What is an expression?

Expression Definition

An expression is a part of a math sentence. They are kind of like the math version of a subject or a predicate in an English sentence.

Usually, expressions have multiple numbers or variables that are connected by operations like addition, subtraction, multiplication, division, powers, or roots. 

Examples of Expressions

Expressions can be very simple, like a single number or a variable. Or they can be very complex, like the quadratic formula.

Simple 

\(28y\)

\(x+7\)

 Moderate 

\(12x^{2}-4x+5\)

\(a^{2}+b^{2}\)

Advanced 

\(4 log_{a}b+m\)

\(\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)

Expressions in Math Sentences

Click here to learn more about the difference between expressions and equations. 

Expressions can be written on their own (like the examples above) or they can be written as part of a math sentence. 

Most math sentences are equations. The sentence structure of an equation looks like this...

Expression = Expression

Some math sentences are inequalities and their sentence structures look like this...

Expression \(\geq\) Expression

Expression \(\leq\) Expression

Expression \(>\) Expression

Expression \(<\) Expression

Examples of Expressions in Math Sentences

\(1 + 1\) \(=\) \(2\)

In this equation, 1 + 1 is an expression and 2 is an expression.

\(y\) \(<\) \(5x-1\)

In this inequality, is an expression and 5x+1 is an expression.

\( (x-h)^{2}+(y-k)^{2}\) \(=\) \(r^{2} \)

In this equation, \((x-h)^{2}+(y-k)^{2}\) and \(r^{2}\) are expressions.

How to Use Expressions

How to Decode Algebraic Expressions

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How to Simplify Expressions

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How to Evaluate Expressions

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English phrases and sentences communicate ideas by connecting words together.

Similarly, expressions and equations are used to communicate relationships between numbers and variables. 

Before you do anything with an algebraic expression, I recommend that you decode the expression.

This will help you make sure you understand the meaning that the expression is communicating.  

After you've decoded it, you can simplify the expression and convert it into a different form.

If you are given the values of the variables, you can evaluate the expression. 


If the expression is part of an equation or inequality, you may be asked to solve or graph the equation (or inequality). 

How to Solve Equations

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How to Graph Equations

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How to Solve Inequalities

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How to Graph Inequalities

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Resources

Free Printable Worksheets

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Free Online Practice Problems

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