In mathematics, especially in algebra, we look for patterns in the numbers that we see. Using mathematical verbs and variables, expressions can be written to describe a pattern. An algebraic expression is a mathematical phrase combining numbers and/or variables using mathematical operations. We can describe patterns using phrases as well, and we want to be able to translate these phrases into algebraic expressions.
Consider a theme park charging an admission of $28 per person. A rule can be written to describe the relationship between the amount of money taken at the ticket booth and the number of people entering the park. In words, the relationship can be stated as “The money taken in dollars is (equals) twenty-eight times the number of people who enter the park.”
The English phrase above can be translated (written in another language) into an algebraic expression. Using mathematical verbs and nouns learned from previous lessons, any phrase can be written as an algebraic expression.
Write an algebraic expression for the following phrase.
Write an expression to describe the amount of revenue of the theme park described above.
Some phrases are harder to translate than others.
Translate the phrase "5 less than 2 times a number."
Algebraic expression: An algebraic expression is a mathematical phrase combining numbers and/or variables using mathematical operations.
A student organization sells shirts to raise money for events and activities. The shirts are printed with the organization's logo and the total costs are $100 plus $7 for each shirt. The students sell the shirts for $15 each. Write an expression for the cost and an expression for the revenue (money earned).
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Patterns and Equations (13:18)
For exercises 1 – 15, translate the English phrase into an algebraic expression. For the exercises without a stated variable, choose a letter to represent the unknown quantity.
In exercises 16 – 24, write an English phrase for each algebraic expression
In exercises 25 – 28, define a variable to represent the unknown quantity and write an expression to describe the situation.
Use your sense of variables and operations to answer the following questions.