RULES FOR ASSIGNING OXIDATION NUMBERS
for KMnO4, we can assign K (Rule 4a) and O (Rule 3c) . . . K+1MnO-24
however, the total oxidation number for four oxygens is not -2, it's -8 . . . K+1+1MnO-2-84
now, we can create an equation to solve for the oxidation number of manganese . . . K+1+1Mn+x+xO-2-84 = 0
solving for x gives K+1+1Mn+x+7O-2-84 = 0
the oxidation number of Mn is +7
for the dichromate ion, Cr2O72–, we can assign O (Rule 3c) . . . Cr2O-272–
however, the total oxidation number for seven oxygens is not -2, it's -14 . . . Cr2O-2-1472–
now, we can create an equation to solve for the oxidation number of chromium . . . Cr+x+2x2O-2-147 = -2
solving for x gives Cr+62(+6)2O-2-147 = -2
the oxidation number of Cr is +6