Question

If a =-11/27 b =4/9 c=-5/18
Then varify that a+(b+c)=(a+b)+c

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{QUESTION}}}}}$

If a =-11/27 b =4/9 c=-5/18 Then varify that a+(b+c)=(a+b)+c.

$\Large{\underline{\bf{\:Given}}}$

$\star\sf{\:a\:=\:\dfrac{-11}{27}} \\\\ \star\sf{\:b\:=\:\dfrac{4}{9}} \\\\ \star\sf{\:c\:=\:\dfrac{5}{18}}$

$\Large{\underline{\bf{\:To\:Proof}}}$

$\mapsto\sf{\:a+(b+c)\:=\:(a+b)+c}$

$\Large{\underline{\bf{\:Prove}}}$

$\:\:\:\:\:\small\sf{\:(Keep\:above\:values)}$

$\mapsto\sf{\:\dfrac{-11}{27}+\left(\dfrac{4}{9}+\dfrac{-5}{18}\right)\:=\:\left(\dfrac{-11}{27}+\dfrac{4}{9}\right)+\dfrac{-5}{18}}$

$\mapsto\sf{\:\dfrac{-11}{27}+\left(\dfrac{8-5}{18}\right)\:=\:\left(\dfrac{-11+12}{27}\right)+\dfrac{-5}{18}}$

$\mapsto\sf{\:\dfrac{-11}{27}+\dfrac{3}{18}\:=\:\dfrac{1}{27}+\dfrac{-5}{18}}$

$\mapsto\sf{\:\dfrac{-11\times18+3\times27}{27\times18}\:=\:\dfrac{18-5\times27}{27\times18}}$

$\mapsto\sf{\:\dfrac{-198+81}{27\times18}\:=\:\dfrac{18-135}{27\times18}}$

$\mapsto\sf{\:\dfrac{-117}{486}\:=\:\dfrac{-117}{486}}$

=>L.H.S. = R.H.S.

That's Proved.

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