Type a formula, the element you are interested in and the overall charge, and get that element’s oxidation state by the standard rules (peroxides and hydrides are the known exceptions).
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From the article How to Find Oxidation Numbers — The 7 Rules with Examples.
K is Group 1 → +1 (rule 4). O is normal oxide → −2 (rule 6). Let Mn = x.
(+1) + x + 4(−2) = 0
1 + x − 8 = 0
x = +7
+7 is the highest possible for manganese (group number 7), which is why permanganate is such a powerful oxidising agent — it can only gain electrons.
Neutral salt K₂Cr₂O₇:
2(+1) + 2x + 7(−2) = 0
2 + 2x − 14 = 0 → 2x = 12 → x = +6
Dichromate ion Cr₂O₇²⁻ — the sum equals −2, not 0:
2x + 7(−2) = −2
2x − 14 = −2 → 2x = 12 → x = +6 ✔ same answer, as it must be.
The potassium ions are spectators, so removing them cannot change chromium's oxidation number. If your two answers disagree, you forgot the ionic charge on the right-hand side.
Worked in full in How to Find Oxidation Numbers — The 7 Rules with Examples.
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