Question

Explain how you know that -5 and 1/5 are multiplicative inverses.

Answer 1

Hey!

We know that if we see a number that apparently doesn't have a denominator, we can plug a "1" as a denominator because it's a whole number, for example, we could write.
$-5= -\frac{5}{1}$
Finding the inverse would be taking the reciprocal of it, that implies switching the fractions, the signs would change too, so, this would mean that the reciprocal of $-\frac{5}{1}$ would be,
$\frac{1}{5}$

Using Math, we can verify this is correct. To do that, we would have to use exponents.
$\frac{1}{5}^{-1} =5$

Thanks!
-TetraFish

Answer 2

-5(-1)=5
(5^-1)=1/5
to find multiplicacative inverses find negative reciprocal or, in other words, put to -1st power and multiply by -1.