Lesson 2: Variables, Constants, and Algebraic Expressions

Property

A variable is a letter that represents a number or quantity whose value may change.
A constant is a number whose value always stays the same.
In algebra, letters of the alphabet are used to represent variables. Letters often used for variables are $x$, $y$, $a$, $b$, and $c$.

Examples

• In the expression $c+5$, $c$ is the variable because its value can change, and $5$ is the constant because its value is fixed.
• If a movie ticket costs 8 dollars, the number of tickets you buy is a variable ($t$), but the price of each ticket is a constant (8 dollars).
• Sarah is 5 years younger than her brother, Mark. If Mark's age is $m$, Sarah's age is $m-5$. Here, $m$ is a variable and $5$ is a constant.

Explanation

In algebra, we use letters (variables) for numbers that can change, like your height. Numbers that always stay the same, like the number of days in a week, are constants. This helps us write rules for changing situations.

Property

In an algebraic expression, terms are the parts separated by addition or subtraction signs. The coefficient is the numerical factor of a term that contains a variable. A term without a variable is called a constant.

Examples

Property

An algebraic expression is the same as an arithmetic expression, except that some of the entries are letters representing numbers.
An algebraic expression, or simply an expression, is any meaningful combination of numbers, variables, and operation symbols.

To write an algebraic expression:

1. Identify the unknown quantity and write a short phrase to describe it.
2. Choose a variable to represent the unknown quantity.
3. Use mathematical symbols to represent the relationship.

Examples

• The phrase "a number x increased by 12" translates to the expression $x + 12$.
• To represent "8 times the price p", you write the expression $8p$.
• "The total cost C split among 4 friends" is written as the expression $\frac{C}{4}$.