Variables and Expressions
A variable is a letter that stands for an unknown or changing number.
About this topic
A variable is a letter standing for a number that can change or is not yet known. An expression combines variables, numbers and operations, like 3x + 5, without an equals sign. In 3x + 5, 3 is the coefficient, x the variable and 5 the constant.
Expressions let us describe patterns and relationships in general terms, such as the cost of n tickets at $7 each, written 7n. Translating words into algebra is the first step in solving almost any word problem. Phrases like "more than" signal addition, "product" signals multiplication and "less than" often reverses the order: 5 less than x is x − 5.
Think of a taxi charging a 4 dollar flag-fall plus 2 dollars per kilometre. For k kilometres the fare is 4 + 2k. The letter k stands for any distance, so one expression covers every trip. Terms are the parts separated by plus or minus signs, so 4 + 2k has two terms. Variables can be any letters, though x, y and n are common.
A common mistake is treating 3x as if it were 3 and x written side by side, like the number 35. It actually means 3 times x. Another is thinking a variable always stands for one fixed value. In an expression it can take many values, whereas in an equation it may be limited. Writing a clear meaning for each letter keeps your work organised.
Key ideas
- Expressions combine numbers, variables and operations
- Terms are separated by + or −
- Coefficients multiply variables
Quick check
Use cases: where Variables and Expressions helps
- Homework: review the key idea behind Variables and Expressions before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Variables and Expressions without notes.
- Visual learning: play with the interactive lab to see how Variables and Expressions changes when you adjust its inputs.
- Teaching a friend: explain Variables and Expressions in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Variables and Expressions?
A variable is a letter that stands for an unknown or changing number.
What will I learn in Variables and Expressions?
Expressions combine numbers, variables and operations. Terms are separated by + or −. Coefficients multiply variables.
Is Variables and Expressions part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Variables and Expressions lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Variables and Expressions?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.