Are Fractions Useless, or Are Americans Just Stupid?

April 19, 2014 at 5:07 pm Leave a comment

I don’t know how else to say it, so I’m just gonna say it.

Fractions are full of sh*t.

Okay, not really. But if I have to hear one more time about how fractions are useful because of applications to cooking, I may commit hari-kari.

Before I jump into a diatribe, though, I absolutely have to share this improper fraction cartoon from Fat Rooster Studios (warning: rated PG-13).

It’s really hard to continue after that. But I’m gonna try.

There are three reasons that fractions are not really important in cooking.

  • First, fractions only appear important because Americans are stupid. We insist on using the imperial system, and we measure dry ingredients in fractional parts of a cup. In other parts of the world, they don’t add 1 3/4 cups of flour to their recipe for croissants. Instead, they use 450 ml of flour. So making a half, a third, or a double recipe doesn’t involve operations with fractions.
  • Second, ratios are important when cooking, not fractions. The exact amount of flour, sugar and baking powder in your chocolate chip cookies isn’t critical, so long as the ratio is 96 : 48 : 1. Approximately. Cooking is not an exact science. If your ratio of flour : sugar : baking powder = 98 : 45 : 2, you should still end up with a tasty dessert.
  • Third — and, in my opinion, most importantly — great cooking derives from experience and approximation, not from exact measurements. My mother used to drive me crazy when she’d state, “But I followed the recipe,” if her normally fantastic lasagna came out less than fantastic.

Don’t believe me? Then watch the chef on a cattle drive as he makes chili over an open fire, and notice how he throws in a bucket of beans, two buckets of tomato sauce, and as much ground beef as he thinks is appropriate. You can bet your ass that Cookie ain’t got no measuring cups in the back of the chuck wagon. Or better yet, watch him make a cup of “six shooter coffee,” where his recipe is one handful of ground beans per cup of water. How much coffee is in a handful? Depends on the hand.

Maybe you think it’s just cowboys who estimate. Nope. Watch Emeril Lagasse as he adds a pinch of this, a dash of that, and — BAM! — the result is a grilled pork chop for which tourists pay $30 when they visit New Orleans.

If you need proof that ratios are the key mathematical element to successful cooking, listen to Dr. Mark Hadley. He claims that perfect ravioli is obtained when the ratio of pasta : filling : sauce = 45 : 45 : 10, which includes just enough olive oil “to give a thin layer of 200 microns over the surface of all the pasta – enough to make it glisten, resulting in the perfect mouthful.”

But, you know what? We shouldn’t let reality get in the way of a good story. Let’s please continue to perpetuate the myth that fractions are important — nay, critical — by including exorbitant numbers of cooking problems in the fraction units of textbooks. As far as I can surmise, the majority of fraction problem authors have never actually cooked. Here’s a typical problem:

The following recipe for Blueberry Bubble Loaf makes 12 servings.

  • 2 cups cereal that contains blueberries
  • 1 cup brown sugar
  • 1/2 cup butter
  • 2 packages of refrigerated buttermilk biscuits

Rewrite the recipe so that it makes 4 servings.

Let’s assume that this isn’t stupid. (Though it is, right? I mean, it might be reasonable to make 6 servings, since that would require just one package of refrigerated buttermilk biscuits. But to make just 4 servings? That means you’ll only need 2/3 package of refrigerated biscuits. What are you supposed to do with the other 1/3 of the package?)

But as presented, the solution requires that each ingredient be divided by 3. That gives 2/3 cup cereal, 1/3 cup brown sugar, 1/6 cup butter, and the aforementioned 2/3 package of refrigerated buttermilk biscuits. I decided to make this recipe.

  • I have a 1/3-cup measure in my cooking drawer, so the first two ingredients were no problem.
  • I don’t have a 1/6-cup measure. I could have measured 1/3 cup of butter and used an educated guess to divide the amount in half. Instead, I can just filled a 1/4-cup measure, and decided that that was close enough. Good enough for government work.
  • I’ll only need 6 2/3 of the 10 biscuits that come in a 12-ounce container of refrigerated buttermilk biscuits. WTF? I decided that 7 biscuits is close enough, and I gave 3 uncooked biscuits to my dog. He’s happy at this development. I hope he doesn’t get worms.

I cooked the blueberry bubble loaf as directed, and it came out fine. Except that the total mixture only filled 1/3 of a bread pan, and it created a loaf that was only one inch tall. That’s not a loaf; that’s a tortilla.

But generally speaking, there was no material difference between the original loaf and my reduced-height loaf, despite the imprecision in my measurements. And do you know why there was no difference?

Because fractions are full of sh*t.

Now check this out. The following is a cake recipe from About.com.

  • 2 cups cake flour
  • 2 teaspoons baking powder
  • 1/2 teaspoon salt
  • 1/2 cup butter, softened
  • 1 cup sugar
  • 3 large eggs
  • 2 teaspoons vanilla
  • 3/4 cup milk

And here’s a vanilla cake recipe from Country Living.

  • 1 1/2 cups cake flour
  • 1 1/2 teaspoons baking powder
  • 1/4 teaspoon salt
  • 1/2 cup butter, softened
  • 1 cup sugar
  • 2 large eggs
  • 1/2 teaspoon vanilla
  • 1/2 cup milk

The second recipe requires 3/4 as much flour as the first recipe. If fractions really mattered, then every ingredient in the second recipe should have an amount that is 3/4 as much as the first recipe. But they don’t. There is 1/2 as much salt, the same amount of butter, the same amount of sugar, 2/3 as many eggs, 1/4 as much vanilla, and 2/3 as much milk.

So I’ll say it again.

Fractions are full of sh*t.

At least when it comes to cooking.

Fractions are, however, fodder for some great jokes.

Five out of four Americans have trouble with fractions.

Sex has a lot in common with fractions.
It’s improper for the larger one to be on top.

It’s hard to tell the difference between a numerator and a denominator. There is a fine line between them.

Two-thirds of Americans have trouble with fractions. The other half can handle them just fine.

Son: Can you help me find the lowest common denominator of 1/2 and 1/3?
Dad: You mean they still haven’t found it? They were looking for that when I was a kid!

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Humor at #NCTMNOLA Games My Brain Plays

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About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.

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