Monday, 9/30

Ok, guys. I know the combining like terms thing is a little stressful, so let's take some time to go over how it works. 

1) Remember that, no matter what you're doing in math, you must always follow PEMDAS. 

2) Keep the distributive property in mind. Check out this graphic from scimathmn.org:

(The main thing is to remember that whatever's outside the parenthesis gets multiplied by what's inside. 

3) Remember that, with addition and subtraction, you may online combine like terms (the stuff with the same variables). 

Example:

5(3x +2) - 6x +4   ---> First step: Distribute the 5 by multiplying:

15x + 10 - 6x +4   ---> Next step: Combine like terms (they're highlighted in purple):

9x + 10 + 4

= 9x + 14

b

As you complete the following problems, if you have any questions, leave a comment below. Here is your assignment:

1) 6 + x - 4x + 3

2) 3(w + 3) + 4w

3) -3z + 8(z + y)

See you tomorrow!

Thursday, 9/26

Howdy, y'all. Please watch the following video. It will show you a bit more about combining like terms. Aaaaaand have a really wonderful evening! See you tomorrow!

https://www.khanacademy.org/math/algebra/introduction-to-algebra/manipulating-expressions/v/combining-like-terms

If for some reason the link doesn't work, please visit Khanacademy.org and search for the video called "Combining Like Terms." You can also do the exercise on Khan Academy and practice online. 

8/29 - Did you find it???

Hello all and welcome to the Pre-Algebra blog!

If you've found the blog and would like some extra credit, complete the following problems to turn in on Tuesday:

If x = 3 and y = 5:

1) 3x + y
2) 2xy
3) (9+y) - x

Don't be scurred of rational numbers!

Hey guys. I know a lot of you are scratching your heads trying to remember how we graph rational numbers.  Look back at your old test if you have it - many of you graphed them correctly on the test. Here is a video that might help you understand the "why" to graphing rational numbers (after you watch, continue to read below please):
http://www.showme.com/sh/?h=X4EovCa

For those of you having a hard time, let's review:
- A rational number is any number that can be expressed as a fraction (which is, pretty much, any number!)
- All of the rational numbers we've graphed have been LESS than one (between zero and one)

Just so you know, BOTH rational numbers on your final will be "tenths". Just to make things a little easier.

Here's a quick rundown:

If I need to graph 7/10, I know my number lands somewhere between zero and one. Make sure your number line goes from zero to one:

Now, because I'm dealing with tenths, that means I need to divide my number line into ten different sections. It's like saying I'm dividing a giant cake into ten pieces, or cutting a pizza into ten different slices. Just place your lines so that there are ten little sections between 0 and 1:

Now that we have a graph of "tenths" - we can graph our fraction. 7/10 is "seven tenths". So we count seven places from zero to reach our destination (it's like finding the "seventh piece of cake"):

What if you have a decimal? Either turn it into a fraction or say it aloud so you have an understanding of where it goes. For example, 0.3  is "three tenths". Applying what we learned above, we can graph 0.3:

Does this help?

Final Review Questions

Hello mathlings. Your final review questions are as follows. We will be working through these problems and reviewing the concepts for the week leading up to finals.

Final Review Assignment/Guide

Complete these problems on the following pages:

CHP. 4 Concepts (pg. 230)

Exponents:

13, 14, 15, 63

Prime Factorization:

28

GCF:

34, 38

Simplifying Fractions:

39, 44

Graphing Rational Numbers:

45, 46

Chp. 5 Concepts (pg. 286)

LCM:

1, 3

Comparing and ordering fractions:

5, 6, 11

Converting fractions to decimals and decimals to fractions:

13, 16, 19, 21

Operations with fractions:

25, 26, 38, 31, 33, 36

Equations with fractions:

43, 44, 46

Final Study Guide

'ello, everyone! Here are the concepts that will be included on your Pre-Algebra Final. The jist of it is:
Exponents, GCM, Fractions, LCM, Equations. In more detail:

Chp. 4: Sections 2, 4, 6, 7, 8

- Exponents - How they work & what to do if you must add, subtract, multiply, or divide them

- Greatest Common Factor using Prime Factorization

- Simplifying Fractions

- Rational Numbers (you will need to graph two rational numbers, just like your Chp. 4 test)

Chp. 5: Sections 1, 2, 3, 4, 7, 8

- Finding the Least Common Multiple (use Prime Factorization for large numbers)

- Fractions:
   - Comparing/ordering fractions
   - Turning a fraction into a decimal (and a decimal into a fraction)
   - Adding & subtracting fractions
   - Mixed numbers: How to turn them into improper fractions, how to add & subtract them
   - Multiplying and Dividing fractions

- Solving equations by adding, subtracting, or multiplying fractions

Your test will not be super long but it will include all of these concepts using at least one question for each. And remember, don't stressed - we have plenty of time for review!

5-8 Solving Equations by Multiplying Fractions

Okay. Last section. You can do it!!! :)

We are now solving equations in which we must use multiplication or division. This is no different than what we've done in the past:

3x = 33 ----- To solve, we do the opposite of what's happening to x. Since we're multiplying x by 3,
                      the OPPOSITE would be to divide both sides by 3.

3x  =  33
 3        3

We now solve both sides and are left with x = 11.

What we're doing today is no different - we're just going to see some pesky fractions.

Take a look at Example 1 for this section:

5a = 1/7

Since we're multiplying a by 5, we do the OPPOSITE to both sides (Divide by 5). Here's the thing, though - how do you divide 1/7 by 5??? Going back to what we learned about dividing when there are fractions involved, we know we can multiply instead by the reciprocal (or "inverse"). Remember?

So all we have to do is turn that right side into a multiplication problem:

a = 1/7 x 1/5
a = 1/35

Now jump ahead to see Example 3. I know it looks like a hot mess, but pay close attention to what they're doing - they're remembering their negative rules, and then simplifying by using common factors before solving. I know we haven't touched on simplifying BEFORE solving, but it's there as an option for you if you'd like to try it. Otherwise, be SURE to simplify your answer after you've solved.

Example 4 shows us that, as always, when dealing with mixed numbers in an equation, it's easier to convert them to improper fractions first, and then solve.

Let's try a few:

Pg. 274, 1 - 20 EVENS ONLY