4. Add 12 3 and 4 together. Ans. 14 Ans. 17 Ans. 2011 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 53 74 and 15. I find the sum of 3 and 4 to be 11 7. Add and 17 together. 8. Add 25, 8 and of off Ans. 17 Ans. 33 F2 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 VIII. in Reduction, and then add them in their proper terms. 9. Add of a shilling to 3 of a pound. 2d Method. Ans. 8 034 10. Add lb. Troy, to of a pwt. Ans. 7oz.4pwt. 131gr. .11. Add of a ton, to of a cwt. Ans. 12cut. Iqr. 8lb. 12oz. of a furlong. 12. Add♣ of a mile to 13. Add of a yard, gether. 14. Add of a week, Ans. 6fur. 28po. of a foot, and of a mile to Ans. 1540yds. 2ft 9in. of a day, of an hour, and of a minute together. Ans. 2da. 2ho. 30min. 45ṣec. SUBTRACTION OF VULGAR FRACTIONS. RULE.* PREPARE the Fraction as in Addition, and the difference of the numerators written above the common denominator will give the difference of the fraction required. EXAMPLES. 1. From take of } of } = 11-12 Then and the Ans. Therefore 9-7=}}}= 2. From take Answers. 9. From of a pound, take of a shilling. & of 150 £. Then from £. take £. Ans.}¤. 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 proper terms. 10. From £. take 37 shilling. Ans. 5s. 6d. 23 qrs 11. From of an oz. take of a pwt. Ans. 11pwts. 3gr. 12. From of a cwt. take of a lb. 13. 3 weeks, take an hour. Ans. 1gr. 27lb. 6oz. 10,dr. of a day, and of of of Ans. 3w. 4da. 12ho, 19min. 174sec. * 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 reminder over the denominator, then taking one from the whole number. MULTIPLICATION OF VULGAR FRACTIONS RULE. REDUCE whole and mixed numbers to the improp er 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. 8. Multiply of by of 34 9. What is the continued product of of, 7, 51⁄2 and of §? Äns. 96 DIVISION OF VULGAR FRACTIONS. RULE. PREPARE the fractions as before; then invert the divisor and proceed exactly as in Multiplication :-The product will be the quotient required. 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, in the same name with the second or middle term. Ell. £. Ell. :: And ×× of a pound, what will of 8 or Ells English. s. d. qrs. =54£.=10 3 14 Ans. 2. If of a yard cost of a pound, what will 40% yards come to? Ans. £59 8s. 6d. 3. If 50 bushels of wheat cost 173. what is it per bushel ? Ans. 7s. Od. 133qrs. 4. If a pistareen is worth 143 pence, what are 100 pistareens worth? Ans. £6. 5. A merchant sold 5 pieces of cloth each containing. 24 yds. at 9s. ¿d. per yard; what did the whole amount Ans. £60 10s. Od. 3 qrs. 6. A person having of a vessel, sells of his share for 312,; what is the whole vessel worth? Ans. £780. 7. If of a ship be worth of her cargo, valued at 80001. what is the whole ship and cargo worth? Ans. £10031 14s. 112d. to? PREPARE the fractions and state the question as before, then invert the third term, and multiply all the three terms together the prodnet will be the answer EXAMPLES. 1. How much shalloon that is yard wide, will line 5 yards of cloth which is 14 yard wide? Yds. yds. yds. As 17 5 = Yds. days. And 7××3516, 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 3. If 13 men in 11 days, mow 12 days will 8 men do the same? 4. How much in length that is 7 make a square foot? acres, in how many Ans. 1823 days. inches broad will Ans. 20 inches. 5. If 254s. will pay for the carriage of a cwt. 145† miles; how far may 6 cwt. be carried for the same Ans. 22 miles. money ? 6. How many yards of baize which is 14 yards wide, will line 187 yards of camblet yd. wide? Ans. 11 yds. 1qr. 1źna. 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. 1. If of a yd. cost 7, of a pound; what will 15 yds. come to? Yds. £. 7875,583+aud * =,75. Yds. £. £. s. d. qrs. As .875,583 :: 15,75: 10,494—10 9 19 2,24 Ans. 2. If 1 pint of wine cost 1,2s. what cost 12,5 hhds? Ans. £378. 3. If 4 yds. cost 33. 44d. what will 30 yds. cost! Ans. £1 4s. 3d. 3grs.+ |