Properties

	There are a number of 'properties' that you need to know that are very important when you are working with the various algebra operations. The properties help you perform algebraic operations with confidence as well as help you to prove your answers! Being able to recognize them by name is important because on many standardized tests, these names are used and without knowing the names, you are stuck between a rock and hard place…



	Okay, this property is going to seem awfully dumb. Seriously. If you look at the root of the Reflexive Property, though, it actually makes a lot of sense! We're dealing with reflections here, i.e., looking in a mirror = any quantity is equal to itself! tee-hee!






					Which of the following is an example of the Reflexive Property? ab = cd, cd = ef, so ef = ab 14 = 14 If x = 8 and y = 8 then x = y





	Do you remember when you made pretty little pictures that showed lines of symmetry, maybe back when you were learning about M.C. Escher or every February when you cut out hearts for Valentine's Day? What was the most important thing that you recall? Did you answer, "both sides are the same" or "there's a balance between the two sides?" Guess what! That's pretty much what the Symmetric Property is: a balance or equalness on both sides of an equation. This is the fundamental rule/property you must remember when solving equations—whatever you do on one side ya gotta do on the other.

Once again, we're going to use the root word to help us out (who would have thought that your Language Arts class would be such a help in your MATH class, eh?). In the Transitive Property the prefix trans- which goes along with words like transportation or transition is what will help remind you what this property means: move across forming a connection. In algebra, the connections are made using variables.

You walk into class and there is some strange adult sitting at your teacher's desk. OH NO! Where's my teacher? It's substitute teacher time.

The Substitution Property is just that; if two things are the same, then it doesn't matter if one thing substitutes for the other.

Simplify each of the following expressions by substituting a = 2, b = 5, and c = 9

One of the most widely-used properties is the Distributive Property. It is one that SHOULD be learned and memorized because it can help make simplifying expressions and solving equations so much faster! Truly!

The Distributive Property can be thought of as part of the 'G' in GEMA (order of operations) because there's a set of parenthesis involved.

In GEMA, you do whatever is in the grouping symbols (aka, the parenthesis) first, right?

Simplify each of the following using the Distributive Property.

In the order of operations you would normally 'do' whatever is in the parenthesis first. The problem is you cannot combine a variable and a number because these are not like terms.

This is where the Distributive Property comes in.

Step 1: Take the multiplier (7) and multiply it across the parenthesis to the a and then to the 8.

The 7 has been distributed across each of the terms in the parenthesis.

Step 2: Do the math and you are done!

When you have several terms then it may seem complicated but, it really isn't. It just takes a few more steps to simplify your problem.

Step 1: Take the multiplier across the parenthesis.

Be sure to do EACH 'set' as though they were separate problems because, technically, they are.

Step 2: Do the math. Be careful! Follow through with EACH term.

Step 3: Combine like terms. I recommend doing this in a VERTICAL format (it is so much easier!!).

That's it! Easy-peasy, lemon-squeasy!

Do you have a specific table where you sit down to everyday at lunch? Are the people who eat lunch with you the same group of friends each day? Sometimes, do you sit next to one friend and then maybe, the next day, because you were late getting your lunch, you sit next to someone else but since you're all friends, it really doesn't matter, right?

The Commutative Property is kind of like that. It deals with moving around or 'commuting' and if you look at the root word in commutative and you can remember that the Commuter Lane on the freeway is only for those people who have two or more people in a car, then you can remember this property.

With the Commutative Property you are dealing with changing the order of your group members. So, let's take a look at it with some pictures.


	Andrea, Jocelyn, Manny, Lupita, and David always eat lunch together. They sit at the same table every single day. On Monday, they were sitting on the bench in this order.


	On Tuesday, David and Andrea wanted to discuss their history test. Manny had stopped at the library before heading to lunch. Their bench order had changed. This is an example of the Commutative Property where the order changed because the students had moved around.