HAPPY HOLIDAYS!!! HAPPY VACATION!!!

Have a great break (remember to complete the packet), and I'll see you in 2007!

CU,
Mrs. Collins

Look It Up!!!



What is math vocabulary? Math vocabulary is easier than any other vocabulary because you must provide examples of what the answer can be or a counter example of what the answer can’t be. Providing these examples is easy as well because there is always going to be a definite answer. For math vocabulary there will always be examples. There will be examples because they are used to explain and to prove or disprove theories. As you expand your math vocabulary you will find that most definitions are rules that can or can’t be broken unless there are exceptions. In the following terms you will see examples and definitions that explain what I mean.

Definitions

Domain: what the variable can equal, all real numbers EXCEPT ZERO.


Factor Tree: a method used to factor radicals in a tree form.


Principal Root: positive square root of a number.


Radical: principal nth root of the number


Radicand: the number underneath the radical sign


Rational Expression: a rational expression is a polynomial fraction that contains variables and anything you do with regular fractions you can do with rational. But there are exceptions.



Directions: Match the examples with the correct vocabulary word!!


1. Radical a. 2b²a³/a

2. Rational Expression b. √16x

3. Principal Root c. All Real Numbers, X ≠ O

4. Factor Tree d.√64←

5. Radicand e. √8
√2 √4
2 2 2

6. Domain f.√81=√9x9=9


As you can see vocabulary is very important. If you don’t know vocabulary how were you supposed to solve the problems? Vocabulary is very important because it allows you to understand examples and answers. In addition to that understanding vocabulary helps you prove and disprove theories. When you apply vocabulary it gives you a better understanding of the topic!!!! Hope

Adding and subtracting rational expressions.

Group members: Billy Wilson, David Guilty, Steven Fernandez

By reading this you will learn exactly how to add and subtract rational expressions with the same denominator. This means 2 fractions with variables in them being added and subtracted. To do this you must do the following:

1) Add or subtract the top only, leave the denominator the same.
2) Simplify if possible.
3) Box final answer
Here is an example of this:

9x/2x+3x + 5x/2x+3x

Step 1: 14x/2x+3x
Step 2: 14x/x(2+3) à 14/2+3 à 14/5 à 2 4/5
Step 3:
2 4/5


Adding and subtracting rational expressions using fractions for the class

1.2x/12x + 8x/12x =
2.4x/x+2 + 6/x+2=
3.9d/5+d + 8/d+5=
4.7x/x^2+24 + 8x/x^2+24=
5.4/d+2 + 56+6d/d+2=
6.d^2/d+2 – d/d+2
7.9x/x+4 – 7x/4+x=
8.f/x+4 – f/4+x=
9.2x^2/d+2 – 5x/d+2=
10.hg/d+9 – h^2g/d+9=

Adding and Subtracting Rational Expressions.
1) 9X/3+3X/3=12X/3=4X
2) 12X/5+18X/5=30X/5=6X
3) 7X/6-3X/6=4X/6=2X/3
4) 13X/4-9X/4=4X/4= X
5)17X/8Y-7X/8Y=10X/8Y=5X/4Y


It is very difficult to add and subtract rational expressions. You need to make sure you follow the steps. You may get some answers wrong if you do not follow these steps exactly. Make sure you follow the steps exactly. Basically, you should just follow the steps in the introduction and you should be fine.

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Adding and Subtracting Rational expressions

Not every problem you have will be easy. When you have two different views to something it might it a little hard to solve. This is what happens when you have Ration expressions with different denominators. Simply there’s only one way to add or subtract them with out any complication and that’s find the LCD so the answer can already be in simplest form.

