Balancing Using Oxidation Numbers

1st step: Balance all atoms with the exception of Hydrogen and Oxygen.
2nd step: Calculate the change in oxidation number for the reduced and oxidized element.
3rd step: Put coefficients in front of the reduced and oxidized elements so the gain of electrons made by the reduced species equals the loss of electrons by the oxidized species.
4th step: Add H2O to balance the oxygen atoms.
5th step: Add H+ to balance the hydrogen atoms.
6th step: If basic, add OH to both sides equivalent to the amount of H+ and eliminated duplicate water molecules on either side of the equation.
7th step: Double check that the final charge balances.

Example 1) Write a balanced equation for HClO2 and I- when they react to
produce Cl2 and HIO in acidic solution.

Example 2) Write the balanced equation for ClO3-  and MnO2 when they react
in basic solution to form Cl2 and MnO4-