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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.
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