A fraction's reciprocal is simply the numerator and denominator being switched.
Let's convert your proper fraction, -8 2/7 to an improper fraction.
The reciprocal of -58/7 is 1/-58/7 = -7/58.
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It is -8/7
negative one and two fifths
(8/35) / (-2/7) = (8/35) * (-7/2) = -4/5
26.4642857143
try googling it... a calculator will pop up with the answer