817 Math Blog

Chapter Two: Combining Like Terms and The Distributive Property

Script:

Podgy: Hello!

Cappie: Hi. Who are you?

Podgy: Well, I'm Podgy, and I'm a student! I want to learn about destructive properties, and mining bike germs!

Cappie: Destructive properties and miming germs? Don't you mean distributive property, and Combining like terms?

Podgy: Oh, yes. Those things... Say... You wouldn't happen to know about distributive property and combining like terms .. would you?

Cappie: Oh, yes. I do. Would you like to learn, Podge meister?

Podgy: Oh, ah. Sure. I mean. I wouldn't mind... I mean. Learning about those things woudn't be too bad... I mean... If you don't mind teaching ... me, Podgy... That is. Hehe...

Cappie: Calm down Podge meister. I'll teach you, in one condition, though.

Podgy: So, uh. Cappie... Dude, guy, mister, sir... I mean, teacher... Sea foo... You know, they call the teachers Sea Foo in Japan that... I think it'd be okay to call you that.

Cappie: Quiet Down! The condition is for you to stop being a blubbering fool, you've been rambling all this time! So, there! I'll start off teaching you about combining like terms. It is more simple..

Podgy: OKAY THEN! Combining like terms it is!

Cappie: I have a practice question. n+3-5n+12 . First, look at the question.
n+3-5n+12.
Now, identify the constants (integers that won't change), and variables (letters).
n +3 -5n +12
So now, you need to group them together. Or "combine like terms"! Once you know that, you know all you need to know about combining like terms!

Podgy: OK! I'll start with the variables... There are n and -5n. So... If I add another n to it, it should be -6n. Now for the consanants. All positives, woot woot! 3 and 12, make 15. So, is it -6n+15 ?

Cappie: No, it is not. Think about the steps! You made a little error in your thinking process. Remember that when you add a positive to a negative, the digit decreases. Think about a number line, that should help you a lot.

Podgy: Gee, thanks Cappie! I'll try it once more! Starting off with the variables... n, and -5n ... should be -4n! And, and the 3 and the 12 still make 15, so it must be -4n+15! Aren't I right, sir?

Cappie: Right!

Podgy: Hot dog, am I ever glad! What do you know about Distributive Property?

Cappie: Well, here's an example to work with. 2 + 4(3n+8). You need to multiply the 4 with 3n, and +8, because 4 is touching the brackets. Once you have done that, combine the like terms.

Podgy: Oh, okay! Hmm. 4 multiplied by 3n is 12n. 8 and 2 equals 10 ... So, we add them together. Combine like terms! So the answer must be 12n+10!

Cappie: Podge meister, I'm quite proud of you. But your answer is incorrect. Your flaw was that you forgot to multiply the 4 by 8. Try again.

Podgy: Ok, then. 4 multiplied by 3n is 12n. 4 multiplied by 8 is 32. So, I'm left with 12n+32+2. Combine like terms! 32+4=34. So the answer must be12n+34! I get it! Thanks so much for teaching me Cappie, sir!

Cappie: Oh gosh, you're making me blush. Call me Cappie!

Podgy: Ok! Cappie it is!

Here is my XTRANORMAL movie, Combining Like Terms and Distributive Property (Part One)

Here is my XTRANORMAL movie, Combining Like Terms and Distributive Property (Part Two)

Above is a picture example of how to do addition algebra. A very important part of algebra is knowing I.C.O.B.V, which is an acronym for...

I - Isolate the variable by
C - Cancelling using the
O - Opposite
B - Balance
V - Verify

Now, when confronted with a question such as the one provided, your objective is to isolate the variable. In doing so, you need to cancel out, using the opposite. But, you need to remember that you need to keep things balanced; so what to you do one side, you do to the other side. Once you understand this, you merely simplify to N equals whatever N equals. In this case (referring to the example above) N=3.
So, in the example above, N+3=5 your objective is to isolate the variable. To do that, you need to cancel using oppposites. Remember to keep it balanced; what you do on one side, you do to the other side. N+3-3=5-3 Simplify that. N=2. Now that tells you what N equals. In order to get full marks, you need to verify. Just copy out the question, and substitute N with what N equals.
N+3=5
2+3=5
5=5
Understand it?

Now multiplicative type is a bit different, but no harder, no easier. Above is an example: 2N=10. What you need to do still has to do with I.C.O.B.V. Isolate, cancel, oppositve, balance, verify. Ask yourself, what is the opposite of multiplying? Well, the answer is as simple as the question itself! Division, of course! So, to isolate N, (or, to get it by itself) you divide 2N by 2. But since you've divided 2 on one side, you must do the same to the otherside, leaving you with N=5. Since you know what N equals, you must verify.

2N=10
2(5)=10
10=10

If you don't understand something, feel free to comment! Or perhaps I've made an error, and you'd like to point it out, please comment all the same! :)

As I've said, adding and subtracting are in someways similar, but they're also opposite. Well, since multiplying and dividing are opposite they're also similar is some ways. They're alike because they use eachother to do algebra. Above is an example of how to do dividing type algebra.
N = 6
--
2

With a question like this you need to isolate the variable by cancelling using the opposite. Don't forget to balance it out!
(2) N = 6(2)
------
2

Now simplify.

N=12

Now that it is simplified, verify!

N = 6
--
2

12 = 6
--
2

6=6