frac{3}{5}] + \frac{1}{2}= [\frac{(-2+3)}{5}] +\frac{1}{2}$

$=\frac{1}{5} +\frac{1}{2}$

$= \frac{(1\times2+1\times5)}{10}$

$= \frac{(2+5)}{10}$

$= \frac{7}{10}$

$LHS = RHS$

Hence verified.