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
