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1. Absolute Value of Complex Numbers
2. Absolute Value Equations
3. Absolute Value Inequalities
4. Adding and Subtraction Algebraic Fractions
5. Addition and Subtraction of Complex Numbers
6. Addition and Subtraction of Polynomials
7. Addition or Subtraction Sign
8. Algebra Word Problems
9. Algebraic Solutions to Linear Systems
10. Algebraic Solutions to Simultaneous Equations
11. Algebraic Translations
12. Applied Problems of Inequalities
13. Approximations of Irrational Numbers
14. Associative Property
15. Basic Algebra
16. Basic Counting Principle
17. Binary Operations
18. Closure Property
19. Combining Like Terms (Difficult)
20. Combining Like Terms (Simple)
21. Commutative Property
22. Completing Truth Tables
23. Conditionals [asks for Logic Table]
24. Conjunctions [asks for Logic Table]
25. Counting Principle
26. Cyclic Nature of the Powers of i
27. Determine the Value of Compound (Composite) Functions
28. Disjunctions Using Logic Tables
29. Distributive Property
30. Division of Polynomials by Monomials
31. Definition of a Function
32. Direct Variation
33. Evaluating Expressions
34. Evaluate Expressions with Fractional Exponents
35. Evaluating Formulas
36. Evaluating Variable Expressions
37. Factorial Notation
38. Factorials
39. Find the Square Root
40. Follow Math Directions
41. Function Tables
42. Function Tables with Missing Elements
43. Graphs of Linear Equations
44. Imaginary Units
45. Introduction to Properties of Real Numbers
46. Like Terms
47. Linear-Quadratic Systems
48. Magic Subtraction Cubes
49. Making Sums and Differences
50. Missing Addition or Subtraction Sign
51. Multiplication and Division of Algebraic Fractions
52. Multiplying and Dividing Complex Numbers
53. Multiplication/Division with Scientific Notation
54. Multiplication Math Puzzles
55. Multiplying Polynomials
56. Number line Expressions
57. Number Operations
58. Operations with Signed Numbers
59. Organizing and Interpreting Data
60. Percentiles and Quartiles
61. Polynomial Word Problems
62. Properties of Real Numbers
63. Radical Equations
64. Radical Operations
65. Rational and Irrational Numbers
66. Set-Builder and Interval Notation
67. Signed Number Word Problems
68. Simplify Radicals
69. Simplifying Square Roots with Negative Numbers
70. Simplifying and Reducing Algebraic Fractions
71. Simplify Expressions
72. Simplify Equations
73. Slope of a Line
74. Solve for the Unknown
75. Solving Exponential Equations That Lack a Common Base
76. Solving Equations
77. Solving Inequalities by Adding and Subtracting
78. Solving Inequalities by Multiplying and Dividing
79. Solving Multi - Step Equations
80. Solving Exponential Equations
81. Solving Factorable Quadratic Equations
82. Solving Linear Inequalities
83. Standard Numbers From Complex Numbers
84. Systems of Linear Inequalities
85. Truth Values
86. Truth Values of Compound Sentences
87. Truth Values of Open Sentences
88. Variable Expressions
89. Visual Binary Operations
90. Visual Expressions
91. Working with Translations
92. Writing Linear Equations
93. Writing Sentences as Equations
94. Writing Two-Step Equations

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What is algebra?

Algebra is a method for finding answers to questions about how much, how often or how many.

It does this in two steps. The first step is changing a problem described in words into the same problem described by numbers and symbols. A kind of short-hand recipe that keeps the important information. The second step is using the rules of algebra to change the symbols and numbers around. Done correctly, this shuffling makes the problem easier to understand and answers the original question.

One of the key ideas is to use letters in place of numbers that aren't yet known. By using X or Y to stand in the place of something unknown (or something that can change) the algebraic expression can show us how things are related - even when we don't know exactly how many of those things we have.

Suppose you are interested in how many feet are on six dogs. (Maybe you want to buy them shoes?) You count the feet on one dog (4) and multiply by the number of dogs you have (6). The recipe looks like this: 4 x 6 = 24. Twenty-four feet total.

Algebra introduces the idea of variables. So that this one recipe (for six dogs) could be made into a more general recipe, or formula, for any number of dogs.

Put D for the number of dogs and F for the total number of feet. Then, you get the algebraic formula: 4 x D = F. This works for 6 dogs, or 20 dogs, or any number of dogs at all. It even works for zero dogs. But there is more. The rules of algebra allow us to shuffle the formula around. So, we could rearrange it to show how many dogs we would need to get a certain number of feet. F 4 = D.

How is algebra used in the real world?

Algebra is used to answer all sorts of questions.

• If gas costs X dollars a gallon, and I get Y miles per gallon, how much will it cost me to go a hundred miles?
• How long will it take to do my math homework if I can do X problems in an hour?
• If I can print Y pages a minute on my printer, how many pages can I print in a half-hour?
• If electricity costs X cents, and my computer uses Y amount of electricity, how much does it cost to leave my computer on all day?

A basic problem in algebra.

A common calculation people do is figuring out their mileage. They want to know how many miles per gallon their car is getting. If you asked, they probably wouldn't think of it as algebra, but it is.

In words, the problem is this: I used 15 gallons of gas to go 330 miles, how many miles am I getting per gallon?

Putting this into an algebraic formula (using M to stand for miles and G to stand for gallons) would look like this: M G = miles per gallon.

Using the actual numbers where the letters are gives the answer: 330 15 = 22. The neat thing is that no matter how many miles you drive or how many gallons of gas you use, the formula will still work.

Who invented algebra?

The roots of algebra go back more than a thousand years. Many of the ideas were around even longer, but in 800 AD, a Persian mathematician, Al-Khwarizmi, wrote a book which explained the methods clearly. He described the use of symbols and how to manipulate them in a regular fashion. So, although no one really invented algebra - it grew up over many centuries of problem solving - Al-Khwarizmi is considered one of the 'fathers of algebra'.

An interesting fact about algebra.

The word 'algebra' comes to us from the title of Al-Khwarzmi's book. The Persian word is al-jabr and means something like 'reunite' or 'gather back together'. He used it to explain how quantities in equations could change around and still keep their relationships to each other.