What is the reciprocal of -2/3?

##-3/2##

The reciprocal means the multiplicative inverse of a number. The multiplicative inverse ##n'## of a number ##n## is a number that when multiplied to ##n##, results to the multiplicative identity which is 1.

That is...

##n'*n = 1##

##-2/3x = 1##

##-2x = 3##

##x = -3/2##