Verify the Following by using suitable property: $(\frac{5}{4}+\frac{-1}{2})+\frac{-3}{2}= \frac{5}{4}+(\frac{-1}{2}+\frac{-3}{2})$

Given :

The given expression is $(\frac{5}{4}+\frac{-1}{2})+\frac{-3}{2}= \frac{5}{4}+(\frac{-1}{2}+\frac{-3}{2})$.

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

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

$= \frac{3}{4} - \frac{3}{2}$

$= \frac{(3-3\times 2)}{4}$

$= \frac{(3-6)}{4}$

$= \frac{-3}{4}$.

RHS

$\frac{5}{4}+(\frac{-1}{2}+\frac{-3}{2}) = \frac{5}{4} +\frac{(-1-3)}{2}$

$=\frac{5}{4} +\frac{-4}{2}$

$= \frac{(5-4\times 2)}{4}$

$= \frac{(5-8)}{4}$

$= \frac{-3}{4}$

$LHS = RHS$

Therefore,

 

$(\frac{5}{4}+\frac{-1}{2})+\frac{-3}{2}= \frac{5}{4}+(\frac{-1}{2}+\frac{-3}{2})$ is verified.