Baking, Math and Calories

A late night working, I found myself craving some brownies (gluten-free of course). I pulled out a box of Arrowhead Mills Gluten Free Brownie Mix (http://www.arrowheadmills.com/product/gluten-free-brownie-mix), which I was skeptical about, not having tried it. I mixed the ingredients, popped it in the oven, and looked over the box one more time...

20 servings per box? And they told me to put it in an 8x8 pan? I could cut one side into 5 rows and the other side in 4 columns, but...that's hard to eyeball. I was mathematically inclined to cut both sides into 4. That would make 2in x 2in pieces...how many of them? Yes, 16 pieces.

I'm always curious exactly how good or bad food is for me. I started looking over the nutritional information. At the very top, it said 150 calories per serving. But the suggested number of servings is more than how I wanted to cut it. So how many calories are in my 2in x 2in servings?

So, first, I calculated how many calories are in the whole batch.
20 servings x 150 calories per serving=3000 calories (Don't eat the whole box in one day!)

Next, divide that by my number of servings: 16.
3000 calories/16 servings=187.5 calories per serving

Now, let's recap. First I multiplied by 20, then I divided by 16. We can actually combine this into one step: multiplying by 20/16. That's called a scaling factor; scaling the size of the serving scaled the number of calories. (It's actually kind of a relative scaling, since the serving size is based on the whole size, but you can understand the idea that the bigger the piece of brownie you eat, the more calories you are consuming.) Why stop there? We can figure out all the nutritional information for my preferred serving size. But before we make all those conversions, let's simplify our scaling factor.
20/16=(4x5)/(4x4)=5/4

So instead of multiplying all the nutritional information by 20/16, we can multiply by 5/4. We'd get the same answer anyway, because they are equivalent fractions.

Original Serving Size:
Fat 1.5g
Sodium 110mg
Carbohydrate 21g
Dietary Fiber 1g
Sugars 16g
Protein 1g

My 16 2inx2in servings:
Fat 1.5gx5/4=1.875g
Sodium 110mgx5/4=137.5mg
Carbohydrate 21gx5/4=26.25g
Dietary Fiber 1gx5/4=1.25g
Sugars 16gx5/4=20g
Protein 1gx5/4=1.25g

Well, this was enough to make me only eat one piece. Okay, I ate two - but at least I didn't eat the whole box! That's a lot of sodium and sugar! They were very tasty though.