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it's been a while since I last solved such questions >_< I would love to explain it, but my memory is unfortuantely failing me
The problem has to do with oxidation states of the matter. The oxidation state of oxygen will always be -2 with the exception of peroxides which will have a state of -1. The overall balanced state of chemical compounds will be 0, so the oxidation state of Mn in MnO2 will be +4. The oxidation state of MnO4- will then be +7 to balance out to the negative one charge. The state change from +4 to +7 is 3, thus three electrons have to be lost in order for this to happen; a loss of a charge of -3 results in an increase of charge of 3. Oxidation is always the process of 'losing' electrons.
Good reply Furiouslyfapping. You have to look for a change in oxidation number of the main elements in the half reaction. You should know how to calculate the oxidation number of the elements in a compound first. The Fe3+ to Fe 2+ is a simple one. You can see the Ox number of Fe has changed from +3 to +2 and is therefore a reduction half reaction. This is a redox half reaction.