Sept. 10, 2014

Today: Algebra Rules

Vocabulary Basic Formulas

Warm – Up Questions Review Class Work

Algebra Rules:When solving for unknown quantities, always assign the variable to the smallest quantity. (Smallest may be lightest, least expensive, shortest, etc. depending on the type of value.Bob weighs 10 more pounds than Mike. Don weighs 15 more pounds than Bob. The sum of their weight is 440 pounds. How much does each weigh?Who weighs the least?

We’ll use ‘m’ as the variable. Now, the key part of our solution: For the other

two, what are their weights relative to Mike’s weight? Bob is...

m + 10

Don is...

m + 10(Bob) + 15, or

m + 25

Putting them all together, we have...

m + (m + 10) + (m + 25) = 4403m + 35 =

4403m = 405

Mike = 135, Bob = 145, Don = 160

2. Like Terms:

Vocabulary:

In algebraic expressions & equations, like terms are terms that contain the same variables raised to the same power. Only the coefficients of like terms can be different.

1. Coefficient:

Examples include: 7x x -2x

(1/3)xy2 -2y2x 6xy2

Write the expression or equation. Then, identify the number of: a) terms What are the: b) like terms, c) coefficients, & d) constants1. 3 + 7x + 3x

+ xNo. of Terms?Like Terms?

Coefficients?Constants?

2. 2a + 5c – a + 6a

3. 7x – 3y + 3z - 2

Are these expressions or equations?

Vocabulary:

Formulas:

1. Perimeter of a Square: 2. Area of a Square:

3. Perimeter of a Triangle:

= Side

+ Side

+ Side

4. Area of a Triangle:x

height= ½ baseor, ½ (base x

height)

P =

4SThe area of a square is actually the same as the area of a rectangle: LxWHowever, since the lengths of the sides

are the same, you are multiplying a number by itself. So, the formula for the area of a square is:

A =

S2

Warm-Up:

1. Translate & Solve: The difference between a number and four. The sum of three times a number and

eight.

a2 + a + a2

Four less than the product of four and a number is nine. The quotient of a number and eight is one

and five-tenths.Three times the quantity of a number decreased by three is nine.2. Simplify the Expression:

2x + 3y – 5x + 2y

5(a – 2b) – 3(a – 2b)

And finally…

Test #1 Topics:

1. Simplifying Expressions --Key Concept: Combining Like Terms2. Solving Simple Equations (1 or 2 step) --Key Concepts: a.) Variable replaced by value which make the sentence true. b.) Isolate the variable (get the variable by itself) on one side of the equation by correctly using the rules. 3. Translating Sentences into Expressions or Equations --Key Concepts: sum, difference, product, quotient, less than, the quantity of.