It is obvious that five iron atoms are required for every manganese atom, in order that the changes in oxidation numbers cancel:



Eight hydrogen ions are needed to use up the four oxygen atoms on the left, leading to four water molecules on the right:

In choosing a 1-to-5 ratio of Mn-to-Fe, we ensured that oxidation number was conserved. By adding the hydrogen ions we obtained an equation that balanced the number of each atom. As a final check, the net charge on each side of the equation can be tested, and found to be the same: +17. This oxidation-reduction equation now is balanced with respect to electrons, atoms, and charge.