Question

Verify associative law
a+ (b+c) =(a+b) +c
Where a= 7/5, b= -2/5, c= -1/3​

Answer 1

☯GIVEN :

• a = $\bf {\dfrac{7}{5}}$

• b= $\bf {\dfrac{-2}{5}}$

• c = $\bf{\dfrac{-1}{3}}$

☯TO DO :

• Verify associative law :$\bf {a+(b+c) =(a+b) +c}$ .

➲SOLUTION :

★$\bf{LHS = a+(b+c)}$

• Substituting the given values :

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

$: \longrightarrow\sf{LHS = \dfrac{7}{5} + \left( \dfrac{ - 2}{5} + \dfrac{ -1 }{3} \right)}$

$: \longrightarrow\sf{LHS = \dfrac{7}{5} + \left( \dfrac{ - 6 + ( - 5)}{15} \right)}$

$: \longrightarrow\sf{LHS = \dfrac{7}{5} + \left( \dfrac{ - 6 - 5}{15} \right)}$

$: \longrightarrow\sf{LHS = \dfrac{7}{5} + \dfrac{ - 11}{15} }$

$: \longrightarrow\sf{LHS = \dfrac{21 + ( - 11)}{15} }$

$: \longrightarrow\sf{LHS = \dfrac{21 - 11}{15} }$

$: \longrightarrow\sf{LHS = \dfrac{\cancel{10}}{ \cancel{15}} }$

$: \longrightarrow \underline{\boxed{ \purple {\bf{LHS = \dfrac{2}{3}}} }}$

★$\bf{RHS = (a+b) +c}$

• Substituting the given values :

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

$: \longrightarrow\sf{RHS = \left( \dfrac{ 7}{5} + \dfrac{ -2}{5} \right) + \dfrac{ - 1}{3} }$

$: \longrightarrow\sf{RHS = \left( \dfrac{ 7 + ( - 2)}{5} \right) + \dfrac{ - 1}{3} }$

$: \longrightarrow\sf{RHS = \left( \dfrac{ 7 - 2}{5} \right) + \dfrac{ - 1}{3}}$

$: \longrightarrow\sf{RHS = \left( \cancel{\dfrac{ 5}{5}} \right) + \dfrac{ - 1}{3}}$

$: \longrightarrow\sf{RHS = 1+ \dfrac{ - 1}{3} }$

$: \longrightarrow\sf{RHS = \dfrac{3 + ( - 1)}{3} }$

$: \longrightarrow\sf{RHS = \dfrac{3 - 1}{3} }$

$: \longrightarrow \underline{\boxed{ \purple {\bf{RHS = \dfrac{2}{3}}} }}$

Here,

$: \longrightarrow \underline{\huge{\boxed{ \green {\bf{LHS = RHS }}}}}$

$\huge {\pink {\therefore}}$ Verified.