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The half reactions for a chemical equation, as you may have guessed, represent two parts of the equation... the oxidation half and the reduction half.
During oxidation, electrons are lost.
During reduction, electrons are gained.
One way to remember this is the acronym OILRIG
it stands for Oxidation Is Loss - Reduction Is Gain and of course we are talking about electrons here
OK so let's look at the equation. We need to decide which of the reactants is being oxidized and which is being reduced. You will always have both.
It looks like we are starting with elemental Nickel and Silver ions.
As products we have Nickel ions and elemental silver.
When you have elements in their neutral, uncombined state, they have an oxidation state of zero.
So Nickel goes from zero to a +2 that means it has to have lost 2 electrons. (Oxidation)
Silver goes from +1 to a zero (reduction)
Ni --> NiČ+ + 2e-
This show us that nickel is now a nickel ion and 2 electrons
2Ag+ + 2e- --> 2Ag
This shows us that 2 silver ions each gained an electron to create 2 silver atoms.
This is a quick nutshell version of redox and half reactions. Basically we need to show what is happening with the electrons. | 
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