Ionic Equations:

Acidic: $\text{MnO}_4^- + 8\text{H}^+ + 5e^- \longrightarrow \text{Mn}^{2+} + 4\text{H}_2\text{O}$

Neutral: $\text{MnO}_4^- + 2\text{H}_2\text{O} + 3e^- \longrightarrow \text{MnO}_2 + 4\text{OH}^-$

Basic: $\text{MnO}_4^- + e^- \longrightarrow \text{MnO}_4^{2-}$

Memory hook: Electrons gained go 5 → 3 → 1 as medium goes Acid → Neutral → Base. The colour sequence is Purple → Colourless / Brown / Green.