Question

answer with explanation ​

Answer 1

Answer :

$\sf\implies\::\:\dfrac{-1}{3}\:+\:(\dfrac{-2}{6}\:+\:\dfrac{5}{8})\:=\:(\dfrac{-1}{3}\:-\:\dfrac{2}{6})\:+\:\dfrac{5}{8}$

$\sf\implies\::\:\dfrac{-1}{3}\:+\:(\dfrac{-8}{24}\:+\:\dfrac{15}{24})\:=\:(\dfrac{-2}{6}\:-\:\dfrac{2}{6})\:+\:\dfrac{5}{8}$

$\sf\implies\::\:\dfrac{-1}{3}\:+\:(\dfrac{-8\:+\:15}{24})\:=\:(\dfrac{-2\:-\:2}{6})\:+\:\dfrac{5}{8}$

$\sf\implies\::\:\dfrac{-1}{3}\:+\:(\dfrac{7}{24})\:=\:(\dfrac{-4}{6})\:+\:\dfrac{5}{8}$

$\sf\implies\::\:\dfrac{-8}{24}\:+\:\dfrac{7}{24}\:=\:\dfrac{-16}{24}\:+\:\dfrac{15}{24}$

$\sf\implies\::\:\dfrac{-1}{24}\:=\:\dfrac{-1}{24}$

L.H.S = R.H.S

Answer 2

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

$\sf If \: x \: = \dfrac{ - 1}{3} , \: y \: = \dfrac{ - 2}{6} \: and \: z \: = \dfrac{5}{8} , \: show \: that : \\ \\ \sf x + (y + z) = (x + y) + z$

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

$\large \underline{\tt Given} :$

• $\sf x \: = \dfrac{ - 1}{3}$

• $\sf y \: = \dfrac{ - 2}{6}$

• $\sf z \: = \dfrac{5}{8}$

$\large \underline{\tt To \: Prove} :$

• x + (y + z) = (x + y) + z

$\large \underline{\tt Proof} :$

We have to prove :

• x + (y + z) = (x + y) + z

We have :

• $\sf x \: = \dfrac{ - 1}{3}$

• $\sf y \: = \dfrac{ - 2}{6}$

• $\sf z \: = \dfrac{5}{8}$

So, by substituting values in LHS [x + (y + z)] :

$\sf : \implies \underline{\bf LHS} = \dfrac{ - 1}{3} + \Bigg(\dfrac{ - 2}{6} + \dfrac{5}{8}\Bigg)$

$\sf : \implies \underline{\bf LHS} = \dfrac{ - 1}{3} + \Bigg(\dfrac{ - 16 + 30}{48}\Bigg)$

$\sf : \implies \underline{\bf LHS} = \dfrac{ - 1}{3} + \Bigg(\cancel{\dfrac{14}{48}}\Bigg)$

$\sf : \implies \underline{\bf LHS} = \dfrac{ - 1}{3} + \dfrac{7}{24}$

$\sf : \implies \underline{\bf LHS} = \dfrac{ - 8 + 7}{24}$

$\sf : \implies \underline{\bf LHS} = \dfrac{ - 1}{24}$

$\: \: \: \: \: \: \dag \: \pink{\underline{\boxed{\bf LHS = \dfrac{ - 1}{24}}}}$

Now, by substituting values in RHS [(x + y) + z] :

$\sf : \implies \underline{\bf RHS} = \Bigg(\dfrac{ - 1}{3} + \dfrac{ - 2}{6}\Bigg) + \dfrac{5}{8}$

$\sf : \implies \underline{\bf RHS} = \Bigg(\dfrac{ - 1}{3} - \dfrac{2}{6}\Bigg) + \dfrac{5}{8}$

$\sf : \implies \underline{\bf RHS} = \dfrac{ - 2 - 2}{6} + \dfrac{5}{8}$

$\sf : \implies \underline{\bf RHS} = \dfrac{ -4}{6} + \dfrac{5}{8}$

$\sf : \implies \underline{\bf RHS} = \dfrac{ -32 + 30}{48}$

$\sf : \implies \underline{\bf RHS} = \cancel{\dfrac{ -2}{48}}$

$\sf : \implies \underline{\bf RHS} = \dfrac{ - 1}{24}$

$\: \: \: \: \: \: \dag \: \pink{\underline{\boxed{\bf RHS = \dfrac{ - 1}{24}}}}$

$\: \: \: \: \: \: \: \blue{\underline{\boxed{\bf As, \: LHS = RHS = \dfrac{ - 1}{24}}}}$

$\: \: \: \: \: \: \: \: \blue{\underline{\boxed{\bf Hence, \: Proved }}} \: \dag$