Dear Mathman,
I've been learning about the "Order of Operations" in Math class. I don't like following orders. Do I really need to? Why?
Thanks,
Ivanna Havitall
Dear Ivanna,
Order is a fabulous concept. I mean without orders, how would you get what you want at a restaurant?
Oh wait, I just reread your question. I guess that wasn't the proper answer. Let's try again:
First a bit of history. Actually, a bit of your history. What was the first thing that you learned in math class after you learned how to count. (Please don't say "flush" or "wash hands"). I hope you said "Add". Those were the days... It wasn't too long before the next thing to do showed up on the scene: Subtract. Now you probably didn't like subtract as much as you liked add, because we're all a bit selfish and don't want things taken away. Wasn't it better to say, "You have 3 m and m's (not the rapper) and I give you two more - How many do you have?" rather than "You have 5 m and m's and I take away two." Simple so far, eh?
The next amazing thing you learned to do was multiply. I don't know about you, but when I was back in school I found multiplication to be a fantastic shortcut when I had to repeatedly add a collection of numbers. Example: 3+3+3+3+3+3+3+3+3+3+3+3 = 3 x 12 (the 3+3 was hard to even type -try it!). Just after getting pretty good at multiplication, division came along and ruined the whole party. I mean seriously, subtraction was hard enough - now equal groups?! Come on!
Let's recap: Divide, Multiply, Subtract, Add- those are the operations in reverse order we learned them. If you learned a saying for the "Order of Operations" it probably was PEMDAS (which isn't even a word) or "Please Excuse My Dear Aunt Sally." Personally, I'm not a fan of either. PEMDAS sounds like a contagious disease (Did you hear about Joe? He didn't wash his hands and came down with a nasty case of PEMDAS.) And "Please Excuse My Dear Aunt Sally?" doesn't make any sense to me at all. I don't have an Aunt Sally, and if I did, why would she need continually excused? Is she uber-rude? Does she have a gatrointestinal disorder? I might as well say, "Prickly Elvises Maim Deer And Studebakers" or even "Portly Elephants Make Doilies After September." All nonsense.
Not really, but the saying is incomplete. It's missing something. We don't always do things in the order of Multiply, Divide, Add, and Subtract. If we take the "big 4" and slightly switch the order we get the MDAS of the end of that saying. I personally think (in regards to the saying) we think Multiply before Divide because we prefer to Multiply first. Likewise with Add and Subtract. (It does make sense that the Multiply comes before Add because Multiplication is the "shortcut" for repeated addition.)
In reality, sometimes Divide comes before Multiply and Subtract before Add. You see, Multiply and Divide are in a "special relationship". They are equal and opposite. It's like they're "going out"- but permanently (unlike typical junior high "special relationships" which may not even outlast a sock change). When you encounter Multiply and Divide in a problem remember they <3 each other. Do the operation that comes first when you read the problem normally (left to right).
Add and Subtract have the same thing going on between them. This is getting too mushy so I'll stop there in explaining their situation.
So (hopefully) we've got the MDAS covered. We haven't dealt with the PE part of the saying (Note: PE doesn't stand for gym class). Since this post is getting a bit long, we'll save PE for another time.
Ivanna, hopefully this starts to answer your question a bit.
Stay radical.