041, 242. VULGAR FRACTIONS. EXAMPLES. 3. Reduce s and to al 5. Changes, and it to common denominator. fractions having a common 2X4-8 new nu. for ! denominator. 3X3–96 66 Ans. 196, 1 and 33. * 8X4=12 com. denom. 6. Express and of a then and Ans. | dollar in parts of a dollar of 4. Reduce , and to the same magnitude. a cuinmon denominator. Ans. ds and 241. TO REDUCE FRACTIONS TO THEIR LEAST COM MON DENOMINATOR. ANALYSIS 1. Reduce , , , and to their least common denominator. The common denominator found by ihe foregoing rule is a common multiple of the denominators of the given fractions, but wol always the least cominon multiple, and consequently not always the least (eommon denomipator. The least coinmon multiple of the denominators, 3, 4, 8 and 12 is 24" (238), which may be divided into titrds Fourthis, eighths and twelfths; for the new numerators we must therefore take such parts of 24 as are denoted by the given fractions; and this is done by dividing 24 by each of the denominators ( 238, 236, 2433, and 4 2), and multiplying the quotients by the respective numerators, 18X18, 6X3=18, 3X515, and 2x11= 2), and the new numerators 18, 18, 15 and 22) written over 24, the common denominator, give and 2 for the new fractions, baving the least possible common denominator. "Hence, 242. To reduce fractions of different denominators to equivalent fractions having the least common denominators. RULE.--Reduce the several fractions to their least terms (235). Find the least common multiple of all the denoninators for a common denominator. Divide the common denominator by the denominators of the several fractions, and multiply the quotients by the respective numerators, and the products will be the new numerators' required. QUESTIONS FOR PRACTICE. 2. What is the least com- ' 3. What is the least com. mon denominator of , 4 and | mon denominator of 1, 4 and Ans. , , - 2)2, 3, 4 4. What is the least com mon denominator off and 1, 3, 2 ? Ans. 14, t. Then 2x3x2=12, least 5. Express and of a common denominator. dollar in the least possible And | similar parts of a dollar. 12:2=6 and 6x1=6) Ans. $$ and . 12)(3=4 4X2-8 1 6. Reduce it is and to 12)|4=3 383-9 ) ( the least common denomina. Then 1983, 15, Ans. ltor. Ans. 125, tis, aga . 243. REDUCTION OF FRACTIONS. (52) ANALYSIS ...] 1. What part of a shilling 1. What part of a pound is is t of a pound? of a shilling? Pounds are reduced to shillings by To change shillings to pounds, dimultiplying them by 20 (138), and vide them by 20 (138). 20) = 4X 4 (220), and 1= (221), and Tho (235). (235). t of a pound, then, is of a shilling is, then, ? of a pound. of a shilling: DESCENDING, ASCENDING 244. To change fractions of 245. To change fractions of higher into those of a loxoer a lower into those of a higher denomination. denomination. RULE.-Reduce the numer - RULE.--Multiply the denomator to the lower denomina- | inator by the number which tion by. Art. 139, and write it is required to make one of the over the given denominator. 'next higher denomination, and so on (140); and write the last product under the given nu. merator. QUESTIONS FOR PRACTICE. 2. What part of a pound is! 2. What part of a cwh is dy of a cwt. ? $ of a pound ? 3X4X.28_336_6 6 6 3 392 3925 7X28X4734–394 Ans. Ans. 3. Reduce 4 of a pound 3. Reduce 49. to the frac. to the fraction of a penny. tion of a pound. 4. What part of a pound is 4. What part of a guinea of a guinea ? is of a pound ? 4 28 112 4 4 of 20_80_4 7 01 2014035 Ans. 5. What part of a rod is 5. What part of a mile 18 to of a mile ? 2 rods? 6. What part of a minute 6. What part of an hour is is +267 of an hour? 160f of a minute ? 7. What part of a pwt. is 7. What part of a pound is Toolb. Troy? of a pwt. ? 246. To reduce fractions to integers of a lower denomination, and the reverse. ANALYSIS. 1. Reduces of a pound to 1. Reduce 78. 