# Multiplication Of Numbers (integers)

Here, we discuss about multiplication of numbers( integers)

For multiplication of numbers (integers) , we use the following rules :

1) Negative times Negative is positive. [ ( - ) x ( - ) ] = +

Example :

a) (- 12) x ( - 6) = + ( 12 x 6 ) = + 72

b) (- 80) x ( - 10) = + ( 80 x 10 ) = + 800

2) Negative times Positive is Negative OR Positive times Negative is Negative. [ ( - ) x ( + ) ] = -
[ ( +) x ( - ) ] = -

Example :

a) ( -10 ) x ( + 6) = - ( 10 x 6 ) = - 60

b) 8 x ( - 13) = - ( 8 x 13 ) = - 104

 Properties of multiplication of numbers (integers) 1) The product of two integers is always an integer.( closure property). 2) For any integers a and b, we have ( a x b = b x a) [ Commutative property]. 3) The multiplication of integers is associative. [ a x ( b x c ) = ( a x b ) x c]. 4) The multiplication of integers is distributive over addition. [ a x( b + c) = a x b + a x c]
Some solved example :

1) ( - 115 ) x 8 = - ( 115 x 8 ) = - 920

2) 9 x ( - 3) x ( -6 )

Solution :

9 x ( - 3) x ( -6 )

= { 9 x ( - 3) } x (- 6)

= - ( 9 x 3 ) x – 6

= - 27 x ( - 6)

= 27 x 6 = 162
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3) ( -12 ) x ( - 13 ) x ( -5)

Solution :

( -12 ) x ( - 13 ) x ( -5)

= { (- 12) x ( - 13) } x ( - 5)

= ( 12 x 13 ) x ( - 5)

= 156 x ( -5)

= - ( 156 x 5 )

= - 780
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4) ( -1 ) x ( - 2) x ( - 3) x ( - 4 ) x ( - 5)

Solution :

( -1 ) x ( - 2) x ( - 3) x ( - 4 ) x ( - 5)

As all numbers are negative and number of negative numbers are 5 which is a odd number so the product of these integers is negative.

( -1 ) x ( - 2) x ( - 3) x ( - 4 ) x ( - 5)

= - ( 1 x 2 x 3 x 4 x 5 )

= - 120
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5) 15625 x ( -2) + ( - 15625) x 98

Solution :

15625 x ( -2) + ( - 15625) x 98

= ( - 15625 ) x 2 + ( - 15625) x 98
[ since 15625 x ( -2) = - ( 15625 x 2) = ( -15625) x 2]

= ( - 15625) [ 2 + 98 ] [ since (-15625 ) taken as common ]

= ( - 15625) x 100

= - ( 15625 x 100 )

= - 1562500

Integers

Absolute value of Integers
Absolute Value Equation