Scaling recipe ingredients to smaller batches? How do AAUs scale?

Question

I plan on brewing 1 gallon batches. The problem is that most recipes are for 5 gallon batches.

The scaling seems obvious: divide the amount of each ingredient by 5.

With this in mind, a few questions:

• What about hops measured in AAUs (seen below)? Do these still get scaled down, even though they are a relative measure of acidity?
• How does yeast scale? I can't imagine dividing a small pack of yeast by 5 and having my beer ferment appropriately...
• Are there any other "gotchas" that I should consider when scaling back ingredients?

Example recipe from howtobrew.com:

Cincinnati Pale Ale
Ingredients for a 5 gallon batch
3-4 lb. Pale malt extract syrup, unhopped
2 lb. Amber dry malt extract
12 AAU of bittering hops (any variety) For example, 1 oz. of 12% AA Nugget, or 1.5 oz. of 8% AA Perle
5 AAU of finishing hops (Cascade or other) For example, 1 oz. of 5% Cascade or 1.25 oz. of 4% Liberty
2 packets of dried ale yeast

After my proposed scaling:

Cincinnati Pale Ale
Ingredients for a 1 gallon batch
0.6-0.8 lb. Pale malt extract syrup, unhopped
0.4 lb. Amber dry malt extract
?? AAU of bittering hops (any variety) 
?? AAU of finishing hops (Cascade or other) 
?? packets of dried ale yeast

Answer 1

You can scale malt, hops and volumes linearly.

While in principle hops don't scale linearly, it's almost linear, and depends upon your kettle geometry. It's not enough of a difference to worry about - the difference is less than the error introduced due to measuring your hops to the nearest 0.1g.

Evaporation is also due to kettle geometry, although this is simply a matter of adding top-up water if too much water is evaporated.

Answer 2

I am primarily a one-gallon brewer. I have never adjusted a recipe, so I can't answer the question on AAUs. But I can tell you from experience that you can "scale" dry yeast on pretty much a linear basis.

My method: I use the Mr. Malty Pitching Rate Calculator, and then use this $6 digital scale to weigh the dry yeast. I overpitch slightly from Mr. Malty's recommendation (adding a gram or so to be safe, and rounding up). I rehydrate according to Fermentis' instructions (weighing my water on the same scale by tare-ing out my container and weighing out 1 g per ml of water), and have never had a fermentation not take off properly.