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The answer is +5 for the Nitrate anion and -3 for the Ammonium cation.

Here's how I came up with that answer:

NH4NO3 = (NH4)+ and (NO3)-

So we start with the known oxidation numbers, such as Hydrogen which is +1 and Oxygen which is -2.

Ammonium has 1 Nitrogen atom and 4 Hydrogen atoms with an overall Oxidation number of +1, so the algebraic equation is:

X + 4(+1) = (+1)

X + 4 = 1

X = -3

Nitrate has 1 Nitrogen atom and 3 Oxygen atoms with an overall Oxidation number of -1, so the algebraic equation is:

X + 3(-2) = (-1)

X - 6 = -1

X = 5

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