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underset("(aq)")(MnO(4)^(-)) + underset(...

`underset("(aq)")(MnO_(4)^(-)) + underset("(aq)")(Br^(-)) to underset("(aq)")(MnO_(2))+ underset("(aq)")(BrO_(3)^(-))`

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equation increase and decrease in oxidation number
`underset("(aq)")(2MnO_(4)^(-))+underset("(aq)")(Br^(-)) to underset((s))(2MnO_(2)) + underset("(aq)") (BrO_(3)^(-))`
Reaction is in basic medium, and the ionic charges are not equal on both sids, add 2 `OH^(-)` ions on the right to make ionic charges equal.
`underset("(aq)")(2MnO_(4)^(-)) + underset("(aq)")(Br^(-)) to underset("(s)")(2MnO_(2)) + underset("(aq)")(BrO_(3)^(-)) + underset("(aq)")(2OH^(-))`
Add one `H_(2)O` to L.H.S. to achieved balanced redox change
`underset("(aq)")(2MnO_(4)^(-)) + underset("(aq)")(Br^(-)) + underset((I))(H_(2)O) to 2Mn underset((s))(O_(2))+ underset((aq))(BrO_(3)^(-)) + underset((aq))(2OH^(-))`
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