8. Required the value of 1% of a pound apothecaries. Ans. 2 oz. 3 grs. Ans. £4 13s. 54d. of 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. 3. Reduce 16s. to the fraction of a guinea. 4. Reduce 1 hhd. 49 gals. of wine to the fraction of a tun.. 5. What part of 4 cwt. 1 qr. 24 lb. is 3 cwt. 3 8 oz.? Ans. Ans. Ans. d 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 51 and of together. 5- and of Then Y,, reduced to their least common denominator by Case VI. Rule II. will become 13, 1, Then 132+18+14=W=623 or 64 Ans NOTE 1.-In adding mixed numbers that are not compounded 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 52, 74 and 15. 7. Add and 171⁄2 together. 8. Add 25, 81 and of of 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 4 of ‚—‚4£. 20 140 Then +£ 120 Whole value by Case VIII. is 8s. Od. 3 qrs. Ans. 2d method. 37s. 6d. Oqrs. 4s. 0 6 3 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. 9. From of a pound, take of a shilling. O remains. of. Then from £. take £. Ans. 31£. 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 grs. 11. From of an oz. take of a pwt. Ans. 11 pwt. 8 gr. 12. From of a cwt. take of a lb. Ans. 1 qr. 27 lb. 6 oz. 10, dr. 13. From 33 weeks, take of a day, and ¦ of of of an hour. 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 over 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 different integers to the same; then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator. 9. What is the continued product of of 3, 7, 51 and 8. Multiply of 3 by 3 of 34 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 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 sanre name with the second or middle term. EXAMPLES. 1. If of a yard cost of a pound, what will of an Ell English cost? Syd.= of 4 of }=2% or } Ell English. Ell. £. Éll. s. d. qrs. As And 4×4×£.10 3 1 Ans. 2. If of a yard cost of a pound, what will 40 yards come to ? el? 3. If 50 bushels of wheat cost 4. If a pistareen be worth 143 reens worth? Ans. £59 8s. 6d. 1737. what is it per bush Ans. 7s. Od. 133 grs. pence, what are 100 pista Ans. £6 of cloth, each containing 5. A merchant sold 51 pieces 24 yards at 9s. d. per yard; what did the whole amount to? Ans. £60 10s. Od. 33 qrs. 6. A person having 3 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 80007. what is the whole ship and cargo worth? Ans. £10031 14s. 11d. 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 answers |