Algebraic Expressions: Translating Verbal Phrases

Algebraic Expressions

Definition of an Algebraic Expression

• An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols (such as +, -, *, /). It does not have an equality sign.

Task: Writing Algebraic Expressions

• The exercise requires us to translate a verbal phrase into an algebraic expression.

Example Phrase: "Eighteen more than a number"

• Unknown Variable Identification: Let the variable we are working with be denoted as x.

• Translation: The phrase "Eighteen more than a number" can be interpreted as follows:

  • Step 1: Identify the unknown number, represented by x.
  • Step 2: Apply the phrase structure: "more than" indicates an addition operation. Therefore, we need to add 18 to the unknown number.
  • Final Algebraic Expression: The final expression becomes:

  $ext{x} + 18$

Additional Notes

• The process of translating phrases into algebraic expressions often requires an understanding of key phrases indicating mathematical operations:

  • "more than" implies addition.
  • "less than" implies subtraction.
  • "times" or "product" implies multiplication.
  • "divided by" or "quotient" implies division.

• Importance of Variables: Using variables (like x) is crucial in algebra to represent unknown quantities and formulate expressions that can be solved or manipulated mathematically.

• Examples of similar phrases:

  • Twelve less than a number would be represented as: $ext{x} - 12$
  • Three times a number would be represented as: $3 imes ext{x}$ or $3 ext{x}$

• Contextual Application: Understanding how to create algebraic expressions from verbal phrases is a foundational skill in algebra that applies to problem-solving in various contexts, including real-world applications such as calculating costs, determining quantities, and analyzing data.