reciprocal of negative fraction

Question

The reciprocal of -1/y is (the negative sign is front of the whole fraction, not just the numerator)

A 1/y

B -y

C y

D 1 + 1/y

Answer 1

"Reciprocal" is the multiplicative inverse of a number or expression. It does not change the positive or negative character. If two expressions, a and b, are multiplicatve inverses, then a x b = 1, so b = 1/a and a = 1/b.

So if b is the multiplicative inverse, or reciprocal of -(1/y), then b x [-(1/y)] = 1;

Doing some algebra,

multiplying both sides by y and dividing both sides of by -1 gives b = -y.

Finally, checking, -(1/y) x (-y/1) = (-1 x -y) / (y x 1) = y/y = 1 CHECK :)