Understanding Mathematical Expressions
When you write 3 + 5 or 12 − 4, you are writing a mathematical expression. Understanding what an expression is — and how it differs from an equation — is a crucial step in all of mathematics.
What Is a Mathematical Expression?
A mathematical expression is a combination of numbers, operation symbols, and sometimes variables, that represents a value. An expression does not have an equals sign (=).
| Expression | What it contains |
|---|---|
| 7 + 3 | Two numbers and an addition operator |
| 15 − 6 × 2 | Three numbers and two operators |
| 4(x + 2) | A number, a variable, brackets, and multiplication |
Expression vs Equation
People often confuse expressions and equations. The key difference is simple: an equation has an equals sign; an expression does not.
| Expression | Equation |
|---|---|
| 5 + 3 | 5 + 3 = 8 |
| 2x − 1 | 2x − 1 = 7 |
| 4 × 6 + 2 | 4 × 6 + 2 = 26 |
Evaluating an Expression
To evaluate an expression means to calculate its value. You substitute any known values and apply the operations in the correct order (following BODMAS).
Evaluate 3 + 4 × 2 → multiply first: 4 × 2 = 8 → then add: 3 + 8 = 11
Parts of an Expression
- Terms are the individual parts separated by + or − signs. In 3x + 5, there are two terms: 3x and 5.
- Coefficients are numbers in front of variables. In 7y, the coefficient is 7.
- Constants are fixed numbers with no variable, like the 5 in 3x + 5.
Common Mistakes
- Writing an expression when an equation is needed (forgetting the = sign).
- Treating every number group as an expression when some are equations in disguise.
- Ignoring the order of operations when evaluating multi-step expressions.
Key Takeaways
- An expression is a mathematical phrase with no equals sign.
- Evaluating means finding the numerical value of an expression.
- Expressions can contain numbers, operators, brackets, and variables.
Practice Questions
- Is 4 + 9 an expression or an equation? Why?
- Evaluate 6 × 3 − 4.
- How many terms does 5a + 3b − 7 have?
- Write one expression that contains addition and multiplication.
- Evaluate 2 × (8 − 3) + 1.