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Question
Verify the property x × (y + z) = x × y + x × z of rational numbers by taking.
`x = (-1)/5, y = 2/15, z = (-3)/10`
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Solution
Given, `x = (-1)/5, y = 2/15, z = (-3)/10`
Now, LHS = x × (y + z)
= `(-1)/5 xx (2/15 + (-3)/10)`
= `(-1)/5 xx (2/15 - 3/10)`
= `(-1)/5 xx ((4 - 9)/30)`
= `(-1)/5 xx (-5)/30`
= `1/30`
And RHS = x × y + x × z
= `(-1)/5 xx 2/15 + ((-1)/5) xx ((-3)/10)`
= `(-2)/75 + 3/50`
= `(-4 + 9)/150`
= `5/150`
= `1/30`
∴ LHS = RHS
Hence, x × (y + z) = x × y + x × z
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