Question

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

\[x = \frac{- 7}{3}, y = \frac{12}{5}, z = \frac{4}{9}\]

Answer 1

\[\text{We have to verify that} x \times (y \times z) = (x \times y) \times z . \]
\[(i) x = \frac{- 7}{3}, y = \frac{12}{5}, z = \frac{4}{9}\]
\[x \times (y \times z) = \frac{- 7}{3} \times (\frac{12}{5} \times \frac{4}{9}) = \frac{- 7}{3} \times \frac{16}{15} = \frac{- 112}{45}\]
\[(x \times y) \times z = (\frac{- 7}{3} \times \frac{12}{5}) \times \frac{4}{9} = \frac{- 28}{5} \times \frac{4}{9} = \frac{- 112}{45}\]
\[ \therefore \frac{- 7}{8} \times (\frac{15}{5} \times \frac{4}{9}) = (\frac{- 7}{8} \times \frac{15}{5}) \times \frac{4}{9}\]
\[\text{Hence verified .} \]