Learners review the fundamental laws of algebra including the commutative law of addition, the commutative law of multiplication, the associative law of addition, the associative law of multiplication, and the distributive law. Examples are given.

In this animated object, learners examine the concept of gear ratios. The number of teeth, diameters, and velocity relationships are discussed and calculated using linear ratio equations. A quiz completes the activity.

Solving Systems of Linear Equations Using the Substitution Method

In a series of practice problems, learners use the substitution method to solve systems of linear equations, also called "simultaneous linear equations."

Learners read definitions of the terminology associated with algebraic operations and then follow steps to use the fundamental laws of division to simplify algebraic expressions.

Simplifying Algebraic Fractions that Contain Addition and/or Subtraction

In this interactive object, learners follow step-by-step instructions for reducing algebraic fractions, which contain addition and/or subtraction, to their simplest form. This activity has audio content.

Learners follow step-by-step instructions for finding the lowest common denominator for a group of algebraic fractions and then enter their answers to three problems. Immediate feedback is provided. This activity has audio content.

In part 2 of this series, learners follow the steps of the “mathemagician” to examine these numerical curiosities: The 189 Challenge; An Armstrong Number: What’s Special About 153? Is 495 Different or Indifferent? Is 6174 Different or Indifferent? It is always 618, and Beginning and Ending the Same.

An Algebraic Word Problem Involving Motion: Case 2

In this animated object, learners use an algebraic formula to solve the following problem: An airplane travels a certain distance with the wind in the same amount of time that it takes to travel a shorter distance against the wind. Given a constant wind speed, what is the speed of the plane without a wind?

Learners read definitions of the terminology associated with algebraic operations and then follow steps to use the fundamental laws of multiplication to simplify algebraic expressions.

Simplifying Algebraic Fractions that Contain No Addition or Subtraction

In this highly interactive and animated object, learners follow a step-by-step process to reduce algebraic fractions, which contain no addition or subtraction, to their simplest, most elementary form. Immediate feedback is provided. This activity has audio content.

Learners follow step-by-step instructions for dividing algebraic fractions. They begin by reducing the fractions to their simplest form. Immediate feedback is provided. This activity has audio content.

Finding the Lowest Common Denominator for Algebraic Fractions

In this interactive and animated object, learners follow instructions for finding the lowest common denominator for a group of algebraic fractions. Immediate feedback is provided. This activity has audio content.