Question

what is the reciprocal of a rational number between -2/3 and 1/4

Answer 1

there are infinite numbers between two rational numbers so let us take one of them
between -2/3 and 1/4
Lcm= 12 of denominators so
-2/3= -8/12
1/4= 3/12
and one no. between -8/12 & 3/12 is 5/12 and its reciprocal is just its reverse i.e. 12/5.

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Answer 2

First you need to find a rational number between -2/3 and 1/4 
I found it as -7/12
the reciprocal of this rational number will be -12/7