Question

If x=2/5 ,y=-4/3 ,z=8/9 ,then verify the following relation :x+(y+z)=(x+y)+z​

Answer 1

118/45=118/45. it will help you thanks......

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO VERIFY

$\displaystyle \sf{ x + (y + z) = (x + y) + z \: \: \: for \: x = \frac{2}{5} , y = - \frac{4}{3} , z = \frac{8}{9} }$

CALCULATION

LHS

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

$\displaystyle \sf{= \frac{2}{5} + \bigg( \: - \frac{4}{3} + \frac{8}{9} \bigg) }$

$\displaystyle \sf{= \frac{2}{5} + \bigg( \: \frac{ - 12 + 8}{9} \bigg) }$

$\displaystyle \sf{= \frac{2}{5} - \frac{4}{9} }$

$\displaystyle \sf{= \frac{18 - 20}{45} }$

$\displaystyle \sf{= - \frac{2}{45} }$

RHS

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

$\displaystyle \sf{= \bigg( \frac{2}{5} \: - \frac{4}{3} \bigg)+ \frac{8}{9} }$

$\displaystyle \sf{= \bigg( \frac{6 - 20}{15} \: \bigg)+ \frac{8}{9} }$

$\displaystyle \sf{= - \frac{14}{15} + \frac{8}{9} }$

$\displaystyle \sf{= \frac{ - 42 + 40}{45} }$

$\displaystyle \sf{= - \frac{ 2}{45} }$

Therefore LHS = RHS

Hence Verified

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ADDITIONAL INFORMATION

The above mentioned property is ASSOCIATIVE PROPERTY UNDER ADDITION FOR THE SET OF REAL NUMBERS

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Show that the set Q+ of all positive rational numbers forms an abelian group under the operation * defined by a*b= 1/2(ab)

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