Department of Mathematics
Integers
Multiplication

Multiplication:

by zero: a x 0 = 0 , -b x 0 = 0
                         132 x 0 = 0
                         -20 x 0 = 0

by -1: a x -1 = -a , -b x -1 = b
                         242 x -1 = -242
                         -132 x -1 = 132

Positive and negative multiplication:
            -a x +b  = -(ab)=> (neg x pos = neg)
            -a x -b =  +(ab)=>(neg x neg = pos)
                         2 x - 3 = -6
                        -3 x -4 = 12
                        -2 x - 3 x -2 = (-2 x -3) x -2 = 6 x -2 = - 12
                        -2 x - 3 x - 2 x - 1 = (-2 x -3) x -2 x -1 = 6 x -2 x -1 =(6 x -2) x - 1 =-12 x - 1 = 12

Cancellation Property: if ac = bc, then a = b (c not equal to 0)
                         12a = 12b, then a = b
                          13a = 26 = 13 x 2, so a = 2