Algebra 101

You are probably used to seeing empty squares or a question mark in math, asking you what number belongs there. In Algebra, letters are used to stand for a number. These letters are called variables. Here is an example:

x + 5 = 8

"x" Is the variable in this example. Variables can be any letter in the alphabet, but the letters x, y and z are used more often.

A very helpful thing that variables allows us to do is use different variables in one problem. So we can have terms that consist only of numbers, these are called like terms.

Example: 5, 3, 0.4

Terms that use the same variable are like terms.

Example: 5x, 3x, 0.4x

A number and a variable are unlike terms.

Example: 5 and x

Terms that use different variables are unlike terms.

Example: 5x and 3y and 0.4z

In Math, we do operations like addition, subtraction, multiplication and division.  Sometimes we see these operations in the same problem.  To solve these types of problems, we must follow a special guide called the Order of Operations. 

Distributive Property

a • (b + c) = a • b + a • c

Example:

6 • (4 + 2) = 6 • 4 + 6 • 2

Commutative Property of Addition

a + b = b + a

Example:

2 + 4 = 4 + 2

Commutative Property of Multiplication

a • b = b • a

Example:

6 • 4 = 4 • 6

Associative Property of Addition

a + (b + c) = (a + b) + c

Example:

2 + (4 + 6) = (2 + 4) + 6

Associative Property of Multiplication

a • (b • c) = (a • b) • c

Example:

2 • (4 • 6) = (2 • 4) • 6

Equations are a mathematical sentence with an equal sign. There are 4 steps on how to deal with one-step equations:

1. Simplify like terms on each side of the equal sign.

2. Add and/or subtract like terms. Remember to do the same on both sides!

3. Multiply and/or divide like terms. Remember to do the same on both sides!

4. Simplify if necessary.

Sometimes there could be complex equations where there are more steps to solving them. In this case, simply repeat the steps until the problem is solved.

1. Simplify like terms on each side of the equal sign.

2. Add and/or subtract like terms. Remember to do the same on both sides!

3. Multiply and/or divide like terms. Remember to do the same on both sides!

4. Simplify if necessary.

5. Repeat until completely simplified.

The horizontal axis (left to right) in the coordinate plane is called the x-axis. The vertical axis (up and down) is called the y-axis. The point at which the two axes intersect is called the origin. The point where it is 0 on the x-axis and 0 on the y-axis, or the point where both the y-axis and the x-axis intersect is called the origin.

The intersecting x and y axis divides the coordinate plane into four sections. These four sections are called quadrants. Quadrants are named using the Roman numerals I, II, III, and IV beginning with the top right quadrant and moving counter clockwise.

Whenever you are plotting points, the first number in the parenthesis is "x", which goes left to right. The second number in the parenthesis is "y",  which goes up and down.