= tain 4 of these parts. Hence, in. in. In this case, we make the denominator of the fraction 4 times as large, by making 4 times as many parts in the whole. It then takes a numerator 4 times as large to represent the same fractional part of an inch. This relation holds whether we are dealing with inches or with any other thing as a unit. 10. Reduction to Higher Terms.-When we raise a fraction to higher terms, we increase the number of parts in the whole, as just shown, and this likewise increases the number of parts taken. Therefore, the numerator and denominator both become larger numbers. A fraction is raised to higher terms by multiplying both numerator and denominator by the same number. 3 16 Suppose we want to change of an inch to 64ths. To get 64 for the denominator, we must multiply 16 by 4 and, therefore, must multiply 3 by 11. Reduction to Lower Terms.-When we reduce a fraction to lower terms, we reduce the number of parts into which the whole unit is divided. This likewise reduces the number of parts which are taken. A fraction is reduced to lower terms by dividing both numerator and denominator by the same number. When there is no number which will exactly divide both numerator and denominator, the fraction is already in its lowest terms. There is no number that will exactly divide both 9 and 32 and, therefore, the fraction is reduced to its lowest terms. 12. Reduction of Improper Fractions.-When the numerator of a fraction is just equal to the denominator, we know that the value of the fraction is 1 (see Art. 6): In each of these cases we have taken the full number of parts into which we have divided the unit. Consequently, each of these fractions is one whole unit, or 1. When the numerator is greater than the denominator, the value of the fraction is one or more units, plus a proper fraction, or a whole plus some part of a whole. From these examples we may see that to reduce an improper fraction to a whole or mixed number the simplest way is as follows: Divide the numerator by the denominator. The quotient will be the number of whole units. If there is anything left over, or a remainder, write this remainder over the denominator since. it represents the number of parts left in addition to the whole units. We now have a mixed number, or an exact whole number, in place of the improper fraction. These show that a fraction represents unperformed division. In fact, division is often indicated in the form of a fraction. The numerator is the dividend and the denominator is the divisor. 13. Reduction of Mixed Numbers.-It is often necessary or desirable to change mixed numbers to improper fractions. The method of doing this may be seen from the following examples. If 7 17 1 4 were to be reduced to an improper fraction we would say: Since there are 4 fourths in 1, in 7 there are 4×7, or 28 fourths. 28 fourths plus 1 fourth equals 29 fourths." The rule which this gives us is very simple: Multiply the whole number by the denominator of the fraction and write the product over the denominator. This reduces the whole number to a fraction. Add to this the fractional part of the mixed number. The sum is the desired improper fraction. In working problems like the above, the work should be arranged as in the following example. Note.-Thirty days are generally considered as one month, though the number of days differs for different months. 2. Name some fractions of an inch commonly used. 3. Write the following as fractions or mixed numbers. Five-sixteenths 5. Indicate the proper fractions, the improper fractions, and the mixed numbers among the following: 9. Reduce the following mixed numbers to improper fractions: in.? 4 3 3 10. Reduce the following improper fractions to whole or mixed numbers: 11. I want to mix up a pound of solder to be made of 5 parts zinc, 2 parts tin, and 1 part lead. What fraction of a pound of each metal-zinc, tin and lead-must I have? 12. If a train is running at the rate of a mile a minute, how many feet does it go in 1 second? 13. An apprentice who is drilling and tapping a cylinder for in. studs, 7 .8 3 tries a 14. The tubes in a certain boiler are 15 ft. 11 in. long. How many inches long are they? 15. How many seconds in an hour? 40 seconds is what fraction of an hour? 16. An 8-ft. bar of steel is cut up into 16 in. lengths. What fraction of the whole bar is one of the pieces? 17. When a man runs 100 yd. in 10 seconds, how many feet does he go in 1 second? 18. Wood screws are generally put up in boxes containing one gross. If 36 screws are taken from a full box for use on a certain job, what fraction of the gross is used on this job and what fraction is left in the box? Reduce both fractions to their lowest terms. 19. A steel plate 2 ft. 6 in. wide is to be sheared into four strips of equal width. How wide will each strip be in inches? 20. In one plant all drawings are dimensioned in inches, while in another all dimensions above 2 ft. are given in feet and inches. If a dimension is given as 89 in. in the first plant, how would the same dimension be stated in the other plant? |