Algebraic Expressions – Building Blocks of Algebra
An algebraic expression is a combination of variables, constants, and operations. Expressions are the sentences of algebra — they describe a value that can be calculated once the variables are known.
The skill of translating between everyday language and algebraic expressions goes back to the earliest algebra texts, including Al-Khwarizmi’s 9th-century treatise al-Kitab al-mukhtasar fi hisab al-jabr wal-muqabala, which described methods for solving problems entirely in prose before symbolic notation existed. Being fluent in both directions — writing an expression from a word description, and reading an expression back into plain language — is exactly the skill needed to turn a real-world word problem (a spreadsheet formula, a pricing rule, a physics equation) into workable maths.
What Is an Expression?
An expression is a mathematical phrase built from numbers, variables, and operations (+, -, times, /) that does NOT contain an equals sign. It represents a value, not a statement about equality.
Examples of Expressions
| Expression | Read As | Number of Terms |
|---|---|---|
| 3x | Three x | 1 |
| x + 7 | x plus seven | 2 |
| 4a - 2b + 5 | Four a minus two b plus five | 3 |
| x squared + 3x - 1 | x squared plus three x minus one | 3 |
Expressions vs Equations
| Expression | Equation | |
|---|---|---|
| Contains = | No | Yes |
| Example | 3x + 2 | 3x + 2 = 8 |
| Can solve for x? | No (just evaluate) | Yes |
Evaluating Expressions
To evaluate means to find the numerical value of an expression by substituting given values for the variables.
5(4) - 3 = 20 - 3 = 17.
2(9) + 5 = 18 + 5 = 23.
Writing Expressions from Words
| Word Phrase | Expression |
|---|---|
| A number n increased by 8 | n + 8 |
| Three times a number x, minus 4 | 3x - 4 |
| Half of y | y / 2 |
| The square of p, plus 1 | p squared + 1 |
| Five less than twice m | 2m - 5 |
Key Takeaways
- An expression has no equals sign — it represents a value, not a fact.
- Evaluate by substituting numbers for variables and calculating.
- Expressions can be written from word descriptions by translating key phrases.