Example 1:   2Na  +  S Na₂S
                       Na° Na⁺¹  (oxidized)
                         S°  S^-2     (reduced)
Oxidation:   2Na  2Na⁺¹ + 2e^-1
Reduction:   S + 2e^-1 S^-2
Overall:       2Na  +  S  2Na⁺¹ + S^-2
Overall equation is sum of oxidation/reduction equations (electrons always cancel).

Example 2:   2Al_(s) + 3ZnCl_2(aq) 2AlCl_3(aq) + 3Zn_(s)
Here is a single substitution with Al replacing Zn:
                     Al°Al⁺³   (oxidized)
                     Zn⁺² Zn°  (reduced)
                     Cl^-1 Cl^-1   (spectator ion)
Oxidation:   2Al 2Al⁺³ +  6e^-1
Reduction:  3Zn⁺² + 6e^-1  3Zn
Overall:       2Al  + 3Zn⁺²  2Al⁺³ + 3Zn

Next we look at REDOX reactions taking place in water under acidic or basic conditons.
For acidic conditions, balance with H⁺¹, H₂O, or H⁺¹/H₂O
For basic conditions, balance with OH^-1, H₂O, or OH^-1/H₂O
Oxidation & reduction always go together but we begin with half reactions:

Example 3:  AsH₃As  (acidic)
                     As^-3As°    (oxidized)
                  AsH₃As + 3H⁺¹ + 3e^-1  (oxidation)

Example 4:  VO₃^-1 V⁺²   (acidic)
                       V⁺⁵ V⁺²   (reduced)
                  VO₃^-1 V⁺² + 3H₂O
                  VO₃^-1 + 6H⁺¹ + 3e^-1V⁺² + 3H₂O(reduction)

Example 5:  U⁺⁴ UO₂⁺¹   (acidic)
                     U⁺⁴ + 2H₂OUO₂⁺¹
                  U⁺⁴ + 2H₂OUO₂⁺¹  +   4H⁺¹ + 1e^-1  (oxidation)

Example 6:  MnO₄^-1 Mn⁺²    (acidic)
                     MnO₄^-1Mn⁺² + 4H₂O
                  MnO₄^-1 +  8H⁺¹ +  5e^-1Mn⁺² + 4H₂O  (reduction)

But oxidation always accompanies reduction reaction. We now look at full (overall) reactions.

Example 7:  MnO₄^-1 +  Br^-1Mn⁺²  + Br₂     (acidic)
                        Mn⁺⁷  Mn⁺²  (reduced)
                       Br^-1 Br°     (oxidized)
Oxidation:       2Br^-1   Br₂+  2e^-1
Reduction:   MnO₄^-1  +  8H⁺¹ +  5e^-1 Mn⁺² + 4H₂O
Multiply oxidation by 5 and reduction by 2 (e^-1 lost must equal e^-1 gained):
[2Br^-1  Br₂+  2e^-1] 5
[MnO₄^-1  +  8H⁺¹ + 5e^-1Mn⁺² + 4H₂O]2
Oxidation:     10Br^-1   5Br₂+  10e^-1
Reduction: 2MnO₄^-1 +  16H⁺¹ +  10e^-1 2Mn⁺²  + 8H₂O
Overall:        2MnO₄^-1 + 16H⁺¹ + 10Br^-1  2Mn⁺²  +  5Br₂  +  8H₂O

Example 8:  Co + NO₃^-1 Co⁺³  + NO₂     (acidic)
                        Co°  Co⁺³   (oxidized)
                      N⁺⁵ N⁺⁴   (reduced)
Oxidation:    CoCo⁺³  +  3e^-1
Reduction:   [NO₃^-1  + 2H⁺¹ + 1e^-1NO₂ +  H₂O] 3
Overall:       Co  + 3NO₃^-1 + 6H⁺¹ Co⁺³  +  3NO₂  +  3H₂O

For REDOX under basic conditions, use OH^-1/H₂O to balance or first balance under acidic conditions followed by complete neutralization of H⁺¹ with OH^-1.

Example 9:   MnO₄^-1MnO₂   (basic)
                     Mn⁺⁷ Mn⁺⁴  (reduced)
                    MnO₄^-1  +  4H⁺¹ + 3e^-1MnO₂ +  2H₂O        (4H⁺¹ + 4OH^-1 ® 4H₂O)
                                       +4OH^-1                          +4OH^-1
                               MnO₄^-1 + 4H₂O + 3e^-1MnO₂ + 4OH^-1 + 2H₂O (subtract 2H₂O from each side)
                  MnO₄^-1 + 2H₂O + 3e^-1MnO₂ + 4OH^-1

Example 10:   ClO^-1 Cl^-1 (basic)
                      Cl⁺¹ Cl^-1    (reduced)
                   ClO^-1 + 2H⁺¹ + 2e^-1  Cl^-1 + H₂O
                                +2OH^-1                     +2OH^-1
                   ClO^-1 + H₂O + 2e^-1 Cl^-1 + 2OH^-1

Example 11:   Br₂ BrO₃^-1 (basic)
                      Br°  Br⁺⁵     (oxidized)
                      Br₂ +  6H₂O 2BrO₃^-1  + 12H⁺¹ + 10e^-1
                            +12OH^-1                  +12OH^-1
                   Br₂ + 12OH^-1  2BrO₃^-1  +  6H₂O  + 10e^-1

Example 12:   Sn  Sn(OH)₄^-2    (basic)
                   Sn  + 4OH^-1  Sn(OH)₄^-2  + 2e^-1  (oxidized)

Example 13:   Al  +  S  HS^-1 + Al(OH)₃     (basic)
                      Al°  Al⁺³   (oxidized)
                       S°  S^-2   (reduced)
Oxidation:      [Al  +  3OH^-1 Al(OH)₃ +  3e^-1]2
Reduction:     S + H⁺¹ + 2e^-1 HS^-1
                        +OH^-1             +OH^-1
                      [S + H₂O + 2e^-1 HS^-1  + OH^-1]3
Overall:        2Al  +  3S + 3H₂O + 3OH^-1 3HS^-1 + 2Al(OH)₃

Example 14:   NO₂^-1  + Al  NH₃ + Al(OH)₄^-1   (basic)
                       Al°  Al⁺³   (oxidized)
                       N⁺³ N^-3   (reduced)
Oxidation:      [Al + 4OH^-1  Al(OH)₄^-1 + 3e^-1]2
Reduction:  NO₂^-1 + 7H⁺¹ + 6e^-1  NH₃+  2H₂O
                           +7OH^-1                     +7OH^-1
              [NO₂^-1 + 5H₂O  + 6e^-1 NH₃+  7OH^-1]
Overall:      2Al + NO₂^-1 + 5H₂O  + OH^-1 2Al(OH)₄^-1  + NH₃