60. to the shillings and pence. fraction of a pound. £?x20=60s. and 60s.-745.; 7s. 6d. 90d. £1=20$240d.: but 45.X12_480., and 48.d.-ud. then 7s. 6d.S£ =£3. Hence, *Then £3=7s. 6d. Hence, 247. To reduce fractions to l 248. To reduce integers to integers of a lower denomina- fractions of a higher denomination. |tion. RULE.-Reduce the numer- RULE.-Reduce the given · ator to the next lower denom- number to the lowest denomiination, and divide, by the de- nation mentioned for a numernominator; if there be a re- ator, and a unit of the higher mainder, reduce it still lower, denomination to the same for and divide as before:; the sev- | a denominator of the fraction eral quotients will be the an- required, gwer. ... QUESTIONS FOR PRACTICE. 2. In of a day, how many | 2. What part of a day are hours.? 8 hours ? In & of an hour, how 3. What part of an hour many minutes and seconds ? are 6m. 40s. ? 4. In g of a mile, how many 4. What part of a mile are rods? 120 rods ? 5. In 7 of an acre, how | 5. What part of an acre many roods and rods? J are 1 rood and 30 rods ? 249. ADDITION OF FRACTIONS. ANALYSIS 1. What is the sum of of a dollar and of a dollar ? As both the fractions are 9ths of the same unit, the magnitude of the parts is the same in both the nunber of parts, 3 and 4, may therefore be added as whole numbers, and their sum, 7, written over 9, thus, fi ex presses the sum of two given fractions 2. What is the sum of 4 of a yard and of a yard? As the parts denoted by the given fractions are not similar, we cannot add them by adding their numerators, 3 and 2, because the answer would be neither nor ; but if we reduce them to a common denominator, a becomes , and (240). Now each fraction denotes parts of the same unit, which are of the same magnitude, namely, 24ths; their numerators, 8 and 9, may therefore be added; and their sum, 17, being written pver 24 we have 47 of a yard for the sum of 2 and 8 of a yard. 250. To add fractional quantities. Rule.-Prepare them, wher necessary, by cbanging compound fractions to single ones (224), mixed numbers to improper fractions (218), fractions of different integers to those of the same (247, 248), and the whole to a common denominator (240); and then the sum of the numeratcrs written over the.common denominator, will be the sum of the fractions required. 251, 252. 103 251. SUBTRACTION OF FRACTIONS. : ANALYSIS. 1. What is the difference between of a dollar and % of a dollar ? By evidently expresses 2 tonths more than 3 tenths ; Zg then is the differenee. 2. What is the difference between & of a yard and of a yard? Here we cannot subtract from , for the same reason that we could not add them (49). We therefore reduce them to a common denominator, G ), and then the difference of the numerators (9-851), written over 24, the common denominator, gives at for the difference of the fractions. RULE. Prepare the fractions as for addition (250), and then the differcnce of the numerators written over the common denominator will be the difference of the fractions required. QUESTIONS FOR PRACTICE. 3. What is the difference. 6. From 964 take 146. between 4 and 1 ? Ans. 814 7. From 15 take g. 4. From zz take Ans. 187. Ans. 1. 8. From 7 weeks take 970 5. From take fe of days. Ans. 4. 1 Ans. 5w. 44. 7h. 12m. 252. RULE OF THREE IN VULGAR FRAC TIONS. ROLE.—Prepare the fractions by reduction, if necessary, and state the question by the general rule (198); invert the first term, and then maltiply all the numerators together for a new numerator, and all the denominators together for a new denominator; the new numerator, written over the new denominatot, will be the answer required. QUESTIONS FOR PRACTICE. 1. If şoz. cost £7, what is hyd. wide, will line 134 will loz. cost? yards of cloth that is 24 yde. M. £ 02. wide ? 1375 and 24= Extxt=£f=£1 1s. 91. 527: *** Ans. 2. How much shalloon that 1264=44yds. 6in. Ans. |