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Question
Verify the property x × (y + z) = x × y + x × z of rational numbers by taking.
`x = (-2)/3, y = (-4)/6, z = (-7)/9`
Solution
Given, `x = (-2)/3, y = (-4)/6, z = (-7)/9`
Now, LHS = x × (y + z)
= `(-2)/3 xx ((-4)/6 + (-7)/9)`
= `(-2)/3 xx ((-4)/6 - 7/9)`
= `(-2)/3 xx ((-12 - 14)/18)`
= `(-2)/3 xx (-26)/18`
= `26/27`
And RHS = x × y + x × z
= `(-2)/3 xx ((-4)/6) + ((-2)/3) xx ((-7)/9)`
= `4/9 + 14/27`
= `(12 + 14)/27`
= `26/27`
∴ LHS = RHS
Hence, x × (y + z) = x × y + x × z
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