ADDITION REACTIONS

An addition reaction is the "most characteristic" reaction between alkenes and alkynes. It's pretty simple really: "a reactant is added to the two atoms that form the multiple bond."
An example:
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As you can plainly see, the double (or pi) bonds between the carbons were broken to free the electrons, which attach to the bromines.
Hydrogenation:
This is when H2 is added to and alkene, which makes an alkane. Addition reactions like these hardly ever happen under normal temperatures and pressures, due to the strong hydrogen-hydrogen bond.



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Sources:
Brown, LeMay, and Bursten. Chemistry: The Central Science. Ninth Ed., pub. 2003.