Question

Why does the multiplicative inverse of a number have the same sign as the number?

a
Multiplicative inverses do not have the same sign.
b
Multiplicative inverses must multiply to equal 0, so they need the same sign.
c
Multiplicative inverses must multiply to equal 1, so they need the same sign.
d
Multiplicative inverses must multiply to equal -1, so they need the same sign.

Answer 1

c. Multiplicative inverses must multiply to equal 1, so they need the same sign.

Explanation:

If two numbers are multiplicative inverses of each other, then their product will be equal to 1, which is a positive number. If both numbers being multiplied are positive, then the result is positive. And if both numbers being multiplied are negative, then the result is still positive. But if one number is positive and the other is negative, then the result is negative. -1 and 1 are the Only Numbers that are equal to its Multiplicative Inverse.