MT7 Working With Rationals

MT7 Working With Rationals

MT7 is going to be a longer topic than some of the other Algebra MT’s. If you don’t know how to GCF (Greatest Common Factor), Diamond Method (Factor an ABC Quadratic), or factor using Difference of Two Squares, then you should not even try this topic entire you have passed MT4.

After starting your 7.1 and 7.4 vocab assignment, you are going to start this topic by reviewing how to factor (7.2). After taking 7.2 Quiz, you will move to Reduce Rationals (7.3). Do the homework and take the 7.3 Quiz. I suggest skipping 7.51, 7.52, and 7.53 until the end and going straight to 7.6 and 7.7. They are almost the same as 7.3 and the Quiz is pretty easy. Do 7.5 last! It will take you a week to get through it, and you’ll want to have that section fresh in your mind when you take the EOT.

Lesson for 7.2: Review Factoring

There are three types of factoring you are going to have to master if you are going to pass MT7. They are GCF, Diamond Method, and Difference of Two Squares. We are going to look at a practice worksheet similar to your homework and go over several problems from each type of factoring.

If you have more questions after practicing your homework, be sure to use online resources, friends, fellow students, and your LF to help you gain understanding.

Lesson for 7.2: Review Factoring

This is an example of your homework for 7.2, Factoring Review. Let’s look at GCF Factoring First.

Lesson for 7.2: Review Factoring

Notes: This is GCF Factoring (Greatest Common Factor). Find numbers or variables that go into any of your numbers. Factoring means “Make Parenthesis”, so we should always start by making parenthesis. When choosing from variables, all terms must have the variable and we always choose the smallest exponent.

Make Parenthesis.

( )Find a number that goes into 35 and 15.5I choose 5.

Now Divide

7 3

Now place your new numbers in the ( )

7 - 3

Do they share a variable (yes). r2 is also shared!

r2

Finish the ( )

r3

Why is it r3? What happened to the r2?

5r2(7r3 – 3)

Do it again…

( )10

5 1

x2 x2

10x2(5x2 – 1)

5 + 1

Lesson for 7.2: Review Factoring

Now GCF with three terms.

Lesson for 7.2: Review Factoring

Notes: These are a little bit longer, but still easy to do. Just be precise!

The same process, except now we have 3 terms..

Start with ( ). Find a GCF. Divide by the GCF. Put your numbers into the ( ). Decide if they share a variable. Finish it off.

( )5

5 1

xy x2y35 +1 +10

10

Notice this problem did not share a variable for all three terms. Therefore, the variables are not changed.

5(5xy+x2y3+10)

( )2

-6 -7

m3n n2-6 -7 -3

-3

Notice we have a choice of pulling out a -2 instead. This would change all the signs in the ( )

2mn2(-6m3m – 7n2 – 3)

mn2

The “m’s” lose 1, the “n’s” lose 2.

Lesson for 7.2: Review Factoring

Difference of 2 Squares. (The easiest factoring of all)

Lesson for 7.2: Review Factoring

(

Notes: This only work if both pairs of numbers are perfect squares. Here is a limited list of some perfect squares: 1, 4, 9, 16, 25, 36… and x2, x4, x6, x8. I hope you get the idea.

First make two sets of ( ) and put + and – in each one.

( + )( - )Break down your perfect squares.

3•3 xx and 7•7

Each ( ) gets to share the numbers.

3x 7 3x 7

(3x+7)(3x-7)

Again with the same pattern…

8•8 and 3•3 vv

8 3v 8 3v( + )( - )

Lesson for 7.2: Review Factoring

And last of all, Diamond Method

Lesson for 7.2: Review Factoring

(

Notes: You must have an ABC pattern to do Diamond Method. Watch Out! Diamond Method when a>1 can be tricky (#8).

You must be an expert at this by now!

Please pay attention to the steps.( )( )

A B C

AC: 1 • -28

-28 B: +3

+3

Make a list1•282•144•7

7 -4

r + 7 r - 4

(r+7)(r-4)

( )( )A little different

5n n

-10

+910 -1

5 goes into 10, 2 times

+ 2

1 goes into -1, -1 times

- 1-1 10