 ## Tutoring on Variables and Variable Expressions

Learning Objectives:

#### Understand and apply Variables and Variable Expressions.

Math Tutoring on Variables and Variable Expressions

A Variable is a letter that represents an unknown quantity. For example:

X = the number of hours you will study per day or C = the cost of the car repair per month. The value of the ‘X’ is ‘C’ is not fixed; it will vary from time to time.

A Variable Expression consists of Variables, Constants. Numbers and Operations like addition, subtraction, multiplication, and division. For example, 2x-5, 3m+4n, m÷6n etc.

Often Mathematical Expressions and Variable Expressions are used interchangeably. The difference is a Math Expression may not contain a Variable while a Variable Expression does.

Some vocabulary of Algebraic Expressions:

Terms: Parts of an Algebraic Expression separated by addition or subtraction symbols.

Constant Term: A number with no Variable factors; a term whose value never changes.

Factors: Numbers or Variables that are multiplied together.

Coefficient: The number that multiplies the Variable.

When two terms have Variable factors, or Variable parts, that are exactly the same, the terms are called Like or Similar Terms.

The Distributive Law states, for any numbers a, b, c For combining Like Terms we might right .

The Distributive Law enables us to combine or collect Like Terms. Sometimes when we try to simplify an expression inside parentheses, we can’t because the terms are not like terms, the Distributive Property provides a way to eliminate the parentheses.

The Property of -1:

For any real number ‘a’: . (Negative one times ‘a’ is the opposite of    ‘a’)

The Opposite of a Sum:

For any real numbers ‘a’ and ‘b’: . (The opposites of a sum are the sum of the opposites.)

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Hook Questions:

1.    What are Variable and Variable Expressions?

2.    What is the Distributive Law of Variables?

3.    What are Factors and Coefficient of an Algebraic Expressions?

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