. Practical mathematics : an elementary treatise covering the fundamental processes of arithmetic, algebra, and geometry, with a practical presentation of logarithms and curve plotting. > t» and f- 13- —» —»—,and—. m n mp np 8. J, f\, and T4T. 14. —, —,and—. xy xz yz 9. A, fi i> and 4- 15. —, —,and yz xy y ADDITION OF FRACTIONS 30. To add together two or more fractions, the fractional unitsmust be of the same size; in other words, they must be reduced to acommon denominator before the addition can be accomplished. For example, suppose it is desired to add the fractions — and — These may
. Practical mathematics : an elementary treatise covering the fundamental processes of arithmetic, algebra, and geometry, with a practical presentation of logarithms and curve plotting. > t» and f- 13- —» —»—,and—. m n mp np 8. J, f\, and T4T. 14. —, —,and—. xy xz yz 9. A, fi i> and 4- 15. —, —,and yz xy y ADDITION OF FRACTIONS 30. To add together two or more fractions, the fractional unitsmust be of the same size; in other words, they must be reduced to acommon denominator before the addition can be accomplished. For example, suppose it is desired to add the fractions — and — These may for convenience represent —and — of a foot. Now, it 4 o is well known that a foot contains 12 inches, and the — mav be con- 4 3 sidered a^ 3 inches or — of a foot, the — as 4 inches, or -— of a foot. 10 PRACTICAL MATHEMATICS The required sum is then 3 + 4=7 inches, or j = — 1 12T12 12 This process is graphically illustrated in Fig. 1. Fig. 1. Graphical Representation of Addition of Fractions Now if an example be taken in which there are more than two 5 7 fractions, it will be noted that the procedure is the same. — -j (- 8 12 11 3 r^r 4- -j- = ? It may be seen by inspection or by the process already given that 24 is the least common denominator of the several next step is to change the numerators of the fractions so thatthey will express the same value with the common denominator 24 5 15 as they now express with their respective denominators. — = —- tt: = ^rr- 7T-r will stand as written: -—- = -—-. Adding the several 12 24 24 4 24 8 numerators and placing the sum over the common denominator the r o required sum is found to be—, which is an improper fraction. Re-ducing the improper fraction to a mixed quantity gives 2^-f, or finally 9 5 Again, to add -—, —-3 and —— first find the least common de-2p 5p Sp . , . , . 0_ m, d 15d d 6d d lOdnominator, which is SOp. lhen — = —— ,*
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