Rant Help with algebra/general logic?

[Scav]

I'm starting to think maybe there's something wrong with my logical acumen/critical thinking skills.

The problem:

I passed Basic College Math early on in my term (I'm almost done pursuing my AAS in Networking Development) two years ago, and I've been thrown under the bus having been signed up for College Algebra this term.

I'm terribly rusty with all of this, and have forgotten more than I learned early on. The conception I seem to be taking from what I've been exposed to is that equations don't equal out, and imaginary numbers and variables mean anything.

Example:

Solve using the principles together. Check your answer.
7y-9=24-4y

The first step is to get all the terms with variables on the left side.

How can you get all the terms with the variables on the left side?

A) Subtract 7y from left side.
B) Subtract 4y from both sides.
C) Add 4y to both sides.
D) Add 7y to both sides.

C ended up being the correct answer to this part. I can buy that. Adding 4y to -4y cancels it out.

Add 4y to both sides.

7y-9=24-4y
-7y-9+4y=24-4y+4y

Answer was 11y-9=24.

(I don't understand where this came from. 7-9+4 is 2, not 11. Moreover, 24-4+4 is 24, not 11.)

I don't know. Are there, in fact, four lights?

Where am I going wrong? :idk:

(P.S. The $130 book that came with the course that I bought has been next to useless. Extremely vague, explaining nothing, and assuming a complete mastery of basic concepts. My class instructor isn't even using the book. )

 

[Zatnikitelman]

You can only add numbers when they have the same variable. So for example 2y+3 does not equal 5y, but 2y + 3y does.
In the specific example, you'd be adding 4y to 7y so you'd get the answer, 11y-9=24.
I don't know if this helps or hurts, but adding the two equations below you only add the numbers corresponding to each variable, x to x, z to z, y to y.

3x+5z=7y
5x-8z=3y
+_______
8x-3z=10y

 

[Scav]

You can only add numbers when they have the same variable.

:facepalm:

I looked at it again. I see it.

Thanks for replying right away. I'd like to leave this open in case I have another bonehead moment (which might happen immediately).

 

[RGClark]

I'm starting to think maybe there's something wrong with my logical acumen/critical thinking skills.

The problem:

I passed Basic College Math early on in my term (I'm almost done pursuing my AAS in Networking Development) two years ago, and I've been thrown under the bus having been signed up for College Algebra this term.

I'm terribly rusty with all of this, and have forgotten more than I learned early on. The conception I seem to be taking from what I've been exposed to is that equations don't equal out, and imaginary numbers and variables mean anything.

Example:



C ended up being the correct answer to this part. I can buy that. Adding 4y to -4y cancels it out.



Answer was 11y-9=24.

(I don't understand where this came from. 7-9+4 is 2, not 11. Moreover, 24-4+4 is 24, not 11.)

I don't know. Are there, in fact, four lights?

Where am I going wrong? :idk:

(P.S. The $130 book that came with the course that I bought has been next to useless. Extremely vague, explaining nothing, and assuming a complete mastery of basic concepts. My class instructor isn't even using the book. )

Also, I assume that minus in front of the 7y in the line after you added the 4y to both sides was a typo.
This is the type of question that could quickly be cleared up by the instructor or in the math tutoring room. But you'll have us as your back up. :thumbup:


Bob Clark

 

[asbjos]

OK, here it is:

7y-9=24-4y
7y-9+4y=24    -    Put "-4y" together with the other "y"s and change to the oposite of minus (plus)
7y+4y=24+9    -    Put "-9" togehter with the other known numbers and change to the oposite of minus (plus)
11y=33    -    Put together the equals, like variabels with "y" and known numbers
y=3    -    divide with 11 (that you had on "y") on both sides to get the value of one "y"

And there you go, y=3.
You can check it afterwards when putting the answer (that y is 3) into the equation.

7*3-9=24-4*3    -    the y's are exchanged with 3. Remember to calculate multiplication and dividing before adding and subtracting
21-9=24-12
12=12    -    12 is 12, so it's true

It turned out it was right. And that was the math for today...:tiphat:

 

[RisingFury]

What book are you using? Since you said something about College math, I have a book by Bronštajn and Semendjajev, written in 1945, translated from Russian. Maybe this is the Russian title for it, I don't know:
Справочник по математике для инженеров и учащихся ВТУЗов <--- copied off Wikipedia. Not sure if you can get an English copy of the book, I had to kill 10 people just to get my Slovenian copy, but if you can, get it.

