If $a = - 11 / 27, b = 4 / 9$ and $c = - 5 / 18$ , then verify that $a + (b + c) = (a + b) + c$ .

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Solution

Given
$a = - 11 / 27, b = 4 / 9$ and $c = - 5 / 18$
$a + (b + c) = (a + b) + c$
Consider,
$L . H . S . = a + (b + c)$
$= - 11 / 27 + {4 / 9 + (- 5 / 18)}$
$= - 11 / 27 + (4 / 9 - 5 / 18)$
On simplification, we get
$= - 11 / 27 + (8 - 5) / 18$
$= - 11 / 27 + 3 / 18$
Taking L.C.M. we get,
$= (- 22 + 9) / 54$
$= - 13 / 54$
$R . H . S . = (a + b) + c$
$= (- 11 / 27 + 4 / 9) + (- 5 / 18)$
On further calculation, we get
$= {(- 11 + 12) / 27} + (- 5 / 18)$
$= (1 / 27) + (- 5 / 18)$
$= (2 - 15) / 54$
$= - 13 / 54$
Hence,
$L . H . S . = R . H . S .$

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