Expert: Ahmed Salami - 11/23/2009

Question
When two positive or negative directed numbers are multiplied then answer is positive, e.g
(+3)x(+7) = +21 and (-3)x(-7) = +21
What is logic behind it? or what is another way of describibg it?

Also when two numbers of different signs are multiplied then answer is a negative number. e.g.

(+3)x(-7) = -21

How......???????

Please explain

Answer
Hi Rashid,
There is a general multiplication rule of signs in mathematics.
+ x + = +
- x - = +
+ x - = -
- x + = -
These are conventions that follow standard logic.
Consider the multiplication of a positive and a negative number, say, 7 and -2
+7 x -2 = (+)(-)(7)(2)
       = -4
Now, this can be explained by the fact that -2 x 7 is simply repeated addition of -2 seven times i.e
(-2) + (-2) + (-2) + (-2) + (-2) + (-2) + (-2)
we know that it should be -14 and that only happens when (+)(-) results in (-) and the expression becomes
-2 - 2 - 2 - 2 - 2 - 2 - 2 = -14
You can also consider the addition of, say, 9 and -4
We know that -4 increases 9 in the negative direction i.e decreases it
And so,
9 + (-4) has to be 9 - 4

I hope i have helped.

Regards