# 1.6: Patterns and Expressions

**Basic**Created by: CK-12

**Practice**Patterns and Expressions

Jeremy read that degrees Celsius converted to degrees Fahrenheit is "the sum of 32 and

### Guidance

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.

#### Example A

Write an algebraic expression for the following phrase.

*The product of c and 4.*

**Solution:**

The verb is *product*, meaning “to multiply.” Therefore, the phrase is asking for the answer found by multiplying

#### Example B

Write an expression to describe the amount of revenue of the theme park described above.

**Solution:**

An appropriate variable to describe the number of people could be

Some phrases are harder to translate than others.

#### Example C

*Translate the phrase "5 less than 2 times a number."*

**Solution:**

The word *less* lets you know that you are going to take away, or subtract, a number. Many students will want to turn this expression into

### Vocabulary

**Algebraic expression:** An ** algebraic expression** is a mathematical phrase combining numbers and/or variables using mathematical operations.

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### Guided Practice

*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).*

**Solution:**

We can use

### Video Review

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### Practice

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.

### My Notes/Highlights Having trouble? Report an issue.

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algebraic expression

An**is a mathematical phrase combining numbers and/or variables using mathematical operations.**

*algebraic expression*Algebraic Equation

An algebraic equation contains numbers, variables, operations, and an equals sign.domain

The domain of a function is the set of -values for which the function is defined.Equation

An equation is a mathematical sentence that describes two equal quantities. Equations contain equals signs.horizontal axis

The horizontal axis is also referred to as the -axis of a coordinate graph. By convention, we graph the input variable on the -axis.Range

The range of a function is the set of values for which the function is defined.Variable

A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a, b, x, y, m, and n.vertical axis

The vertical axis is also referred to as the -axis of a coordinate graph. By convention, we graph the output variable on the -axis.### Image Attributions

Here you'll learn how to take an English phrase and produce an equivalent algebraic expression. You'll also practice taking an algebraic expression and producing an equivalent English phrase.