Display Title

Overview of Variables and Equations

VIDEO: Overview of Variables and Equations

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things. Let’s look at some examples.

  • The Unknown. Remember when you first learned to add numbers? You probably saw “missing addend” problems like this:

A missing addend equation.

In this example the box represents an unknown value. It could also be replaced by a letter.

A missing addend equation.

In this example the letter x represents the unknown value. While x can take on different values, there is only one value for x that makes this equation true.

x equals 6

  • An Input Value. Many equations, functions, and formulas use variables to represent numbers. Look at this example.

An example of a linear function.

By substituting different values for x, you can evaluate this function. Here are some examples. 

Three examples of evaluating a linear function.

What Is an Expression?

A mathematical expression can include numbers, variables, and operation symbols. Let’s start with the simplest type of expression, a numerical expression.

Numerical Expressions

A numerical expression includes numbers and operations. Here are some examples.

A set of numerical expressions.

When a numerical expression includes operation symbols, the expression can often be simplified. These equations show an expression on the left and its simplified form on the right. 

Three equations showing numerical expressions in simplified form.


Algebraic Expressions

An algebraic expression includes numbers, variables, and operation symbols. An algebraic expression can look like a polynomial. Here are some examples.

Three examples of algebraic expressions.

Algebraic expressions are sometimes referred to as variable expressions.

Evaluating Algebraic Expressions

Because algebraic expressions include variables, sometimes you can replace the variable with a specific value for the variable. In such a case, you are left with a numerical expression. Here is an example:

For the expression 2x + 4, let x = 3. Here is the result:

A numerical expression.

The numerical expression on the right can be simplified.

Simplifying a numerical expression


In this video segment, get an overview of variables and equations, along with the evolution of algebraic notation.

Note: The download is an MP4 video file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Video Library

To see the complete collection of math videos, click on this link.

Common Core Standards CCSS.MATH.CONTENT.6.EE.B.7
Grade Range 6 - 9
Curriculum Nodes Algebra
    • The Language of Math
        • Variable Expressions
    • Expressions, Equations, and Inequalities
        • Applications of Equations and Inequalities
        • Variables and Unknowns
Copyright Year 2011
Keywords algebra, variables, equations