A percentage is a fraction with 100 on the bottom. Every percentage question reduces to one of three shapes, and knowing which one you have is most of the work.
Increase then decrease does not return you home
Add 20% to 100 and you get 120. Take 20% off 120 and you get 96, not 100. The two percentages are taken of different bases. To reverse a 20% increase you must divide by 1.2, which is a 16.7% decrease. This is behind a lot of misleading retail pricing and a lot of arithmetic errors in spreadsheets.
Percentage points versus percent
If an interest rate moves from 4% to 6%, that is a rise of two percentage points but a rise of 50 percent. Both are correct and they mean different things. News coverage frequently blurs the two, and the difference is often large.
Compounding percentages
Successive changes multiply rather than add. Three consecutive 10% increases give a factor of 1.1³ = 1.331, a 33.1% rise, not 30%. For the same reason, a 50% loss requires a 100% gain to recover.