Integer Multiplication Properties

When we multiply numbers, we have three possibilities-

  1. If both numbers are positive then product is also positive.

Examples –

  • 6 × 3  = 18
  • 2 × 6 = 12

 

  1. If both numbers are negative then also the product is positive.

 

Examples –

  • – 6 × – 3  = +18  and  – 3 × – 6  = +18
  • – 18 × – 2  = +36  and  – 2 × – 18  = +36

 

  1. If we have any one positive and one negative number to multiply, then we get negative product.

 

Examples –

  • (-3) × (4) = -12 and  3 × (-4) = -12

 

  • (-18) × (2) = -36 and  18 × (-2) = -36

 

Properties of Multiplication of Integers

Closure property for multiplication of integers :

We have two integers, then the product is also an integer; that is if a and b are integers then a × b is also an integer.

Examples –

  • 3 × 6 = 18
  • 210 × 2 = 420
  • -8 × 6 = -48
  1. Commutative law for multiplication of integers :

If we change the order of numbers to multiply then also we get same product, that is, a × b = b × a.

Examples –

  • 3 × 6 = 18 and 6 × 3  = 18
  • 160 × -3 = -480 and  -3 × 160 = -480
  1. Associative law for multiplication of integers :

    If we have three integers to multiply, we get the same multiplication if we carry out the second multiplication first or first multiplication first, that is, we have a, b and c integers then-

(a × b) × c = a × (b × c)

Examples –

  • (5× 3) × 2 = 15 × 2 = 30 and 5× (3 × 2) = 5 × 6 = 30
  • (-6 × 4) × 3 = -24 × 3 = -72 and

-6 × (4 × 3) = -6 × 12 = -72

  1. Distributive law of multiplication over addition :

If we have any three integers a, b and c, we have

a × (b + c) = a × b = a× c

Example –

  • We have , and      and

 

  1. Multiplication property of 0 :

    If we multiply any integer by 0 or 0 by any integer we get 0, that is,
    If we have ‘’ as any integer, then

and
Examples –

 

  • and
  • and

 

  1. Existence of multiplication of identity

    :
    If we multiply any integer by 1 or 1 by any integer, we get the same integer. That is,
    If we have ‘’ as any integer, then

and
Examples –

 

  • and
  • and

 

The integer 1 is the multiplicative identity.

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