– ALGEBRA I – UNIT 1 – Section 1

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– ALGEBRA I – UNIT 1 – Section 1. Variables, Expressions, Simplifying, and Evaluating. In this section, we will be reviewing several concepts…. Pretty darn funny…. variables. expressions. simplifying. evaluating. order of operations. VARIABLES. What is a variable?.

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– ALGEBRA I –

UNIT 1 – Section 1

Variables, Expressions, Simplifying, and Evaluating

In this section, we will be reviewing several concepts…

Pretty darn funny…

• variables
• expressions
• simplifying
• evaluating
• order of operations

VARIABLES

What is a variable?

A variable is a symbol (usually a letter) used to represent a number that you do not know.

The most commonly used variables are…

x

y

n

It is usually a good idea to pick a variable that will remind you what it stands for (i.e. h = hours)

The VALUE OF A VARIABLE is the number that the variable stands for.

EXPRESSIONS

What is an expression?

Do you mean expressions like…

“That’s da bomb…”

“Dude…that was phat.”

“Oh, snap!”

“I’m down with that…homey.”

No… Those are not the expressions I’m talking about. By the way, Mr. Dillon,you are not that cool. Never…never…never use the word “homey” again…

EXPRESSIONS

What is an expression?

An expression is an algebraic statement that contains some combination of variables, numbers, and/or operations..

Examples of expressions are…

2x

4.5·h

6x + 7yx

A NUMERICAL EXPRESSION is an expression that is made up of just a number.

The VALUE OF AN EXPRESSION is the answer when numbers are put in for the variables.

POWERS

What is a power?

A power is an expression that indicates the repeated multiplication of the same number (or variable or expression).

An example of a power is…

The “little” number is called the EXPONENT. This number tells you how many times to multiply the base.

45

The “big” number is called the BASE. This is the number that is multiplied.

45 = 4 4 4 4 4 = 1024

SIMPLIFYING

What does it mean to simplify?

Simplifying means writing an expression in an equivalent form that has the fewest terms possible. If the problem has all numbers, then you simplify to get a single numerical answer.

In order to simplify an expression, you have to use…

ORDER OF OPERATIONS

SIMPLIFYING

The steps in order of operations are:

1) Parentheses (Grouping Symbols)

2) Exponents/Roots

3) Multiply/Divide (Left to Right)

4) Add/Subtract (Left to Right)

Here is an example…

SIMPLIFYING

Simplify the power.

Then subtract.

Try These Problems…

Give these “simplify” problems a try. You will use order of operations to get your answer. Be sure to show your work!

**The answers can be found at the end of the PowerPoint.

EVALUATING

What does it mean to evaluate?

Evaluating an expression means replacing the variables with numbers and simplifying to get the answer.

The first step in an “evaluate” problem is to SUBSTITUTE a number in for each variable.

Then, you simplify by using…

ORDER OF OPERATIONS

Here is an example…

EVALUATING

Substitute