Showing posts with label elementary algebra. Show all posts
Showing posts with label elementary algebra. Show all posts

Friday, November 2, 2012

Simplifying Algebraic Expressions

The properties of real numbers are very important in our study of Algebra. These properties can be applied in Algebra because a variable is simply a letter that represents a real number. The distributive property is one that we apply often when simplifying algebraic expressions. Given real numbers a, b, c:
a(b + c) = ab + ac
When multiplying an expression within parentheses you must multiply everything inside by the number or variable that you are distributing.


Simplify.
When simplifying, we will often have to combine like terms after we distribute.  This step is consistent with the order of operations, multiplication before addition.


Instructional Video: Combining Like Terms

Simplify.

Instructional Video: Simplifying Algebraic Expressions

To combine like terms, the variable parts have to be exactly the same.  But before combining like terms, generally, we will first distribute if necessary.  When distributing negative numbers notice that the operations change.

Simplify.

Profit Word Problem: Profit is equal to revenues less cost of production.  If the revenue R can be represented by
and the cost C can be represented by
where x represents the number of units produced, find an equation that represents the profit.
Subtracting Variable Expressions: What is the difference between 3x − 4 and −2x + 5?
Video Examples on YouTube:
      

J. Redden on G+

Rectangular Coordinate System

Sometimes referred to as the rectangular coordinate system, the Cartesian coordinate system consists of two perpendicular real number lines intersecting at zero. Positions on this grid system are identified using ordered pairs, (xy). The center of the system (0, 0) is called the origin.  The x-coordinate indicates horizontal distance from the origin and the y-coordinate indicates vertical distance from the origin.


The horizontal number line, usually called the x-axis, is typically used for the independent variable. The vertical real number line, usually called the y-axis, is used for the dependent variable.
Ordered pairs with 0 as a coordinate do not lie in a quadrant; these points lie on an axis.

Example: Find the distance and midpoint between the two points: (3, 4) and (−1, 2).
  
Example: Find the distance and midpoint between the two points: (0, 0) and (−3, 4).
               
Example: Find the distance and midpoint between the two points: (−1,−1) and (1,1).
       
Example: Find the distance and midpoint between the two points: (−2,−5) and (−4,−3).
             
Circle Word Problem: If the diameter of a circle is defined by two points (−3, 4) and (7, 4), find the center and radius of the circle.  (Hint: diameter = 2*radius)
       
Area of a Circle: Find the area of a circle given the center (−3, 3) and a point (3, 3) on the circle.
         
Video Examples on YouTube: