5-3 Write Algebraic Expressions

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 $\frac{C}{4}$.

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

Like terms are terms in an algebraic expression that have the exact same variables raised to the exact same powers. Constant terms (numbers without variables) are also considered like terms.

Examples