Steps To Solve Rational Expressions with Different Denominators;
1) First you look at the problem and figure out what’s the LCD (least common denominator)

2/3 + 4x/6x -> since the dominator are factors of 3 and have x in common the must have a LCD

2)Since the second expression has a x you know that the LCD is going to have a x in it and also the first denominator has a 3 and 3x2 is 6 so the LCD should be 2x but you only multiply the first expression because you are trying to have the two denominators equal the same.
2(2x)/3(2x) +4x/6x= 4x/6x+4x/6x

3) Now that you have everything with the same value you can add without any problem.

4x/6x+4x/6x=8x/6x
(Since its 8 x / 6xyou can simplify it so it can give you a reduced answer)

8x/6x -> 1 2x/6x -> 1 1x/3x would be your answer.

Solving rational expressions with different denominators can be a lot of work. You may not always get an easy answer. Some equations may also be complicated for you. There’s always a way to solve some even if the outcome isn’t pretty. The usual method to use is to find the LCD which is used a lot to make your equation easier to solve.Thseseexamples may show you a couple of things you may look out for.

Dividing Rational Expressions
~Jasmine,Deborah,Pasha'

Introduction~

Rational expressions are quotients found by dividing 2 polynomials. To divide rational expressions you must find the reciprocal of the second expression, and then multiply.Really and truly,dividing rational expressions is multiplication.The trick is that rational expressions are fractions and the code operation is division.A number/term over a number/term is division but to get the quotient you must multiply:only one commandment is needed for this project:only terms being multiplied can be cancelled.

Examples~

• y-8/y(y+2)÷y+8/y²+64= 1/y(y+2)
• 5x/x² +5x÷25x/x²+5x=1/5x
• x-2/3x-12÷x²-16/18=6(x-2)/x+4
• b-6/b+5b-24÷b-6/6b-24=1
• 15(x-4)/20(x-4)÷5x-4/20(x-4)=3

Dividing Rational Expresssions

Solve the following problems:
1. (1/2) / 5/4=
2. (3s/5sx) / s/10x=
3. (3x-3/x) / 12x-12/4x=
4. (5x/20y) / x /10y=
5. (3d/5d) / d/10a=
6. (20) / 3/2=
7. (x-y/y-x) / y-x/x-y=
8. (x/2) / x/3=
9. (6y/y-3) / 2y=
10. (m+3/3m) / 6m/m+3=

Conclusion~

Dividing rational expressions are very easy. The key is to flip the second dividend and multiply both expressions. Follow the last of the three commandments to cancel out like terms if necessary. These instructions are all you needed to solve these rational expessions. Hopefully dividing rational expressions will be easier for you after using these strategies.

Math B Winter Project

Hello visionaries!!! Welcome back! You were missed - the high school was so quiet without you(!)

For your next blog posting, you will again be working in teams of three. You can work with the same group as last time, or choose a new group. Here are your choices for topics:

(1) Adding and Subtracting Rational Expressions with the same denominator
(2) Multiplying Rational Expressions
(3) Dividing Rational Expressions
(4) Adding and Subtracting Rational Expressions with different denominators
(5) Factor Trees
(6) Vocabulary
(7) Description of Math B topics in Valley Girl
(8) Description of Math B blog in Valley Girl

You will be using Word. To write the rational expression, use the ' / ' sign to show the fraction.

Each group MUST choose a different topic, and the groups that have the correct number of students and tell me their choice first will get priority.

You will be typing up your project in Microsoft Word today. You should use the same format that you used last time:

(1) Title of project
(2) Names of team members (real names, not nicknames)
(3) Introductory paragraph (5-15 sentences) - introduce your topic, define it, write out steps used for that type of problem, write out real world examples, etc.
(4) Five examples that YOU solve
(5) Ten problems that you DO NOT solve (the class will!)
(6) Conclusion (5-15 sentences) - discuss your blog posting, with references to the examples that you solved

Since there are SIX different parts to the project, each team member should be working on a DIFFERENT part - no one should be sitting at their laptop with nothing to do today.

Save your work to the student server, and we will be back in the lab tomorrow so you can post your work on the blog.

Happy Blogging!