Question

Verify the property $x\times (y+z)=x\times y+x\times z$ by taking $x=\frac{1}{2},y=\frac{-2}{3},z=\frac{5}{6}$
[4 MARKS]

Answer 1

Concept : 1 Mark
Simplification : 2 Marks
Verification : 1 Mark

We have, $x=\frac{1}{2},y=\frac{-2}{3},z=\frac{-5}{6}$

$x\times (y+z)=\frac{1}{2}\times (\frac{-2}{3}+\frac{-5}{6})$

$=\frac{1}{2}\times (\frac{-2}{3}-\frac{5}{6})$

$=\frac{1}{2}\times \left(\frac{-4-5}{6}\right)$

$=\frac{1}{2}\times \left(\frac{-9}{6}\right)$

$=\frac{-3}{4}$

Now,
$x\times y+x\times z=\frac{1}{2}\times (-\frac{2}{3})+\frac{1}{2}\times \left(\frac{-5}{6}\right)$

$=\frac{1\times (-2)}{2\times 3}+\frac{1\times (-5)}{2\times 6}$

$=\frac{-2}{6}+\frac{-5}{12}$

$=\frac{-2}{6}-\frac{5}{12}$

$=\frac{-4-5}{12}=\frac{-9}{12}$

$=\frac{-3}{4}$

Thus, $x\times (y+z)=x\times y+x\times z$
Hence verified.