why product of two numbers is positive and how?

Answer 1

The product of two numbers is positive if both numbers are positive or if both numbers are negative.

If a > 0 and b > 0 then a x b > 0

(see rules of inequalities, operations 3 - if you have 0 < a and then multiply both sides of the inequality by positive number b you have 0 < a x b)

Also, as -1 x -1 = 1 any product of negative numbers can be expressed as (-1 x a) x (-1 x b) where a > 0 and b > 0

That is to say (-1 x -1) x (a x b) by rearranging the brackets.

We already know -1 x -1 > 0
and we also know a x b > 0

So the final product must also be > 0 (ie positive)



However, the product of a positive number and a negative number is negative.

Answer 2

It is so because according to the properties of real numbers"The product of two positive real numbers or the product of two negative real numbers is always positive".e.g. 4*3=12 and -4 * -3=12

Answer 3

product of two numbers is not always a positive number. the product of either two positive or two negative numbers is a positive number,whereas the product of a positive and a negative number is a negative number.

Answer 4

If we consider the number line then the product of two numbers can be understood more conveniently. The positive can be interpreted as forward and the negative as backward.
Let us consider the product AxB. If A is positive it denotes motion in forward A steps. If it is negative it denotes motion in backward direction A steps (I step = 1).
Let us take 4x3. This can be interpreted as motion in forward direction taken three times in forward and hence twelve. If -4x-3 it denotes motion in backward direction taken three times in backward direction. Number system can also be interpreted in terms of money in similar way.

Answer 5

product of 2 numbers isn't always positive:

positive x posiive = positive
negative x posiive = negative
positive x negative = negative
negative x negative = positive

and the neg x neg = pos part is clear if you remember than removing minus one from something is the same thing as adding one...
-(-1) = +1

Answer 6

Probably you can consider going back to school; beleive me they deal these matters with minimum fuss and make us believe so. You are perfectly ok if you disagree with the fact tht product of 2 +ve nos is +ve. You can start a branch of mathematics of your own.
It is all convention dude!!

Answer 7

Only if bouth nombers are positief too!

Answer 8

the first answer i think answers the question