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Properties of Multiplication of Integers - Associative Property of Multiplication of Integers

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Associative Property Of Multiplication Of Integers:

Consider – 3, – 2, and 5.

Look at [(– 3) × (– 2)] × 5 and (– 3) × [(– 2) × 5].

In the first case (– 3) and (– 2) are grouped together and in the second (– 2) and 5 are grouped together.

We see that [(– 3) × (– 2)] × 5 = 6 × 5 = 30 and (– 3) × [(– 2) × 5] = (– 3) × (– 10) = 30

So, we get the same answer in both cases.

Thus,[(– 3) × (– 2)] × 5 = (– 3) × [(– 2) × 5]

Statement 1 Statement 2 Observation
[(7) × (- 6)] × 4 = - 168 7 × [(- 6) × 4] = - 168 [(7) × (- 6)] × 4 = 7 × [(- 6) × 4]
8 × [53 × (−125)] = - 53,000 [ 8 × 53 ] × (−125) = - 53000 8 × [53 × (−125)] = [ 8 × 53 ] × (−125)
(−17) × [−30 × 1] = 510 [(- 17) × (- 30)] × 1 = 510 (−17) × [−30 × 1] = [(- 17) × (- 30)] × 1

Thus, the product of three integers does not depend upon the grouping of integers and this is called the associative property for multiplication of integers.

In general, for any three integers a, b and c - (a × b) × c = a × (b × c).

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