Question

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

\[x = \frac{1}{2}, y = \frac{5}{- 4}, z = \frac{- 7}{5}\]

Answer 1

\[\text{We have to verify that} x \times (y \times z) = (x \times y) \times z . \]
\[x = \frac{1}{2}, y = \frac{5}{- 4}, z = \frac{- 7}{4}\]
\[x \times (y \times z) = \frac{1}{2} \times (\frac{5}{- 4} \times \frac{- 7}{4}) = \frac{1}{2} \times \frac{35}{16} = \frac{35}{32}\]
\[(x \times y) \times z = (\frac{1}{2} \times \frac{5}{- 4}) \times \frac{- 7}{4} = \frac{5}{- 8} \times \frac{- 7}{4} = \frac{35}{32}\]
\[ \therefore \frac{1}{2} \times (\frac{5}{- 4} \times \frac{- 7}{4}) = (\frac{1}{2} \times \frac{5}{- 4}) \times \frac{- 7}{4}\]
\[\text{Hence verified .} \]