If $x=\frac{2}{13}$ , $y=\frac{-3}{5} $ and $z=\frac{-7}{13}$, then verify (i) Associative property.(ii)Distributive property.

Given :

The given values are, $x=\frac{2}{13}$ , $y=\frac{-3}{5} $ and $z=\frac{-7}{13}$.

To do :

We have to verify Associative property and Distributive property for the given values.

Solution :  

(i) Associative property :

$ (a \times b) \times c = a \times (b \times c) $

LHS :

$ (x \times y) \times z = ( \frac{2}{13}\times\frac{-3}{5} ) \times \frac{-7}{13} = \frac{42}{845}$

RHS :

$ x \times (y \times z) = \frac{2}{13}\times(\frac{-3}{5}  \times \frac{-7}{13}) = \frac{42}{845}$

LHS = RHS.

Hence verified.

(ii) Distributive Property:

$a (b+c) = a\times b + a\times c$

LHS

$ x \times (y + z ) = \frac{2}{13}\times(\frac{-3}{5}  + \frac{-7}{13})$

                                    $ = \frac{-2}{13}\times \frac{(3\times13+5\times7)}{13\times5}$

                                    $= \frac{-2}{13}\times \frac{(39+35)}{65}$

                                    $= \frac{-2}{13}\times \frac {74}{65}$

                                    $= \frac{-148}{845}$

RHS

$x\times y + x\times z =  \frac{2}{13}\times(\frac{-3}{5})  +\frac{2}{13}\times (\frac{-7}{13})$

                                             $= \frac{-6}{65} + \frac{-14}{169}$

                                             $= \frac{(-6\times13-14\times5)}{845}$

                                              $= \frac{(-78-70)}{845}$

                                               $= \frac{-148}{845}$

LHS = RHS.

Hence verified.

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Updated on: 10-Oct-2022

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