If two nonzero numbers are opposites of each other, are their reciprocals opposites of each other? Why or why not?
Two numbers that have the same absolute value but have opposite signs are called opposite numbers.
If n is one number, then -n is its opposite.
The reciprocal of a fraction is obtained by interchanging the numerator and the denominator, i.e. by inverting the fraction. The reciprocal of a whole number is 1 over that number.
If $\displaystyle \frac{1}{n}$ is one number, then - $\displaystyle \frac{1}{n}$ is its opposite.
If $\displaystyle \frac{m}{n}$ is one number, then - $\displaystyle \frac{m}{n}$ is its opposite.
If $\displaystyle \frac{n}{m}$ is one number, then - $\displaystyle \frac{n}{m}$ is its opposite.
So, the answer is yes. Opposite numbers are the same distance from zero on the number line - one in the negative direction and one in the positive direction.