What is an Expression in Math?
A mathematical phrase with no equality or inequality sign
An expression is a combination of numbers, variables, and operation symbols (like +, –, ×, or ÷) that represents a value. Unlike equations, expressions do not have an equals sign ( = ) or an inequality sign ( >, < ).
For example, 3x + 2, 5y – 7, and 2a + 3b – 4 are all expressions. Each one is made up of terms that are separated by addition or subtraction signs. In the expression 3x + 2, the terms are 3x and 2.
Expressions can be:
- Numerical expressions: Made up of just numbers and operation signs (e.g., 5 + 7 – 2)
- Algebraic expressions: Made up of numbers, variables, and operations (e.g., 4x + 3y)
What Is Not an Expression?
Anything that includes an equal sign or an inequality sign is not an expression.
- This is an equation because it has an equals sign: x + 5 = 10
- This is an inequality because it has a greater-than sign: y – 2 > 5
Expressions are important in math because they help us:
- Represent real-world situations
- Describe relationships between quantities
- Solve problems without needing an immediate solution
When Do Students Learn About Expressions?
Students are introduced to expressions when they begin working with algebraic concepts. This typically starts in upper elementary school and continues into high school.
Grades 3–5 – Introduction to Expressions
Students begin learning to write and evaluate simple numerical and algebraic expressions.
Grades 6–8 – Working with Algebraic Expressions
Students learn to combine like terms, evaluate expressions, and apply the distributive property.
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Grades 9+ – Advanced Use of Expressions
Students solve complex expressions, work with polynomials, and manipulate expressions as part of larger algebraic equations.
