Question

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

Answer 1

Given,

we have to verify

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

LHS

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

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

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

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

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

RHS

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

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

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

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

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

hence proved LHS=RHS

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