4. Properties of Multiplication of Integers

Multiplication of Integers:    
    (i)    Rule for multiplication between integers of opposite sign - When integers with opposite signs are multiplied, the result will be the product of the integers with negative sign on the product. In general for any two positive integers a and b we can say, a             a x (- b) = (- a) x b = - (a x b)
        Ex.    – 4 x 5 = –(4 x 5) = –20
            4 x –5 = –(4 x 5) = –20     

(ii)    Rule for multiplication between integers of same sign - When integers with same sign are multiplied, the result will be the product of integers with positive sign on the product. In general, for any two positive integers a and b,  (- a) x (- b) = a x b
        Ex.    –5 × –4 = 20
                 5 × 4 = 20
        (a)    The product of two negative integers is a Positive integer.
                Ex.    (-4) x (-7) = 28

        (b)    The product of three negative integers is a Negative integer.
                Ex.    (-4) x (-7) x (-1) = -28

        (c)    The product of four negative integers is a Positive integer.
                Ex.    (-4) x (-7) x (-1) x (-2) = 56