Question

Verify property :-
(x+y)+z=x+(y+z)
x= -2/17
y= 1/51
z= -13/7
In picture 5 ka 4 no

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf\bullet x=\dfrac{-2}{17}\\ \\ \sf\bullet y=\dfrac{1}{51}\\ \\ \sf\bullet z=\dfrac{-13}{7}$

We have to verify

$\boxed{\sf{(x+y)+z=x+(y+z)}}$

Now

$\sf\underline{\sf{\red{\:\:\:\:\:A.T.Q:-\:\:\:\:\:\:}}}$

$\sf\implies (x+y)+z= x+(y+z)\\ \\ \sf\implies \bigg(\dfrac{(-2)}{17}+\dfrac{1}{51}\bigg)+\dfrac{(-13)}{7}\:=\:\dfrac{(-2)}{17}+\bigg(\dfrac{1}{51}+\dfrac{(-13)}{7}\bigg)\\ \\ \\ \sf\bullet L.C.M\:of\:17\:and\:51 =51\\ \\ \\\sf\implies \bigg(\dfrac{-6+1}{51}\bigg)+\dfrac{(-13)}{7}\:\:=\:\:\dfrac{(-2)}{7}+\bigg(\dfrac{7-663)}{357}\bigg)\\ \\ \\ \sf\implies \bigg(\dfrac{-5}{51}\bigg)-\dfrac{13}{7}\:\:=\:\:\dfrac{-2}{17}+\bigg(\dfrac{-656}{357}\bigg)\\ \\ \\\sf\implies\bigg(\dfrac{-35-663}{357}\bigg)=\bigg(\dfrac{-42-656}{357}\bigg)\\ \\ \\ \sf\implies \dfrac{-698}{357}=\dfrac{-698}{357}$

$\sf\:\:\:L.H.S=\:R.H.S....\:\:\:(hence\: proved)$

Answer 2

$\mid \overline\mathbf \red{given}$

• x=-2/17
• y=1/51
• z=-13/7

$\mathfrak \orange{according \: to \: que.}$

$(x + y) + z = x + (y + z)$

$putting \: the \: value$

Now,

$(\frac { - 2}{17} + \frac{1}{51} ) + \frac{ - 13}{7} = \frac{ - 2}{17} + ( \frac{1}{51} + \frac{ - 13}{7} )$

$\underline \mathbf{l.c.m \: of \: 17 \: and \: 51 \: = 51}$

$( \frac{ - 6 + 1}{51} ) + \frac{ - 13}{7} = \frac{ - 2}{17} + ( \frac{7 - 663}{357} )$

$\frac{ - 5}{51} + \frac{ - 13}{7} = \frac{ - 2}{17} + \frac{ - 656}{357}$

$\frac{ - 35 - 663}{357} = \frac{ - 42 - 656}{357}$

$\frac{ - 698}{357} = \frac{ - 698}{357}$

Hence, L.H.S=R.H.S