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FRACTIONS, DECIMALS,
AND PERCENTAGES The most general definition of a fraction states that "a fraction is an indicated division. " Any division may be indicated by placing the dividend over the divisor with a line between them. By the above definition, any number, even a so-called "whole" number, may be written as a common fraction. The number 20, for example, may be written as 20/1. This or any other fraction that amounts to more than 1 is an IMPROPER fraction. For example, 8/3 is an improper fraction, The accepted practice is to reduce an improper fraction to a mixed fraction (a whole number plus a proper fraction). Perform the indicated division and write the fractional part of the quotient in its lowest term. In this case, 8/3 would be 2 2/3. A fraction that amounts to less than 1 is a PROPER fraction, such as the fraction 1/4. To refresh your memory, we are including the following rules in the solution of fractions: 1. If you multiply or divide both the numerator and denominator of a fraction by the same number, the value does not change. The resulting fraction is called an EQUIVALENT fraction. 2. You can add or subtract fractions only if the denominators are alike. 3. To multiply fractions, simply find the prod-ucts of the numerators and the products of the denominators. The resulting fractional product must be reduced to the lowest term possible. 4. TO divide a fraction by a fraction, invert the divisor and proceed as in multiplication. 5. The method of CANCELING can be used to advantage before multiplying fractions (using the principle of rule No. 1) to avoid operations with larger numbers. A decimal fraction is a fraction whose denominator is 10 or some power of 10, such as 100, 1,000, and so on. For example,
are decimal fractions. Accordingly, they could be written as 0.7, 0.23 and 0.087 respec-tively. Decimal fractions have certain char-acteristics that make them easier to use in computations than other fractions. Chapter 5 of NAVEDTRA 10069-D1 deals entirely with decimal fractions. A thorough understanding of decimals will be useful to the Engineering Aid in making various engineering compu-tations. Figure 1-1 shows decimal equivalents of fractions commonly used by Builders, Steelworkers, Utilitiesmen, and other trades.
Figure 1-1. Decimal equivalents.
Figure 1-2.-2-percent grade. In connection with the study of decimal fractions, businessmen as early as the fifteenth century made use of certain decimal fractions so much that they gave them the special designation PERCENT. The word percent is derived from per centum, which means "by the hundredths." In banking, interest rates are always expressed in percent; statisticians use percent; in fact, people in almost all walks of life use percent to indicate increases or decreases in production, population, cost of living, and so on. The Engineering Aid uses percent to express change in grade (slope), as shown in figure 1-2. Percent is also used in earthwork computations, progress reports, and other graphical representa-tions. Study chapter 6 of NAVEDTRA 1-0069-D1 for a clear understanding of percentage. |
 
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