Multiplying and Dividing Rational Expressions

Last piece of material for this unit. Today we learned to multiply and divide rational expressions.

Ms. Talley's students, you have a test today or tomorrow. My 2A and 4A, we will do a quiz on Monday. It will cover:
(1) Simplifying Rational Expressions (see notes 2 blog posts back)
(2) Adding and Subtracting Rational Expressions (see notes in my last blog post), and
(3) Multiplying and Dividing Rational Expressions (see below for the notes)

Here are the notes:

First, multiplying and diving NUMBER fractions (this should be a review):

  Multiplying and Dividing Rational Expressions, with variables and factors, works the same way:

 

Adding and Subtracting Fractions and Rational Expressions

You can add or subtract fractions as long as they have the same (common) denominator:

 

If the denominators are different, you first have to find the LEAST COMMON DENOMINATOR.

That's the smallest number that BOTH denominators will go into evenly:

For example: 

Denominators 3, 4 ; Common denominator is 12 because 3 and 4 both go into 12.

Denominators 15 and 20 ; Common denominator is 60 because 15 and 20 both go into 60.

15*20 = 300, which would be a common denominator but not the smallest one. So you'd have to simplify a lot later.

15 = 3*5

20 = 2*2*5

So the LEAST COMMON DENOMINATOR is 3*5*2*2 = 60.

  

More examples:

 Rational Expressions work the same way. If you already have a common denominator, just add or subtract (whichever it says to do) the numerators, combine any like terms, and simplify if possible:

 If the denominators are not common, you need to find the least common denominator that includes all the factors of both denominators.

This is just like with number fractions!

Notes on Simplifying Rational Expressions (January 11, 2016), + Homework

Here are today's notes and examples:

And here is the homework assignment, due AT THE START OF CLASS WEDNESDAY:

Welcome back!

I'm so glad to see y'all in class again!

Here are the notes from today's Advanced Algebra class - the last problem on it is your homework, due tomorrow!

And, here are the notes from Advanced Algebra Support today, on going back and forth between ROOTS and FACTORS. I strongly suggest that you practice this until you are comfortable. It's very important.

Unit 4 review

Here are some hints for the Unit 4 Practice Test (which you should get in support, and it counts as a quiz grade), and some recent class notes from my 4A and 4B:

Unit 3 test review - hints and help.

As you know, the test is Thursday/Friday.

If you are in my 4A or 4B, I will accept your station papers on Friday, or when you finish your test. If you want to use the papers I already collected, just ask.

In support, you were given a review packet, as a quiz grade. I'm posting it here, with hints. This is not an answer key - I've just put enough to get you started on each question. If you're stuck or not quite getting something, this is for you.

Please ask questions on the GroupMe or in class (and support).

Note: I know some of you have made other arrangements for the quiz grade. I would still advise you to look through this, as I BASED IT ON THE TEST! Just sayin'.

Here's the first 8 pages, which has questions that might show up on your test, no matter whether you are in my class or in Ms. Meade / Ms. Talley's class.

Remember, you can download these images and zoom in on them - I am attaching them at full resolution.

And here is the 2nd section. Only the students in Ms. Meade / Ms.Talley's class have to do this, because they will need to know these skills, without using a calculator, for the test.

Students in my 4A and 4B will be allowed to use a graphing calculator. However, you are also perfectly welcome to  look through this and ask me questions - it will help you understand the math in a different way.