Andy carried 1/2 gallon of water on a hike. he drank 2/3 of the water. how much water did he drink?

So,

All we have to do is multiply the amount of water Andy carried by the fractional amount he drank.

1/2 * 2/3

This is pretty simple.  To halve TWO-thirds, just halve the numerator, since it's such a nice number.

Presto.  Half of two is one.

Therefore, 
1/2 * 2/3 = 1/3

Andy drank 1/3 gallons of water on his hike.  That's 5 1/3 cups of water.  I would estimate his hike to be about 3 miles.  Easy peasy.