What Is the Difference Between an Equation and an Expression?
The difference is one symbol: the equal sign.
Expression
An expression is a mathematical phrase, numbers, variables, and operations combined. It does not have an equal sign.
Examples:
- 3 + 5
- 2x + 7
- 4(n - 3)
- 1/2 × b × h
An expression represents a value but does not make a claim about what that value equals.
Equation
An equation is a statement that two expressions are equal. It has an equal sign.
Examples:
- 3 + 5 = 8
- 2x + 7 = 15
- A = 1/2 × b × h
- y = mx + b
An equation makes a claim: "this side equals that side." It can be solved (find the value of x that makes it true) or verified (is this statement true?).
Why the distinction matters
Your child needs to know the difference because:
- Expressions are simplified. 3x + 2x simplifies to 5x.
- Equations are solved. 3x + 2x = 20 → 5x = 20 → x = 4.
"Simplify the expression" and "solve the equation" are different instructions that require different actions. Confusing them is a common source of errors.
A helpful analogy
An expression is like a phrase: "the big red dog." It describes something but does not make a complete statement.
An equation is like a sentence: "The big red dog is Max." It makes a claim that can be true or false.
Related concepts
- Variables and equations: full teaching guide
- Order of operations: rules for evaluating expressions
- Inequalities: like equations but with >, <, ≥, ≤ instead of =