Applying the 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. For engineers and scientists it is an essential requirement.

The fundamental concepts of algebra are described in the preceding section of this article. How these concepts may be applied to aid in the solution of various types of mathematical problems is explained here.

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 [say "positive 5"] or -5 [say "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:

A diagram such as this is often called a picture of the number line. The point labeled '0' is called the origin (see Numeration Systems and Numbers).

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.

As another example of how real numbers are used, consider 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.