My copy, the 6th edition from 1980 (It's a real shame when the most sought after book of me and my classmates is older than all of us) covers everything from basic algebra to differential geometry.

...in case I have another bonehead moment...

 

[dumbo2007]

Is it this one : http://www.amazon.com/Handbook-Mathematics-I-N-Bronshtein/dp/3540434917

 

[Scav]

What book are you using? Since you said something about College math, I have a book by Bronštajn and Semendjajev, written in 1945, translated from Russian.

"College Algebra, 4th Edition." By Beecher, Penna, and Bittinger. Though at the rate THIS is going, I may have better luck reading something in Russian (or Klingon) as far as understanding what's going on. This book is pretty much comparable to Irish Spring soap. Big, cumbersome . . . and green.

The website I'm actually working from is even worse.

 

[RGClark]

"College Algebra, 4th Edition." By Beecher, Penna, and Bittinger. Though at the rate THIS is going, I may have better luck reading something in Russian (or Klingon) as far as understanding what's going on. This book is pretty much comparable to Irish Spring soap. Big, cumbersome . . . and green.

The website I'm actually working from is even worse.

What section are you up to? There are some basic rules in algebra that you learn early on that are paramount for the rest of the course and will really mess you up if you don't have a firm grasp on them. On the other hand, if you do have a firm grasp of these few rules, the rest of the class is (mostly) gravy.

First, you absolutely have to know signed arithmetic down cold. Calculating (-3)+(-7) and (-3)*(-7) should come just as easily to you as calculating 3 + 7 and 3*7. The nice thing about it is you really can learn the rules for signed arithmetic very well just by practicing them a few days.
When I'm teaching this I have a little fun with my class by asking them various synonyms for "important". I start them off with "essential", "foundational", "fundamental", "crucial", etc. Then after the end of all those words, I say all of those apply to learning the rules for signed arithmetic IF you want to pass this class.

Second, you have to know the "order of operations", i.e., the level of priority by which you do calculations. This is sometimes summarized by the term PEMDAS. This represents the order you do calculations. It's short for Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction.
For instance 3 + 4*5 is calculated 4*5 equals 20, then 3 + 20 equals 23, not 3 + 4 equals 7, then 7*5 equals 35. It is important to note that just because something is written in front does not necessarily mean you calculate that first.

Third, what are "like" terms and how do you add them. This is the topic you asked about.

And fourth, the rules for calculating with powers of variables. These rules are essential for doing calculations with polynomials which make up a large portion of the material covered in the course. There are about 6 or 7 of these rules depending on who's teaching the course.
Getting a firm grasp on these power rules is a little more difficult but you can get there by practicing them. To encourage my class to spend the time practicing them I usually tell them a joke that's about a hundred years old:

A tourist in New York City goes up to a native New Yorker and asks, "How do you get to [ame="http://en.wikipedia.org/wiki/Carnegie_Hall"]Carnegie Hall[/ame]?"
And the New Yorker replies, "Practice, practice, practice."

The point of the matter is pretty much everything in life you get better at it by practicing. Even Michael Jordan had to practice his jump shot hours a day.

Another tip that might help. If you have difficulty seeing a point your professor is making in class you might ask him or her to give you an example and explain how the algebra rules apply in that case. As one of my old professors used to say, "One example is worth a thousand words."


Bob Clark

 

[RisingFury]

Is it this one : http://www.amazon.com/Handbook-Mathematics-I-N-Bronshtein/dp/3540434917

Yes! If you study anything with a lot of math, get it. We're allowed this book as an aid on most non-math exams (Physics exams, for example) and it comes in handy. Of course, pick up the copy you will use. The one you linked to has an emphasis on Numerical math, probability, statistics and info processing. Mine has a bit of probability and statistics, but it doesn't focus on it.

I'm surprised they still sell them. They stopped selling them here quite a few years ago and you have to find your copy used. As I said, mine is from 1980...

 

[Scav]

What section are you up to?

Ahh yes . . . I see now you DID ask me that. I wasn't blowing you off; sorry about that.

We just spent the last class period going through logarithmic functions and what they have to do with the price of whiskey in the Isles.

I got graphing (chapter 5) pretty easily (from plotting basic points to finding the slope of an equation) because I'd done it before in high school, though finding vertexes using the formulas is something I wish I paid better attention to.