Question

Verify the property: x × (y × z) = (x × y) × z by taking:

\[x = \frac{5}{7}, y = \frac{- 12}{13}, z = \frac{- 7}{18}\]

Answer 1

\[\text{We have to verify that} x \times (y \times z) = (x \times y) \times z . \]
\[ x = \frac{5}{7}, y = \frac{- 12}{13}, z = \frac{- 7}{18}\]
\[x \times (y \times z) = \frac{5}{7} \times (\frac{- 12}{13} \times \frac{- 7}{18}) = \frac{5}{7} \times \frac{14}{39} = \frac{10}{39}\]
\[(x \times y) \times z = \frac{5}{7} \times \frac{- 12}{13}) \times \frac{- 7}{18} = \frac{- 60}{91} \times \frac{- 7}{18} = \frac{10}{39}\]
\[ \therefore \frac{5}{7} \times (\frac{- 12}{13} \times \frac{- 7}{18}) = (\frac{5}{7} \times \frac{- 12}{13}) \times \frac{- 7}{18}\]
\[\text{Hence verified .} \]