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Properties of Multiplication of Integers - Distributive Property of Multiplication of Integers

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Distributive Property Of Multiplication Of Integers:

We know,

16 × (10 + 2) = (16 × 10) + (16 × 2).....[Distributivity of multiplication over addition]

Let us check if this is true for integers also.

i) (– 4) × [(– 2) + 7] = (– 4) × 5 = – 20

and [(– 4) × (– 2)] + [(– 4) × 7] = 8 + (– 28) = – 20

So, (– 4) × [(– 2) + 7] = [(– 4) × (– 2)] + [(– 4) × 7]

ii) (– 8) × [(– 2) + (–1)] = (– 8) × (– 3) = 24

and [(– 8) × (– 2)] + [(– 8) × (– 1)] = 16 + 8 = 24

So, (– 8) × [(– 2) + (– 1)] = [(– 8) × (– 2)] + [(– 8) × (– 1)]

iii) (– 2) × (3 + 5) = – 2 × 8 = –16

and [(– 2) × 3] + [(– 2) × 5] = (– 6) + (– 10) = – 16

So,(– 2) × (3 + 5) = [(– 2) × 3] + [(– 2) × 5]

Thus, we say that the distributivity of multiplication over addition is true for integers.

In general, for any integers a, b and c, that is a × (b + c) = a × b + a × c.

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