Back to Negative x Negative = Positive

How can a negative times a negative equal a positive?
When doing number operations, how about thinking
of a number line? (1) 3 x 2 (2) -3 x 2 (3) 3 x -2 (4) -3 x -2 Here's our number line with "|" representing 0 and each minus sign representing one unit, some going to the left of "|" representing "negative" and others going to the right representing "positive". - - - - - - - - - - -|- - - - - - - - - - (1) If I represent 3 x 2 using the number line, it will mean going three spaces to the right two times. |- - - - - - and so 3 x 2 = 6. (2) If I represent -3 x 2 using the number line, I will go three spaces to the left two times. - - - - - -| and so -3 x 2 = -6. (3) If I represent 3 x -2 using the number line, it means going three spaces, but the minus sign before the 2 tells me that I have to be going the opposite direction. This means that instead of going three spaces two times to the right, I have to go three spaces two times on the left, in other words, on the negative side of the number line. - - - - - -| and so 3 x -2 = -6. (4) If I represent -3 x -2 using the number line, I will start on the negative side of the number line the way I did with -3 x 2, but because the direction is changed (indicated by -2) I am going to switch to the other side, which gives me |- - - - - - and so -3 x -2 = 6. |

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