ABE Algebra

Today in class we studied algebra.

Lol. It isn't that bad, I promise.

So there are basically 4 algebra skills that you need for your HSE test:

• Order of Operations
• Substitution
• Simplifying expressions
• Solving equations

Let's take these one at a time.

Order of Operations

Who's heard the old phrase, "Please Excuse My Dear Aunt Sally"? The only reason we remember that old saying is for the first letter of each word: PEMDAS. These signal us to remember the order in which we do math operations:

• Parentheses
• Exponents (and radicals)
• Multiplication
• Division
• Addition
• Subtraction

Math has to be performed in this order. Here's a Math Antics video about the order of operations!

Substitution

Substitution problems are math problems with variables (letters), where they tell you what number the variable stands for and then you substitute the variable for the number and solve like an order of operations problem. I call these PLUG-AND-PLAY problems. Here's an example:

Evaluate 3x + 7, when x = 4.

In this example, you substitute the number 4 for the variable x and solve like this:

3(4) + 7 

12 + 7

Answer: 19

Simplifying Expressions

Expressions are math problems without equal signs, like the substitution problem above. Some problems will just ask you to simplify the expression. In this case, simplifying just means combining numbers that can be combined. Whole numbers can be combined with other whole numbers. Variables can be combined with other similar variables. Here's an example:

Simplify this expression: 3y + 4 - 2y + 6 - 4x - 2 + 6x

In this example, the y's can be combined with other y's (3y - 2y = y), the x's with other x's (-4x + 6x = 2x), and the whole numbers with other whole numbers (4 + 6 - 2 = 8). I've color coded them so you can see them better.

The simplified expression would be: y + 2x + 8

There are more rules for simplifying expressions (i.e. distribution, how to work with exponents), but we will talk about them another time.

Solving Equations

Equations are different from expressions in that they have an equals sign. To solve an equation, you use the order of operations backward! So you take care of your whole number adding/subtracting first, then go on to take care of multiplying/dividing, and so on. The name of the game is ISOLATE THE VARIABLE. Here's Khan Academy's introduction to linear equations so you can get started on them.


In our next class, we will be working more with equations and looking at coordinate graphing and functions, which are a blend of Algebra and Geometry skills. :)

JmC