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# Rational Numbers

 In this chapter you will deal with rational numbers. John has red twice as many books as Bill. John has read 7 books. How many books has Bill read? This problem is easily translated into the equation 2n=7, where n represents the number of books that Bill has read. If we are allowed to use only integers, The equation 2n=7 has no solution. This is an indication that the set of integers does not meet all of our needs. A rational number is a quotient of two integers (divisor and zero). The rational number can be named by fractions. We might define a rational number as many named a/n where a and n name integers and n?0. Every fraction has a numerator and denominator. The denominator tells you the number of parts of equal size into which some quantity is to be divided. The numerator tells you how many of these parts are to be taken. Fractions representing values less than 1, like 2/3 for example, are called proper fractions. Fractions which name a number equal to or greater than 1, like 2/2 or 2/3, are called improper fractions. There are numerals like 1?(one and one second), which name a whole number and a fractional number. Such numerals are called mixed fractions. Fractions, which represent the same fractional number like ?, 2/4, 3/6, 4/8, and so on, are called equivalent fractions. We have already seen that if we multiply a whole number by I we shall leave the number unchanged. The same is true of fractions since we multiply both integers named in fraction by the sane number we simply produce another name for the fractional number. You may conclude that dividing both of the numbers named by the numerator and the denominator by the same number, not 0 or 1 leaves the fractional number unchanged. The process of bringing a fractional number to lower terms is called reducing a fraction. To reduce a fraction to lowest terms , you are to determine the greatest common factor. The greatest common factor is the largest possible integer by which both numbers named in the fraction are divisible.
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