Answer
a. These two numbers are opposite reciprocals.
b. These two numbers are not opposite reciprocals.
c. These two numbers are not opposite reciprocals.
Work Step by Step
a. We can check if two numbers are opposite reciprocals by multiplying them together to see if their product equals $-1$.
$-2(\frac{1}{2})$
Multiply to simplify:
$-\frac{2}{2}$
Simplify the fraction:
$-1$
The product of the two numbers is $-1$; therefore, these two numbers are opposite reciprocals.
b. We can check if two numbers are opposite reciprocals of one another by multiplying them together to see if their product equals $-1$.
$(\frac{1}{4})(4)$
Multiply to simplify:
$\frac{4}{4}$
Simplify the fraction:
$1$
The product of the two numbers is not $-1$; therefore, these two numbers are not opposite reciprocals.
c. We can check if two numbers are opposite reciprocals of one another by multiplying them together to see if their product equals $-1$.
$5(-5)$
Multiply to simplify:
$-25$
The product of the two numbers is not $-1$; therefore, these two numbers are not opposite reciprocals.
