Question

Why negative reciprocals always have a product of negative 1

Answer 1

The negative reciprocal of (a/b) is (-b/a).

Multiply those, then simplify, and you'll see it right away.

Answer 2

They are like that because the negative reciprocal is a positive reciprocal. The product of a number and its reciprocal is 1 and a negative multiplied by a positive is negative.

Example: -4/5
Reciprocal of -4/5 is 5/4
-4/5 x 5/4 = -1

Hope this helps :)