Ans. 13 3. Add and together : Ans. 11 4. Add 12 s4 and 41 together. Ans. 2011 5. Add 4 of 95 and of 141 together. Ans. 4441 Note 1.-In adding mixed numbers that are not com. pounded with other fractions, you may first find the sum of the fractions, to which add the whole numbers of the given mixed numbers. 6. Find the sum of 57 and 15. I find the sum of and to be }}=111 Then 14+5+7+15=281; Ans. 7. Add } and 174 together. Ans. 1715 8. Add 25, 8] and off of to Note 2.—To add fractions of money, weight, &c. reduce fractions of different integers to those of the same. Or, if you please you may find the value of each fraction by Case VIȚI. in reduction, and then add them in their proper terms. 9. Add of a shilling to of a pound. 1st Method. 2d Method. of=tok. i£:=7s. 6d. Oqrs. Then that Yi s. =0 6 3 Whole value by Case VIII. is 8g. Od. Sqrs. Ans. Ans. 8 03 By Case VIII. Reduction, Ans. SS11 10. Add } lb. Troy, to fof a pwt. Ans. 702. 4pwt. 1345r 11. Add of a tc:1, to o of a cwt. Ans. 12cuct. 1gr. alb. 12, 8oz. 12. Add of a mile to to of a furlong. Åns. 6fur. 28po. 13. Add f of a yard, of a foot, and 7 of a mile together. Ans. 1540yds. 2ft. 9in. 14. Add of a week, of a day, of an hour, and of a minute together. Ans. 2da. 2ho. 30min. 45sec SUBTRACTION OF VULGAR FRACTIONS. RULE.* PREPARE the fractions as in Addition, and the difference of the numerators written above the common de. nominator, will give the difference of the fraction required. EXAMPLES. 31 1. From # take of } Therefore 97-= the Ans. %. From f take Answers. 3. From take 4. From 14 take i 134 5. What is the difference of Land HP 6. What differs } from ? 7. From 141 take of 19 17 8. From 7 take it O remains. 9. From t of a pound, take .of a shilling: fty-Thot. Then from ti£. take toke. Ans. 7. Note.--In fractions of money, weight, &c. you may, if you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their pro 10. From £. take 37 shilling. Ans. 58. 6d. 2grs. 11. From of an oz. take } of a pwt. Ans. 11pwt. Sgr. 12. From $ of a cwt. take it of a lb. Ans. Igr. 27lb. 6oz. 103 dr. 13. From 3} weeks, take of a day, and $ off of of : an hour. Ans. 3w. 4da. 12ho. 19min. 174sec per terms. *In subtracting mixed numbers, when the lower fraction is greater than the upper one, you may, without reducing them to improper fractions, subtract the numerator of the lower fraction from the common denominator, and to that difference add the upper numerator, carrying one to the unit's place of the lower whole number. Also, a fraction may be subtracted from a whole number by taking the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number. 166 MULTIPLICATION, DIVISION, &6. THON MULTIPLICATION OF VULGAR FRACTIONS, RULE. REDUCE whole and mixed numbers to the improper fractions, mixed fractions to simple ones, and those of different integers to the same; then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator. EXAMPLES. 1. Multiply by Answers, 4= 2. Multiply by 3. Multiply 5by i 4. Multiply of 7 by * 5. Multiply by 6. Multiply of 8 by 1 of 5 15! 7. Multiply 75 by 91 69. 8. Multiply of iş by of sf 9. What is the continued product of of ,7,5$ and of ? Ans. 45 DIVISION OF VULGAR FRACTIONS. RULE. PREPARE the fractions as before; then, invert the divisor and proceed exactly as in multiplication - The products will be the quotient required. EXAMPLES. 4 x 5 1. Divide by Thus, - Ans. 3 x 7 2. Divide 17 by Answers. 1 3. Divide of by 4. What is the quotient of 17 by ? 593 5. Divide 5 by To 71 6. Divide of of by of S} 7. Divide 4 by of 4 24 8. Divide 71 by 127 9. Divide 52051 by $ of 91 RULE OF THREE DIRECT IN VULGAR FRACTIONS. RULE. PREPARE the fractions as before, then state your question agreeable to the Rules already laid down in the Rule of Three in whole numbers, and invert the first term in the proportion; then multiply all the three terms continually together, and the product will be the answer, the same name with the second or middle term. EXAMPLES s. d. grs. 1. If of a yard cost of a pound, what will is of an Ell English cost? lyd.=of 1 of}=$. or Ell English. Ell. £. El. As :: And {xx=1=10 3 14 Ans. 2. If y of a yard cost ; of a pound, what will 404 yds. come to ? Ans. £,59 8s. 64d. 3. If 50 bushels of wheat cost 17}l. what is it per bushel ? Ans. 7s. Od. izqrs. 4. If a pistareen be worth 147 pence, what are 100 pistareens worth? 5. A merchantsold 54 pieces of cloth, each containing 241 yds. at 9s. dd. per yard; what did the whole amount to 3 Ans. £,60 10s. Od. 3yrs. 6. A person having of a vessel, sells of his share for 3121. ; what is the whole vessel worth? Ans. $780 7. If of a ship be worth of her cargo, valued at 8 700l. what is the whole ship and cargo worth? Ans. £10031 14s. 11,4d. Ans. 66 INVERSE PROPORTION. RULE. PREPARE the fractions and state the question as before, then invert the third term, and multiply all the three terms together, the product will be the answer. EXAMPLES. 1. How much shalloon that is yard wide, will line 51 yards of cloth which is 14 yard wide ? ds. yds. yds. Yds. As 14:51:1 And 3x4X==16, Ans. 2. If a man perform a journey in 3] days, when the day is 12 hours long; in how many days will he do it when the day is but 9 hours. Ans. 4 days. 3. If 13 men in 11 days, mow 213 acres, ¡n how many days will 8 men do the same. Ans. 1893 days. 4. How much in length that is 74 inches broad, will foot ? Ans, 20 inches. 5. If 2545. will pay for the carriage of an cwt. 145+ miles; how far may ő cwt be carried for the same mo Ans. 22 miles. 6. How many yards of baize which is 1+ yards wide, will line 187 yards of camblet tyd. wide? ins. 1 lyds. 1gr. 14 na. make a square ney : RULE OF THREE DIRECT IN DECIMALS. RULE. REDUCE your fractions to decimals, and state your question as in whole numbers ; multiply the second and third together; divide by the first, and the quotient will be the answer, &c. EXAMPLES. of a yd. cost of a pound; what will 154 yds. come to 1=,875 1=,583+and f=,75 Yds. Yds. f. . d. grs. 2. If 1 pint of wine cost 1,2s. what cost 12,5 hhds. ? Ans. £.378 3. If 4žyds. cost 3s. 41d. what wili 304 yds. cost i Ains. 4.144d lary isk |