# Algebra I/Content/Introduction to Basic Algebra Ideas/Variables and Expressions

Back to Table of Contents Algebra I

## Vocabulary

Variable

Term

Operation

Expression

Evaluate

Substitute

## Lesson

A **variable** is a letter or sign that takes place of a number. You use letters like **a, x, y, θ,** or **λ**. People often use the letter x for a variable.

**Examples of using a variable:**

- Do not say
**3 + 5**. Say**3 + x**. In this example the variable x takes the place of the number 5. - Do not say
**4 * 8**. Say**4 * x**or**x * 8**. In this example the variable x takes the place of the number 8 or 4.

A **term** is a number or a variable.

**Examples of terms:**

- 3 + 5 The terms are 3 and 5.
- 6 / x The terms are 6 and x.

An **operation** is a thing you do to numbers, like add, subtract, multiply, or divide. You use signs like **+**, **-**, *****, or **/** for operations.

An **expression** is two or more terms, with operations between all terms.

**Examples of expressions:**

**3 / 4****8 * x****x * 6 + y****a * b * c * d**

To **evaluate** an expression, you do the operations to the terms of an expression.

**Examples of evaluating expressions:**

**3 + 4**evaluates to**7**.**18 / 3**evaluates to**6**.**4 * 5 - 3**evaluates to**17**.

To evaluate an expression with variables, you **substitute** (put a thing in the place of an other thing) numbers for the variables.

**Examples of substituting:** (Substitute 3 for x in these examples.)

**x + 4**is**3 + 4**.**18 / x**is**18 / 3**.**4 * 5 - x**is**4 * 5 - 3**.

## Example Problems

**Evaluate 5*x when x is 2.**

Substitute 2 for x to get 5*2.

Evaluate 5*2 to get the answer 10.

**Evaluate x / 3 + y when x is 9 and y is 4.**

Substitute 9 for x and substitute 4 for y is to get 9 / 3 + 4.

Evaluate 9 / 3 + 4 to get the answer 7.

## Practice Games

http://www.quia.com/cm/29771.html (evaluating expressions) 4(a-1)

## Practice Problems

(Note: put answer in parentheses after each problem you write)

**Evaluate each expression when a = 1, b = 2, c = 3, and d = 5.**

- 5*b (10)
- 9*c (27)
- c-2 (1)
- d-5 (0)
- b/2 (1)
- 36/c (12)
- b*c + 2 (8)
- b*c*d - 5 (25)

**Evaluate each expression if x = 4, y = 2, and z = 3.**

- x+y (6)
- 2*z (6)
- x*z (12)
- x+y+z (9)
- x*y+z (11)
- y*z-x (2)