QUESTIONS FOR PRACTICE. 2. What part of a pound | 2. What part of a cwt is is op of a cwt. ? 16 of a pound? 3x4x28_-336_6 6 6 3 392 3927 Ans. ị Tx28x4784392 ABS. 9. Reduce of a pound | 3. Reduce 4.. to the to the fraction of a penny. | fraction of a pound. 4. What part of a pound is 4. What part of a guinea of a guinea? is of a pound? of 38=148= Ans. 5. What part of a rod is 5. What part of a mile is bio of a mile? 1 2 rods ? . 6. What part of a min-1 6. What part of an hour ute is that an hour ? is test of a minute ? 7. What part of a pwt. is 7. What part of a pound Tbzolb. Troy? j is of a pwt. ? 246. To reduce fractions to integers of a lower denomination, and the reverse. . ANALYSIS. 1. Reduce of a pound 1. Reduce 78. 6d, to the to shillings and pence. fraction of a pound. x20=6 s. and 695 78. 6d.=90d. £1=208. =745. but s. X12=4&d. | =240d. then 7s. 6d. l. and 48 d.=6d. Then = =£ Hence, 78. 6d. Hence 248. To reduce integers to 47. To reduce fractions to 1 fractions of a higher denomina integers of a lower denomina- | tion. RULE._Reduce the given RULL-Reduce the numer | number to the lowest denomiator to the next lower denom nation mentioned for a numer. ipation, and divide by the de. I ator, and a unit of the higher pominator; if there be a re- l denomination to the same for mainder, reduce it still lower | a denominator of the fraction and divide as before: the sev. i required. oral quotients will be the anmer. 249, 250. VULGAR FRACTIONS: 157 QUESTIONS FOR PRACTICE., 2. In } of a day, how 1 2. What part of a day many hours ? are 8 hours ? 3. In of an hour, how 3. What part of an hour many minutes and seconds? | are 6m. 408. ? 4. In of a mile, how 4. What part of a mile many rods ? are 120 rods ? 5. In Je of an acre, how | 5. What part of an acre many roods and rods ? are 1 rood and 30 rods ? AN 249. ADDITION OF FRACTIONS. ANALYSIS. 1. What is the sum of of a dollar and of a dollari As both the fractions are 9ths of the same unit, the magnitude of the parts is the same in both the number of parts, 3 and 4, may therefore be added as whole numbers, and their sum, 7, written over 9, thus y, expresses the sum of two given fractions. 2. What is the sum of 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, e becomes , and g, (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 over 24, we have # of a yard for the sum of and of a yard. 250. To add fractional quantities. RULE. --Prepare them, when necessary, by changing 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 numerators written over the common denominator, will be the sum of the fractions required. 251. SUBTRACTION OF FRACTIONS. ANALYSIS. .. 1. What is the difference between ty of a dollar and Po of a dollar? * evidently expresses 2 tenths more than 3 tenths ; then is the difference, 2. What is the difference between a 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, (9 9 ) and then the difference of the numerators, (9-8 1) written over 24, the common denominator, gives t for the difference of the fractions. RULE. Prepare the fractions as for addition,(250) and then the difference of tbe numerators written over the common de nominator will be the difference of the fractions required. QUESTIONS FOR PRACTICE. * 3. What is the difference | 6. From 961 take 147. between and P Ans. 8116 - = - =i, Ans. ! 7. Froin 48 take of 4. From take the Aus. ist Ans. 4. 8. From 7 weeks take 5. From take fof. 97 days. Ans. $. ! Aps. 5w. 4d. 7h. 19m. 257. $59 252. RULE OF THREE IN VULGAR FRAC TIONS. RULE. Prepare the fractions by reduction, if necessary, and state the questionby the general rule (198); inyert the first term, and then multiply all the numerators together for a new numerator, and all the denominators together for a new denomina. tor; the new aumerator, written over the new denominator, will be the answer required. QUESTIONS FOR PRACTICE. 1. If oz. cost , what | 4. If my horse and chaise will loz, cost ? be worth $175, and the vaOL. oz. lue of my horse be that of : ::1 Then, my chaise, what is the value }x}XT=4%£-hi ls. 93 of each? Ans. 4: 175 :: :$105 horse. 2. How much shalloon i : 175 :: :$70 chaise. that is fyd. wide, will line 5. A lenus B 848 for * 13+ yards of cloth that is of a year; how much must 24 yards wide ?.. | B lend A of a year to 134 * and 2 = balance the favori Ans. $86.40. ideo=44yds. 6in. Ans. 6. A person owning of 3. If & gallon cost , a 'arm, sells of his share what will & tun cost? for $171; what is the of all of oft=gota tun. | whole farm worth? . Ans. €380. MISCELLANEOUS. For miscellaneous exercises, let | 2. One half, 4 of a school, the pupil review Sectiun IV. Partlar 1. and also the following articles : 1 and 10 scholars, make up 51, 52, 55, 56, 57, 58, and 59. . ). In an orchard ? the | lars are there? trees bear apples, & peach- ! Ans. 60. fs, plums, 30 pears, 15 s. There is an army, to cherries, and 5 quinces; which if you add s, } and what is the whole number itself, and take away 5000, of trees ? the sum total will be 100000, *+*+1- ti + 1 = what is the number of the .. then 50th and 1= whole army 50 X 12=600, Ans. Ans. 50400 men. 4. Triple, the half, and as long as his head and half the fourth of a certain num- the length of his body, and ber are equal to 104, what his body as long as his head is that number? . and tail both; what is the . Ans. 2713 / length of the fish ? 5. Two thirds and of al , Ans. 8 feet. person's money amounted 9. What number is that to $760; how much had her whose 6th part exceeds its $600. I 8th part by 20? Ans. 480. 6. A man spent of his | life in England, & in Scot 10. What sum of money land, and the remaining 20 on is that whose 3d part, 4th is years, in the United States: i part and 5th part are 894? Ans. $120. to what age did he arrive ? Ans. 48 years. 11. Il to my age there added be One half, 1 3d and three times 3, 7. A pule is in the mud, Six score aud ten their sum will be ; it in the water, and 12 feet | What is my age ? pray show it me. Ans. 66 years. out of the water; what is its length ? Ans. 70 feet. 12. Seven eighths of a I certain number . exceeds 8. There is a fish whose four fifths, by 6; what is head is 1 foot long, his tall that number? REVIEW 1. What are fractions? Or how | 6. When are fractions said to inany kinds are fractions? In what have a common denominator ? do they differ? 7. What is the common multiple 2. How is a vulgar fraction ex. | of two or more numbers ?--the least presseu? What is denoted by the | common multiple ?-a prime qumdenominator ?(22) by the numera ber?--the aliquot parts of a num. tor? ber?-a perfect number? Explain. 3. What is a decimal fraction ? 8. What is denoted by a vulgar How is it expressed ? How is it | fraction ?(129) How is an improread ? How may it be put into the i per fraction changed to a whole or form of a vulgar fraction ? | mixed number?(216)-a whole or 4. What is a proper fraction ? | mixed uumber to an improper fracan improper fraction? What are | tion ? the terms of a fraction ? What is a 9. How is a fraction multiplied compound fraction ?-à mixed num. ! by a whole number?(219)- divided ber? by a whole number? 5. What is meant by a common 10. How would you multiply s divisor of two numbers by the whole number by a fraction ?(222) greatest coramon divisor? !-a fraction by a fraction ? tion? . |