About This Chapter
Basic Algebraic Concepts & Practice - Chapter Summary
Study this chapter to review and practice basic algebra concepts. As you move through the chapter, you'll study variables, equations, algebraic expressions, linear equations and more. Our instructors walk you through the steps needed to solve word problems involving percents, proportions, ratios, fractions and whole numbers. After studying this collection of basic algebra lessons, you'll be able to:
- Know what an algebraic variable is
- Define a math equation
- Evaluate simple algebraic expressions
- Understand linear equations
- Graph and solve linear inequalities
- Solve word problems that use algebraic addition or multiplication expressions
- Complete multiple-step word problems
- Answer word problems that use percents
- Perform calculations with ratios and proportions
- Simplify word problems with fractions using whole numbers
- Express relationships as algebraic expressions
You can get extra practice applying these algebra concepts by taking the self-assessment quizzes that follow each lesson. You can solidify your understanding of these concepts by printing lesson transcripts that highlight key definitions, formulas and steps. We've included an intuitive Dashboard and interactive timelines to help you easily find particular topics. Reviewing and studying basic algebra is simple and convenient with bite-sized lessons that are available at any time of day. You can also access these study materials on any desktop, laptop, smartphone or tablet.
1. What is a Variable in Algebra?
Did you ever encounter something like a + b = c and wonder how all these letters snuck into a math problem? In this lesson, we'll learn about variables, as well as other parts of equations, constants and coefficients.
2. What is an Equation in Math? - Definition & Examples
In this lesson, you'll get a refresher on number sentences. You will then learn what equations are and how they can be useful in finding out missing information.
3. Evaluating Simple Algebraic Expressions
In this lesson, we'll learn how to evaluate algebraic expressions, which involves substituting numbers for variables and following the order of operations. By the end of the lesson, you'll be an algebraic expression expert.
4. What is a Linear Equation?
Most cars won't be able to run for more than 250,000 miles, so how much longer will your car live? Linear Equations are the most basic kind of algebraic function and can help you answer questions exactly like this. Learn about what they look like, how they come up in your life and why they are powerful tools.
5. Linear Inequality: Solving, Graphing & Problems
If you can solve linear equations, you can solve linear inequalities. In this lesson, you will learn how similar the solving processes are. You will also learn the notations you need to use when graphing linear inequalities.
6. Solving Word Problems with Algebraic Addition Expressions
After going over this lesson, you will be able to solve addition word problems. You will know how to write an algebraic expression that you can solve to find your answer.
7. Solving Word Problems with Algebraic Multiplication Expressions
Watch this video lesson to learn how you can solve word problems that involve the multiplication operation. Learn how to write your expression and then how to solve the expression to find your answer.
8. Solving Word Problems with Multiple Steps
Not all word problems are so straightforward that they only require you to do one operation and you're done. Some are more complicated, requiring several steps. Watch this video lesson to learn how to solve these kinds of problems.
9. How to Solve Word Problems That Use Percents
100 percent of percent problems can be solved if we follow the correct steps. In this lesson, we'll practice solving a variety of different percent problems.
10. Calculations with Ratios and Proportions
Even if only 99 out of 100 people need to know how to work with ratios, the odds that they'll be useful to you are very high. In this lesson, we'll practice performing calculations with ratios and proportions.
11. How to Simplify Word Problems with Fractions Using Whole Numbers
Watch this video lesson to learn how to solve word problems with fractions in them easily by turning your fractions into whole numbers. Learn what you need to do to get rid of your fractions so you can easily solve your problem.
12. Expressing Relationships as Algebraic Expressions
What do you do when you don't know what a number is but you do know how it relates to something else? You use an algebraic expression. In this lesson, we'll learn how to express relationships as algebraic expressions.
13. Linear & Direct Relationships
Learn how to tell when you're dealing with linear and direct relationships and what graphs of these relationships should look like. Then, go further and explore how to interpret the slopes of these graphs.
14. What is an Inequality?
Deciding how to spend your money can be a tricky thing. Should you save it, invest it, or enjoy it? Learn how inequalities can help you make your decision!
15. Evaluating Validity of Nonstandard Computational Strategies
In math, there is no one right way to solve a problem. There are multiple paths we can take to reach a correct solution. However, some paths lead to incorrect solutions. Learn about evaluating these different types of paths in this lesson.
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Other chapters within the MTEL General Curriculum (03): Practice & Study Guide course
- History of the English Language
- Basic Grammar & Mechanics
- Teaching Literature & Literary Analysis
- Literary Genres
- Literary Elements & Concepts
- Children's Literature Genres & Characteristics
- The Writing Process
- Writing Styles & Techniques
- Paleolithic Era to the Agricultural Revolution
- Early Civilizations & the Rise of Western Imperialism
- Modern World History Overview
- The Start of the United States
- American History 1800 to 1900
- American History 1900 to 1950
- American History 1950 to Present Day
- US & Massachusetts Government
- Fundamentals of Economics & Capitalism
- Geography & Human Settlements
- Principles of Life Sciences
- Principles of Physical Science
- Earth & Space Science
- Foundations of Scientific Thought
- Scientific Inquiry & Experimentation
- The Number System
- Fractions, Decimals & Percents Overview
- Factoring & Divisibility Rules
- Number Operations
- Introduction to Functions & Graphs
- Understanding & Solving Linear Functions
- Concepts of Measurement
- Geometric Shapes & Principles
- Understanding Descriptive Statistics
- Understanding Probability
- MTEL General Curriculum Flashcards