Variables & Expressions

Letters stand for numbers — translate, evaluate, and combine like terms.

The idea

A variable is a letter that stands for a number, so that one statement can speak for every value at once. An expression is anything built from variables and numbers by the ordinary operations.

A term is a number, a variable, or a product of the two, such as $2x$ or $-5$. The coefficient of a term is the number multiplying the variable, so in $2x$ it is $2$. Two terms are like terms when their variable parts are identical: $2x$ and $7x$, but not $2x$ and $7y$.

We do two things with an expression. To evaluate it, replace every variable by a given number and compute. To simplify it, rewrite it more shortly without changing any value it evaluates to; the main tool is combining like terms.

Combining like terms is counting: two of something plus seven of the same something is nine of it, so we add the coefficients and keep the variable part unchanged. Unlike terms count different things, so a sum such as $2x + 7y$ has no shorter form.

Ways to work on it

• Walkthrough. Translate words into expressions, evaluate them, and combine like terms.
• Practice. Evaluate and combine like terms with random values.
• Hardest. Evaluate at a negative value where signs matter.

Not sure where to start? Take the ten-question placement test.