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Fundamental Concepts of Algebra
    An understanding of the fundamental concepts of algebra and of how those fundamental concepts may be applied is necessary in many professional and most technical careers. Algebra is an essential requirement for engineers and scientists.

    How the fundamental concepts may be applied to aid in the solution of various types of mathematical problems is explained in the following topics.




USING REAL NUMBERS

    An example of the use of real numbers is in the measurement of temperatures. If it is a very cold day, it may not be enough to tell someone that the temperature is 5 degrees; you may have to indicate whether it is 5 degrees "above zero" or 5 degrees "below zero."

    You may use the real numbers +5 ["positive 5"] or -5 ["negative 5"] to indicate the temperature. The degree temperatures "above zero" are measured by positive real numbers, and the degree temperatures "below zero" are measured by negative real numbers.



It may help to picture the set of real numbers as the set of points on a line:

Set of Real Numbers

A diagram like this is often called a picture of the number line. The point labeled '0' is called the origin.

The number-of-arithmetic 5 is the arithmetic value of the real numbers +5 and -5. The numbers-of-arithmetic are used as measures of magnitude; the real numbers are used as measures of magnitude and direction.

Another example of how real numbers are used would be the measurement of distances above and below sea level. The elevation of Mount McKinley is 20,320 feet above sea level, measured by the real number +20,320. Death Valley has an elevation of 282 feet below sea level, measured by the real number -282. The elevation at sea level is 0; distances above sea level are measured by positive real numbers, and distances below sea level are measured by negative real numbers.




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Real Numbers

Formulas, Functions, Graphs

Linear Functions

Quadratic Functions

Functions of Higher Degree

Properties of Exponents

Products and Factoring

Quadratic Equations

Solving Problems

Algebra Fundamentals