Let us first examine it intuitively. [It doesn’t require mathematics!!]. When I say to Mr. P that “play”, it is positive. When I say to him “do not play”, it is negative. But when I say to him “do not not play”, I am asking him to play!! So, effect of two negatives cancel each other to become a positive.
Now, imagine a number line. Negative numbers on it are nothing but (+) numbers in opposite direction. Now when you say a (-) x (-), you are actually multiplying a oppositely directed number to another oppositely directed number, which makes the resultant in its natural direction, that is, positive direction. Reversing the direction twice takes us back to original one. This can also be proved by vector algebra.
Now some serious stuff! We know that each and every number has an additive inverse, that is, when added to its additive inverse, the resultant is zero. For example -3 is additive inverse of 3 & 4 is additive inverse of -4. We also know that additive inverse of an additive inverse is the number itself.
Let’s consider an example. (-3) x (-4) is inverse of (3) x (-4). But (3) x (-4) is itself inverse of 3 x 4. Therefore, (-3) x (-4) is inverse of -12, which on the other hand is itself an inverse of 12. So, (-3)(-4) is same as (3)(4).
To explain this stuff to 5th or 6th grader is quite challenging. So, an activity can be performed. Give the child 5 red & 5 blue pens. Red one represents -1 rupee & blue one represents 1 rupee. So, the child currently has 0 rupee. Now take back two red pens from him. Tell him to count the amount he has now. He will very happily say 2 rupees. Then explain that though you actually took away 2 pens from him, still it lead to rise in his balance because you subtracted negative quantities which led to overall (+) effect to his balance.
Article submitted by Dhruvin Kaneria.
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