# Algebra Fundamentals 141

“Math: Algebra Fundamentals” provides a detailed overview of the basics of algebra, including the operations needed to solve a single variable equation. Basic algebra is used constantly in manufacturing, from the production floor to the accounting department.

Any time a number is unknown, algebra can be used to determine that missing value. Although algebra uses the same basic operations as other mathematics, there are several new operations used to find missing variables in problems. After taking this class, users will be able to simplify, factor, and balance basic equations, as well as calculate for missing values in equations with only one variable. The user will also be able to use algebra to create an equation based on a simple story problem.

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## Class Details

Class Name:
Algebra Fundamentals 141
Difficulty:
Beginner
Number of Lessons:
23

## Class Outline

• What Is Algebra?
• Variables
• Constants
• Order of Operations
• Grouping
• Symbols in Algebra
• Reducing Terms
• Reducing Terms: In Action
• Factoring
• Factoring: In Action
• Distributing
• Simplification Review
• Balancing
• Balancing: In Action
• Multiplication and Division
• Balancing Review
• Multiple Operations
• Algebra Review
• Creating Equations
• Formulas and Standards
• Working With Equations

## Objectives

• Describe the purpose of algebra.
• Define variable.
• Define constant.
• Describe the proper order of operations.
• Describe proper grouping.
• Explain the meaning of common symbols used in algebra.
• Demonstrate how to reduce like terms of an equation
• Demonstrate how to reduce like terms of an equation.
• Describe factoring in an algebra equation.
• Describe distribution in an algebra equation.
• Describe the process of balancing an equation.
• Describe the additive inverse in an algebra equation.
• Describe the multiplicative inverse in an algebra equation.
• Explain how to use exponents and radicals to solve an equation.
• Explain how to perform multiple operations to solve an equation.
• Explain how to change a story problem into an equation.
• Define formula and standard units.
• Explain how to calculate an unknown variable in a story problem.

## Glossary

Vocabulary Term Definition
additive inverse An addition or subtraction operation that removes a number or variable from an equation. The additive inverse is the opposite of the number or variable that is removed.
algebra A branch of math that uses known quantities to find unknown quantities. In algebra, letters are sometimes used in place of numbers.
area A measurement of the amount of space contained within a flat, enclosed shape. The area of a rectangle is equal to its height multiplied by its length.
balancing Introducing a series of new operations to both sides of an equation to solve for an unknown variable. Whichever operations take place on one side also must take place on the other.
common denominator A term or number that evenly divides all of the terms or numbers that appear below the lines in multiple fractions. The denominator is the term that appears below the line in a fraction.
constant A number that does not change value. Constants may be numbers, letters, or symbols.
distributing Multiplying the individual terms within a group by the same term outside of the group. The grouping symbols can be removed once all of the terms in the group have been multiplied.
distributing Multiplying the individual terms within a group by the same term outside of the group. The grouping symbols can be removed once all of the terms in the group have been multiplied.
exponent A mathematical notation indicating the number of times a quantity is multiplied by itself. Exponents are also known as powers.
expression A mathematical calculation or formula that includes numbers and/or variables using mathematical operations. Expressions do not include an equal side, but equations do.
factoring An operation in which the common number in a set of terms is factored or divided out. Factoring is one method of simplifying algebra equations.
formula A representation of a known equation using letters, numbers, and/or symbols. Common formulas are used to find the area or volume of shapes such as rectangles and cubes.
fraction bar The horizontal line that separates the numerator and denominator in a fraction. In a fraction, the fraction bar acts like a division symbol.
geometry The branch of mathematics that involves the measurements, properties, and relationships of all shapes and sizes of things. Common topics in geometry include lines and angles, triangles, and circles.
greatest common factor GCF. The largest term or number that evenly divides each term of an expression. For example, the GCF of 35 and 14 is 7.
grouping A method of organizing the sequence of mathematical operations by using symbols such as parentheses.
multiplicative inverse A multiplication or division operation that removes a number or variable from an equation. The multiplicative inverse is the reciprocal of the number or variable that is removed.
negative numbers A numbers less than zero that represents a reduction or absence of a quantity. Negative numbers include -1, -2, and -3.
nesting The placement of a group of terms within a larger grouping of terms.
numerator Expression in the top portion of a fraction, above the fraction bar. For example, in the fraction 2/5, 2 is the numerator.
operation A mathematical action or process. Common operations include addition, subtraction, multiplication, and division.
order of operations The mathematical rules that determine the correct order for solving any sequence of math operations. Powers and roots are solved before multiplication and division, which in turn are solved before addition and subtraction.
pi π. A special constant value that relates the diameter of a circle to its circumference. Pi is roughly 3.14 and is used to find the circumference and area of a circle.
powers A mathematical notation indicating the number of times a quantity is multiplied by itself. Powers are also known as exponents.
radical A mathematical symbol representing a root. A radical symbol resembles a checkmark.
reducing The combining of similar terms to simplify an equation. Reducing often takes place through addition and subtraction.
roots A mathematical operation indicating which unknown number, multiplied by itself a specific number of times, equals the number included inside the root sign. For example, the square root of 81 equals 9.
square root A mathematical function that indicates which unknown number is multiplied by itself one time. The square root of 49 is 7.
standard units The most commonly used units for measuring length, volume, or weight. There are different systems of standard units, such as metric and English.
terms Sets of numbers connected to each other through operations such as addition and subtraction.
variable A symbol, such as a letter of the alphabet, that represents an unknown quantity. In the equation x + 30 = 15, x is the variable.
volume A measurement of the amount of space contained within a three dimensional object. The volume of a cube is equal to its height multiplied by its width and length.