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JAMB 1999 · UME · Q14

If m∗n=mn−nmm * n = \frac mn - \frac nm for real mm, nn, evaluate −3∗4-3 * 4.

Worked solution (try it first)
  1. Put m=−3m = -3 and n=4n = 4: mn=−34\frac mn = -\frac34 and nm=4−3=−43\frac nm = \frac{4}{-3} = -\frac43.
  2. So −3∗4=−34−(−43)-3 * 4 = -\frac34 - \left(-\frac43\right)
    =−34+43= -\frac34 + \frac43.
  3. Over 12: −9+1612=712\frac{-9 + 16}{12} = \frac{7}{12}, option C.

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