Balance Cr2O3+Mg -->Cr + MgO

Balancing means there are equal amount of molecules on each side, both reactant and products. This is a method I like to do.

Under, I count how many molecules are in each side.

              Cr2O3+Mg -->Cr + MgO

Cr:              2                    1

O:                     3                            1

Mg:                         1                 1

Let's guess and make the number of oxygens equal on both sides.

              Cr2O3+Mg -->Cr + 3MgO

Cr:             2                    1

O:                      3                           3       EQUAL

Mg:                          1                   3

See what we did there? We multiplied the MgO on the products side by 3 so we can have 3 oxygens. Now let's multiply the Mg on the reactants by three so Mg AND O can be equal.

                Cr2O3+3Mg -->Cr + 3 MgO

Cr:              2                      1

O:                      3                               3        EQUAL

Mg:                         3                        3          EQUAL

Finally, we just need to multiply the loner Cr in the products side by two to make it equal for all elements.

                 Cr2O3+3Mg -->2Cr + 3 MgO