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Study Guides > Prealgebra

Introduction to Evaluating, Simplifying, and Translating Algebraic Expressions

A U.S 1040 individual tax return form with a pencil lying on top of it   Have you ever had to fill out a tax form when starting a new job or filing your tax return at the end of the year? It can be a puzzling task, with lots of instructions such as "enter the sum of line 20 and line 32 into line 33" or "enter the difference between line 8 and line 9 into line 10." The form might be telling you to do simple addition or subtraction, but it's not always obvious due to the wording used. In this section, you'll learn how to untangle algebraic expressions by identifying and combining like terms and translating words and phrases into familiar operations.  

Learning Outcomes

By the end of this section, you will be able to:
  • Evaluate algebraic expressions
  • Identify terms, coefficients, and like terms
  • Simplify expressions by combining like terms
  • Translate word phrases to algebraic expressions
  Before you get started in this module, try a few practice problems and review prior concepts.

readiness quiz

1) [ohm_question]144735[/ohm_question] If you missed this problem, review this example:
Determine if each is an expression or an equation:
  1. [latex]16 - 6=10[/latex]
  2. [latex]4\cdot 2+1[/latex]
  3. [latex]x\div 25[/latex]
  4. [latex]y+8=40[/latex]

Answer:

1. [latex]16 - 6=10[/latex] This is an equation—two expressions are connected with an equal sign.
2. [latex]4\cdot 2+1[/latex] This is an expression—no equal sign.
3. [latex]x\div 25[/latex] This is an expression—no equal sign.
4. [latex]y+8=40[/latex] This is an equation—two expressions are connected with an equal sign.

2) [ohm_question]144745[/ohm_question] If you missed this problem, review this example:
Simplify: [latex]{3}^{4}[/latex].

Answer:

[latex]{3}^{4}[/latex]
Expand the expression. [latex]3\cdot 3\cdot 3\cdot 3[/latex]
Multiply left to right. [latex]9\cdot 3\cdot 3[/latex]
[latex]27\cdot 3[/latex]
Multiply. [latex]81[/latex]

3) [ohm_question]144748[/ohm_question] If you missed this problem, review the video below. https://youtu.be/qFUvF5-w9o0

Licenses & Attributions

CC licensed content, Shared previously

  • Form 1040. Authored by: Philip Taylor. Located at: https://www.flickr.com/photos/9731367@N02/6988157282/. License: CC BY: Attribution.
  • Ex: Evaluate an Expression Using the Order of Operations. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
  • Question ID: 144735, 144745, 144748. Authored by: Alyson Day. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.

CC licensed content, Specific attribution