The math we should have been taught in high school

I love The Oatmeal and they have a funny little bit about what they think should have been taught in high school. I just posted the math for obvious reasons but you can check out the whole strip that covers all the subjects.

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Please Excuse My Dear Aunt Sally

The reason your math teacher made you (most likely) remember PEMDAS, or “Please Excuse My Dear Aunt Sally,” is because without it we wouldn’t be able to properly read mathematics. For example, you can read the sentence, “The quick brown fox jumps over the lazy dog,” and picture what it is trying to convey. There’s a dog, he or she is lazy, maybe laying down. A fox, which is the color brown, jumps over the dog and is doing this at a fast speed. Everyone reads this sentence and understands it in the exact same way. We know which adjectives describe which nouns and what the verb is referring to. We know the fox jumped, not the dog. We know that the word “brown” describes the color of the fox. We learned the rules of English in order to be able to read, write, and communicate so that everyone knows exactly what we are trying to say. The order of operations is the equivalent of this, but for mathematics.

Without the order of operations, everyone would do calculations however he or she wanted and everyone could get different answers. If I say to you, “First add two and eight, then divide your sum by five,” I could write it out as: (2+8)÷5 or (2+8)/5. If you follow the order of operations properly, you will get the solution I was referring to. If you don’t, you don’t understand what I’m trying to say. I also use the knowledge of the order of operations to write those expressions. I couldn’t write 2+8÷5 because the answer you would get, following the correct procedures according to the order of operations, would not be the one I was referring to. The order of operations allows everyone to be able to communicate mathematics correctly, without further explanation or confusion.

PEMDAS stands for: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction and that’s the order you’re supposed to do the mathematics (sort of). You’d think math teachers would love PEMDAS, and I’m sure you thought they did, but most math teachers have a huge problem with it. It makes their students think that multiplication comes before division and addition before subtraction when in fact multiplication and division are essentially the same operation, as is addition and subtraction. With two small examples, let me explain. 2-1 (two minus one) is mathematically equivalent to 2+(-1) (two plus negative one). 4×2 (four times two) is mathematically equivalent to 4÷½ (four divided by one half). If we have a longer expression for which we will use PEMDAS to simplify, like 4÷½-2+4×2, and we don’t use PEMDAS correctly, then when I rewrite the expression but keep it mathematically equivalent, like 4×2+(-2)+4÷½, you’d get a different solution even though both expressions are mathematically equivalent and give you the same solution if you follow the order of operations correctly.

Ok, that was a lot of boring math stuff and I apologize, so here’s an awesome graphic design I found on shirt.woot! to lighten up this post a little. Enjoy!

You can use the order of operations to read this expression!

Fruit

The title of this illustration from xkcd is both awesome and inappropriate so I leave it to you to find it yourself if you so choose.

There are a few I would change (only slightly) but for the most part I agree with their representation of these fruits’ tastiness and difficultly to eat. I also agree with their method of representation 🙂

I know where Larry David would place apricots on this chart…

Curb Your Enthusiasm – Ep.61: Clip – Larry on… Apricots

The Grocery Store

For a while now there’s been talk about obesity (and consequently, food). What is healthy? What is not? What should we eat? Should we count calories, fat, etc? Back in 2007, Wired Magazine published some interesting infographics comparing the costs of the different foods (in dollars, in calories, and in sugar).

Cost (per calorie)

Calories (per 100 grams)

Sugar (per 100 grams)

Not to be preachy about what you should and shouldn’t eat, but knowledge is power and I just love when information is presented in these ways.

Happy Pi Day!

Google may not have celebrated the holiday this year but that’s not going to stop me from presenting you with (probably too much) π!

Possible gifts for Pi Day include:

Pi Ice Cube TrayPi Shirt

Here’s Google’s Doodle from Pi Day 2010:

Another Shirt.Woot! design from the past:

(and the website of the designer)

Foxtrot’s contribution:

What pi sounds like ♫ By Michael John Blake

Here are Six Ways to Celebrate Pi Day and NCTM’s ideas for celebrating.

It’s also Albert Einstein’s birthday!

HAPPY 132nd BIRTHDAY!