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प्रश्न
Give an example and verify the following statement.
Distributive property of multiplication over subtraction is true for rational numbers. That is, a(b – c) = ab – ac
उत्तर
Let a = `2/9`, b = `3/6`, c = `1/3` be three rational numbers.
To prove a × (b – c) = ab – bc
a × (b – c) = `2/9 xx (3/6 - 1/3)`
= `2/9 xx ((3 - (1 xx 2))/6)`
= `2/9 xx ((3 - 2))/6`
= `2/9 xx 1/6`
=`1/27` ....(1)
ab – ac = `(2/9 xx 3/6) - (2/9 xx 1/3)`
= `1/9 - 2/27`
= `((1 xx 3) - 2)/27`
= `(3 - 2)/27`
= `1/27` ....(2)
∴ From (1) and (2)
a × (b – c) = ab – bc
∴ Distributivity of multiplication over subtraction is true for rational numbers.
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