Find the sum and verify using the given rational numbers that (x+y)+z=x+(y+z).
x=(-11)/18,  y=7/(-18),  z=7/9

Dear Student,

Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{We} \mathrm{have} : \\ \mathrm{x} = -\frac{11}{18}; \mathrm{y} = \frac{7}{-18}; \mathrm{z} = \frac{7}{9} \\ \mathrm{Sum} = \mathrm{x} + \mathrm{y} + \mathrm{z} = -\frac{11}{18} + \frac{7}{\left(-18\right)} + \frac{7}{9} \\ =-\frac{11}{18} - \frac{7}{18} + \frac{14}{18} \\ =\frac{-11-7+14}{18} \\ =-\frac{4}{18} \\ =-\frac{2}{9} \\ \underline{\mathbf{VERIFICATION}\mathbf{ }\mathbf{:}} \\ \mathbf{LHS} = \left(\mathrm{x}+\mathrm{y}\right)+\mathrm{z} \\ =\left[-\frac{11}{18}+\left(\frac{7}{-18}\right)\right] + \frac{7}{9} \\ =\left[-\frac{11}{18}-\frac{7}{18}\right]+\frac{7}{9} \\ =\left(-\frac{18}{18}\right)+\frac{7}{9} \\ =-1 + \frac{7}{9} \\ =\frac{-9+7}{9} \\ =-\frac{2}{9} \\ \mathbf{RHS} = \mathrm{x}+\left(\mathrm{y}+\mathrm{z}\right) \\ =-\frac{11}{18}+\left[\left(-\frac{7}{18}\right)+\frac{7}{9}\right] \\ =-\frac{11}{18}+\left[\frac{-7+14}{18}\right] \\ =-\frac{11}{18}+\frac{7}{18} \\ =\frac{-11+7}{18} \\ =-\frac{4}{18} \\ =-\frac{2}{9} \\ \mathrm{So}, \mathrm{LHS} = \mathrm{RHS}, \mathrm{hence} \mathrm{verified}. \end{gathered}$$

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