Learning Objectives:

__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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