8. Required the value of 17 of a pound apothecaries. 9. How much is § of 5l. 9s.? 10. How much is of Ans. 2 oz. 3 grs. Ans. £4 13s. 54d. of of a hhd. of wine? Ans. 15 gals. 3 qts. CASE IX. To reduce any given quantity to the fraction of any greater denomination of the same kind. [See the Rule in Problem III. page 71.] EXAMPLES FOR EXERCISE. 1. Reduce 12 lb. 3 oz. to the fraction of a cwt. Ans. 2. Reduce 13 cwt. 3 qrs. 20 lb. to the fraction of a ton, Ans. 3. Reduce 16s. to the fraction of a guinea. 4. Reduce 1 hhd. 49 gals. of wine to the fraction of a Ans. Ans. .tun. 5. What part of 4 cwt. 1 qr. 24 lb. is 3 cwt. 3 17 lb. qrs. Ans. 8 oz.? ADDITION OF VULGAR FRACTIONS. RULE. Reduce compound fractions to single ones; mixed numbers to improper fractions; and all of them to their least common denominator, (by Case VI. Rule II.) then the sum of the numerators written over the common denominator will be the sum of the fractions required. EXAMPLES. 1. Add 5 and of together. 5- and of 7-14 Then Y,, reduced to their least common denominator by Case VI. Rule II. will become 132, 241 27, 11, 11 Then 132+18+14=-6 or 6 Ans. 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. 7. Add I find the sum of 3 and 4 to be 31=1 and 17 together. 8. Add 25, 81 and of of 33 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 4 of a shilling to of a pound. 1st method 2d method. Ans. 8 0 3 By Case VIII. Reduction. 10. Add lb. Troy, to § of a pwt. Ans. 7 oz. 4 pwt. 13 grs. 11. Add of a ton, to of a cwt. 12. Add of a mile to 13. Add & of a yard, 14. Add of a week, 114 a minute together. Ans. 12 cwt. 1 gr. 8 lb. 12 oz. of a furlong. Ans. 6 fur. 28 po. of a foot, and of a mile together. Ans. 1540 yds. 2 ft. 9 in. of a day, of an hour, and 3 of Ans. 2 da. 2 ho. 30 min. 45 sec. 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 3 of 1 of 11 Then andù h Therefore 9-7-- the Ans. 2. From 3 take 4 7. From 14 take of 19 8. From 37 take 111 Answers. 9. From of a pound, take of a shilling. of={£. Then from £. take £. Ans. 11£. 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 shillings. Ans. 5s. 6d. 23 qrs. 11. From of an oz. take of a pwt. Ans. 11 pwt. 3 gr. 12. From of a cwt. take of a lb. Ans. 1 gr. 27 lb. 6 oz. 1031⁄2 dr. 13. From 33 weeks, take an hour. of a day, and of of 3 of Ans. 3 w. 4 da. 12 ho. 19 min. 174 sec. *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 ver the denominator, then taking one from the whole number. MULTIPLICATION OF VULGAR FRACTIONS. RULE. Reduce whole and mixed numbers to the improper fractions, mixed fractions to simple ones, and those of differen integers to the same; then multiply all the numerators together for a new numerator, and all the denominators to gether for a new denominator. 6. Multiply of 8 by 7 of 5 7. Multiply 7 by 91 8. Multiply of 3 by & of 32 9. What is the continued product of of, 7, 51 and of & ? Ans. 4 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. RULE OF THREE DIRECT IN VULGAR 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. EXAMPLES. 1. If of a yard cost of a pound, what will of an Ell English cost? 05 gyd.= off of =2% or 1 Ell English. Ell. £. Ell. s. d. qrs. As ::: And 4×3×=£.=10 3 1 Ans. 2. If of a yard cost of a pound, what will 403 yards Ans. £59 8s. 61d. come to ? 3. If 50 bushels of wheat cost 1737. what is it bushper el? Ans. 7s. Od. 13 qrs. 4. If a pistareen be worth 143 pence, what are 100 pista Ans. £6 reens worth? 5. A merchant sold 5 pieces of cloth, each containing 241 yards at 9s. 1d. per yard; what did the whole amount Ans. £60 10s. Od. 33 qrs. to? 6. A person having of a vessel, sells of his share for 3127.; what is the whole vessel worth? Ans. £780 7. If of a ship be worth of her cargo, valued at 80007. what is the whole ship and cargo worth? Ans. £10031 14s. 11. INVERSE PROPORTION. RULE. Prepare the fractions and state the question as before. then invert the third term, and multiply all the three terme together, the product will be the answer. |