Water is so abundant, but if hoarding it is your hobby, you need to know the order of operations!

I just looked up "order of operations" on wikipedia. There was some pretty good stuff there. http://en.wikipedia.org/wiki/Order_of_operations


This is an important thing to understand in algebra because if you mess them up, you get the problem wrong and someone could get hurt! If you are recklessly doing math, you become a danger to yourself and those around you. So with that said, you should probably be wondering what an operation is and why they need to stay in order - unless you already know.


( ) ^ * / + - (these are the computer symbols for the operations in the right order.)
"Operation" is a posh way to say: "parentheses, exponents, multiply and divide, add and subtract, etc." (also in the right order) These are the ones used most. (actually parentheses are not an operation, its just a way to keep organized but you can think of it as one for now)


Why do they need to stay in order?
. . .


Thats the harder part


. . .


Did you know that multiplication can be done in rows and columns?

Here is 12 cars. But it is arranged in 4 rows and 3 columns. 3x4=12. It works every time.
That is part of the topic. I promise . . .


lets say you have to figure out 3+4x8. How do you do it? do you start left to right like reading?
(the answer is no. I wanted to tell you that before I did it so that it didn't get stuck in your head the wrong way)
3+4=7 and then 7x8 is 56. So is that what you did on your last test? Well that's bad. You should've gotten that one wrong.


The order of operations says we have to do the multiplication first. Would that really change anything though??? Well lets go back to our rows and columns:
7x8= (7 rows and 8 columns)

its 7 times 8. I promise.
well what the heck! 3+4 is in fact 7 and 7x8 is 56 because just look at the stars! there are 56 of them!


Well here is the right way to do 3+4x8:


4x8 is 32.

So now we add the 3.
3+32 is 35!

So what it comes down to is you will end up with extra rows or columns and stuff. This is the way math language is written. I don't know why. I suppose its easier for math people.What about parentheses? what is up with them?

Suppose you have a strange hobby of collecting bottled water

From the looks of it, you have quite a collection! You should be proud!

Except that its so messy! Maybe you want to get them organized?

I know! Use plastic wrap!!! That stuff is great! you can use it all over the place, and they make it now so that its easy to cut and you don't have to struggle to get the piece you want :)

That is much better! I bet you can make tons of these neat little packages with all the water you have! You don't have to keep the different kinds separate you know. You could put a Dasani in with 3 Aquafina's and 6 Fiji's. or something creative like that.Its a good idea and math people do the same thing with their math. The plastic wrap doesn't weigh anything (so you can add as much as you want to those balance scales of the last blog post and it won't change anything) It looks like this: ( )

Then put the stuff inside:

(6x8+56-7+ . . . )so if you had a math person describe your water, he'd take all the plastic wrapped stuff and write it like this:
( Dasani + 3 Aquafina + 6 Fiji ) or even shorter: (D+3A+6F)now lets say you like that particular set of water a lot because it reminds you of a Led Zeplin concert you went to when you were younger. You happen to have enough water to do some more sets exactly like that with a nice fresh roll of plastic wrap. In fact, you can do 3 more just like it and so now you have 4 total!
(D+3A+6F) + (D+3A+6F) + (D+3A+6F) + (D+3A+6F)That took some serious copy and paste action on my part and if I was doing it by hand, it would take too long because I am hungery right now. Its easier to say 4(D+3A+6F). Its a multiplication problem where we have 4 rows and one column of water packets (and we made the "x" sign invisible probably because it means death if drawn on a cartoon character's eyes and that would've been too confusing while doing math on Saturday mornings)

but if you were to take off all the plastic wrap (even though it was a lot of work) what would you have?

It looks like 4 Dasani's, 12 Aquafina's and 24 Fiji's. Its the same water, nothing changed in your collection, its just organized differently. In the order of operations, you do parentheses first because if not, your water would be counted wrong:
4(D+3A+6F) Remember that there is an invisible "times" sign so if you aren't watching Saturday morning cartoons, feel free to actually write it out.
4x(D+3A+6F) so we already discussed how much water we've got. And if you forget the order of operations, you would think ". . . so I multiply 4 times my Dasani's and then I just add my three Aquafina's and six fiji's and I'm done. That is how much water I have. . ." and you'd be wrong. that "4" means four Led Zeplin concert packs; not just four Dasani's!What if you had a Led Zeplin concert pack and some other package that you give away at Christmas? could you wrap them separately and then wrap them together?

So then what is this equal to?(5x7+(45/5)x(20x2)-6)

Attack the killer-psycho-maniacs that teach mathematics!

What does the word "algebra" make you think of?


Do you picture your math teacher? What does he look like?

Is he just as evil as any horror movie psycho-killer and yet still makes Ben Stein seem like America's next runner up on Last Comic Standing? Have you ever caught him or her plotting another twisted homework assignment that will take hours but not teach you anything?

"Welcome to the government-style-K-through-12-approved-mathematics-curriculum-for-brain-washed-vegetables . . ." he says on the first day of class. Not with words maybe. But you know he was thinking it (and grinning on the inside) . If you know exactly what I am talking about, keep reading. This blog is for you! Those guys have turned math mind-numbing piece of muck. Or at least they try as hard as possible to make it look that way.

My opinion on algebra now is that I was never taught why it is so amazing. It was too hard to "see" since it was just letters and numbers with one of these symbols: =, >, < etc. Most of the K-12 math teachers and teaching that I experienced was very left-brained and technical. Right-brained folk like me hardly stand a chance.
My hope is that I can take the technical left-brained stuff that I was taught and turn it into pictures, stories, and anything else from the artist's world. I am currently attending college working toward a BA degree in mathematics. Why? because after algebra, I took trigonometry and calculus (right-brained stuff like that geometry class you liked) from an amazing teacher who helped me visualize it. I discovered how creative and fun this stuff was. I just had to muddle through the first 18 years of the pre-fun math.
So . . . with all that stuff out of the way, I want to tell you how I picture algebra now.

Algebra looks like this:

(except I don't picture the hanging chains holding the baskets, just bowls bolted right to the balancy-stick)

In class, picture it. But instead of drawing out the whole thing, your math teacher wants you to use a less-fun symbol:

• if it balances, you say that with one of these: =
• if the left side is heavier, go with a "greater than" >
• if right is heavier, then use "less than" <

Did you read those bullet points with your best Ferris Bueller's Day Off voice? Because you can if you want. I won't be offended. But just so you know, That is almost the whole of what algebra is. Once you got that down (and it took me a long time to realize this is what it is) you'll know probably most of what is going on in class.

• Just so you know, if you take something out of one bowl, take it out of both bowls. ( ". . . subtract [whatever blah blah blah] from both sides . . .")
• Same with putting stuff in the bowls. This is a really strong scale. It can hold heaps and heaps of stuff as long as you put it in both sides.
• If its already not balanced, you still might have to add the same amount to both bowls. When it is tipped to one side, it can be something really really small and it can still looks just as tipped (tipsy?) as if there was an extra elephant in that bowl.
• Most of the time, you don't want to change the position of the scale. (don't go from balanced to unbalanced or the other way around)

What do you think? Does that help?