# How can we prove that a negative number multiplied/divided/subtacted by a negative gives a positive result?

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I've always wondered if we could prove this...

I've always wondered if we could prove this...

##### 1 Answer

It's not the case that a negative minus a negative is always positive. For instance,

We can, however, rigorously prove that the product of two negative numbers is always positive. From that conclusion we can additionally prove that the same holds for a negative number divided by a negative number. The proof is not out of reach for an algebra student, either, as long as you are willing to accept that the product of two positive numbers is positive.

Consider that any negative number can be written in the form

Suppose we have two negative numbers,

We have proved that if

Suppose we have negative numbers