CuO + NH3 = Cu + N2 + H2O

balance the equation by oxidation no. method.

CuO + NH3 = Cu + N2 + H2O

(+2)(-2) , (-3)(+1) = (0) , (0) , (+2)(-2)

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As we see, Nitrogen is being oxidised (inc. in oxidation no.) and Cu is reduced here (decrease in oxidation no.)

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Hence, for a balanced equation, the decrease in oxidation number much match an increase.

So as N2 is oxidised from -3 to 0, and Cu reduced from +2 to 0, we multiply the compound reduced by 3 and oxidised by 2 and maintain with no. of water molecules. So we get:-

3CuO + 2NH3 = 3Cu + N2 + 3H2O