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Algebra Worksheets

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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.

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