Question

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

\[x = \frac{- 3}{7}, y = \frac{12}{13}, z = \frac{- 5}{6}\]

Answer 1

\[\text{We have to verify that} x \times (y + z) = x \times y + x \times z . \]
\[ x = \frac{- 3}{7}, y = \frac{12}{13}, z = \frac{- 5}{6}\]
\[x \times (y + z) = \frac{- 3}{7} \times (\frac{12}{13} + \frac{- 5}{6}) = \frac{- 3}{7} \times \frac{72 - 65}{78} = \frac{- 3}{7} \times \frac{7}{78} = \frac{- 1}{26}\]
\[x \times y + x \times z = \frac{- 3}{7} \times \frac{12}{13} + \frac{- 3}{7} \times \frac{- 5}{6}\]
\[ = \frac{- 36}{91} + \frac{5}{14}\]
\[ = \frac{- 36 \times 2 + 5 \times 13}{182}$$$=$$\frac{- 72 + 65}{182}$\]
\[ = \frac{- 1}{26}\]
\[ \therefore \frac{- 3}{7} \times (\frac{12}{13} + \frac{- 5}{6}) = \frac{- 3}{7} \times \frac{12}{13} + \frac{- 3}{7} \times \frac{- 5}{6}\]
\[\text{Hence verified .} \]