Question

If , a = -1/3 , b = 2/5 , c = 1/3 ,Check whether or not associative property holds good for rational numbers under addition.

Answer 1

Associative property states that:

$\sf{a + (b + c) = (a + b) + c}$

$\sf{ \frac{ - 1}{3} + (\frac{2}{5} + \frac{1}{3} ) = (\frac{ - 1}{3} + \frac{2}{5} ) + \frac{1}{3} }$

$\sf\frac{ - 1}{3} + \frac{11}{15} = \frac{1}{15} + \frac{1}{3}$

Taking the LCM,

$\mathbf{\frac{ - 5 + 11}{15} = \frac{1 + 5}{15} }$

$\implies \bold{ \boxed{ \frac{6}{15} = \frac{6}{15} }}$

This means that associative property holds good for rational numbers under addition.