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Question
Verify associativity of addition of rational numbers i.e., (x + y) + z = x + (y + z), when:
Solution
\[x = - 2, y = \frac{3}{5}, z = \frac{- 4}{3}\]
\[\text{so}, (x + y) + z = ( - 2 + \frac{3}{5}) + \frac{- 4}{3} = (\frac{- 10}{5} + \frac{3}{5}) + \frac{- 4}{3} = \frac{- 7}{5} + \frac{- 4}{3} = \frac{- 21}{15} + \frac{- 20}{15} = \frac{- 21 - 20}{15} = \frac{- 41}{15}\]
\[ x + (y + z) = - 2 + (\frac{3}{5} + \frac{- 4}{3}) = \frac{- 2}{1} + (\frac{9}{15} + \frac{- 20}{15}) = \frac{- 2}{1} + \frac{- 11}{15} = \frac{- 30}{15} + \frac{- 11}{15} = \frac{- 30 - 11}{15} = \frac{- 41}{15}\]
\[ \therefore ( - 2 + \frac{3}{5}) + \frac{- 4}{3} = - 2 + (\frac{3}{5} + \frac{- 4}{3})\]
\[\text{Hence verified .} \]
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