**Why minus multiply minus equal to positive number ?**

This simple mathematical question has indeed a profound thinking, since it is hardly related to real life calculations.For instance, the equation 3 X 7 can be interpreted in real life as; if I eat 3 apples daily then in one week I have been eaten 3 X 7 apples i.e. 21 Apples.

In negative-positive terms, the equation -3 X 4 can be expressed like I dig 3 meters hole daily, thus, in four days the depth of this hole is four times the first day which is -12.

However, no such clear interpretation can be found for the case of negative times negative. Therefore, here comes the mathematical proofs to prove that negative multiplied by negative equal positive.

## Two simple proofs **why minus multiply minus equal to positive number:**

**The first Proof:**

without loss of generality, assume that A, B and C in R+0 = A - A multiply the upper equation with -B

0 = -AB -A(-B)

multiply the upper equation with C

0= -C(AB) -A(-B)(C)

CAB= -A(-B)C divide it by C

AB = -A(-B)

**The Second proof: [3]**

- Let a and b be any two real numbers. Consider the number x defined by

- x = ab + (-a)(b) + (-a)(-b).

We can write

x = ab + (-a)[ (b) + (-b) ] (factor out -a)

= ab + (-a)(0)

= ab + 0

= ab.

Also,

x = [ a + (-a) ]b + (-a)(-b) (factor out b)

= 0 * b + (-a)(-b)

= 0 + (-a)(-b)

= (-a)(-b).

So we have

x = ab

and

x = (-a)(-b)

Hence, by the transitivity of equality, we have

ab = (-a)(-b).

11/03/2018 00:03 647