proof why when you multiply two numbers with same signs, the answer is a positive number?

Answer 1

This is true for if both are positive. I shall prove for -ve say
- 1*-1 = 1 this can be simply proved as beow
we know 1 -1 = 0
multiply by -1 on both sides
-1(1-1) = 0
-1 *1 -1(-1) = 0
-1 - 1(-1) = 0 as 1 is multiplicative identity -1 *1 = -1
add 1 on both sides
-1(-1) = 1
QED
Thus it can be proved for any -ve

Answer 2

Use the distributive property of multiplication:
-2*(3-3)=0 since 3-3 is zero and -2 multiplied by zero is zero.
But multiply this out and see what is implied by this conclusion
-2*3-(-2*3)=0
this implies -(-2*3)=2*6
that a negative times a negative is a positive.

Answer 3

If a>0 and b>0 then ab>0 . This is part of the definition of ">" when it is applied to the real numbers.

For the product of two negative numbers first look at this:

(-1)(-1) = 0 + (-1)(-1) since 0+x = x+0 = x for any x
=(1 +(-1)) + (-1)(-1) since x +(-x) = (-x) + x = 0 for any x
=(1 + (1)(-1)) + (-1)(-1) since (1)(x) = (x)(1) = x for any x
= 1 + ((1)(-1) + (-1)(-1)) since (x + y) + z = x + (y + z) for
any x,y,z
= 1 + (1 + (-1))(-1) since xz + yz = (x+y) z for any x,y,z
= 1 + (0)(-1) since x + (-x) = 0 for any x
= 1 + 0 since (0) (x) = (x) (0) = 0 for any x
= 1

So if a>0 and b>0 then -a = (-1)(a) < 0 and -b = (-1)(b) < 0 and
(-a)(-b) =(-1)(a)(-1)(b) = (-1)(-1)(a)(b) = (1)(ab) = ab >0

Answer 4

informal proof

let + mean "friend", - mean "enemy", = mean "is", and * mean "of"

+ * + = + because "a friend of my friend is a friend"
- * - = + because "an enemy of my enemy is a friend"

let x,y<0 and x*y<0 now divide both sides by x (reversing sign as required when divisor is less than 0) to get y>0
but y<0 a contradiction thus x*y>=0 when x,y<0

repeat with x,y>0 and x*y<0 to obtain similar contradiction

Answer 5

very simple...thats the law of mathematics... even it is a negative sign if you multiply that one with same sign it becomes positive.