3.2+Terms

Section 3.2 - Terms

 * A Term is a number, a variable, or a product of numbers and variables.** I'm going to guess that definition doesn't help much yet.


 * Examples of Terms**

A number alone can be a term, so 6, -39, 3.443, and one-half would all be considered terms.

A variable is also a term, so x or M or r, written as variables representing some unknown quantity, would also be considered terms.

Now for the challenging part - a product of numbers and variables. Product means multiplication, but when working with numbers (coefficients) and variables you seldom see a multiplication sign. That actually might help in recognizing terms because they will be written right next to each other. If you multiply 5 and y you get 5y. 5y is a product of a number and a variable, so 5y is a term. If you multiply **y** (a variable) by **z** (another variable), you get **yz**, which is also a term. Finally, putting it all together, suppose you multiply the following factors: -7, b, b, c. The result would be a term. What would it look like?

If you multiply one term by another term, is the answer still a term?


 * What Isn't a Term?**

If you are not multiplying, but rather using some other operation to combine numbers and letters, the answer is not a term. Instead, it is called an ** Expression **, though we will give it other names as well in the chapter on polynomials. An example of something that is __not__ a term is "4f + 5", even though 4f is a term and 5 is a term. 9c - 4 is not a term. If you divide, it may or may not be a term, depending on if it goes in evenly.


 * Like Terms**


 * In order for two terms to be considered "like terms", they must have the exact same variable(s) and exponents. They do not have to have the same coefficient. ** 4x and 6x are like terms, but 9x and 9y are not because they have different variables.



Just add or subtract the coefficients. Let's say you have 4m. We aren't sure how much that is, because we don't really know what m is equal to. But let's think of m as a box of crayons. We still don't know how many there are in a box, but if you have 4m, you have 4 boxes of crayons and they have the same number in each box. Now, if we add two like terms - 4m + 8m -- it's like adding 4 boxes of crayons to 8 boxes of crayons. Obviously we now have 12 boxes of crayons. 4m + 8m = 12m. Leave the variable(s) alone, just add (or subtract) the coefficients.
 * Adding and Subtracting Like Terms**


 * Adding and Subtracting Unlike Terms**


 * You can't!!! ** You cannot add or subtract unlike terms, although you can multiply and divide them! 4x + 3 = 4x + 3 because 4x and 3 are not like terms (one has an x variable and the other has no variable).

Add this section in later?
 * But You Can Multiply Them!**



**Where to from here?**
3.1 Variables and Constants 3.2 Terms 3.3 Equations 3.4 Formulas 3.5 Solving for X 3.6 Two Unknown Relative Values Chapter Three Summary Chapter Three Homework