9. Reduce of a pint to the fraction of a hhd. Ans. Thi 10. Reduce of a pound to the fraction of a guinea. Compounded thus, of 2° of s. Ans. 11. Express 5 furlongs in the fraction of a mile. Thus 5 of }=}} Ans. 12. Reduce of an English crown, at 6s. 8d. to the frac tion of a guinea at 28s.' Ans. of a guinea. CASE VIII. To find the value of a fraction in the known parts of the integer, as of coin, weight, measure, &c. RULE. Multiply the numerator by the parts in the next inferici denomination, and divide the product by the denominator; and if any thing remains, multiply it by the next inferior de nomination, and divide by the denominator as before, and sc on as far as necessary, and the quotient will be the answer. NOTE. This and the following Case are the same with Problems II. and III. pages 70 and 71; but for the scho lar's exercise, I shall give a few more examples in each. EXAMPLES. What is the value of 11 of a pound? Ane 8. G‡d. 2. Find the value of 7 of a cwt. Ans. 3 qrs. 3 ò. 1 oz.123 a 3. Find the value of 7 of 33. id. Ans. 3s. Ofd. 4. How much is of a pound avoirdupois? Ans. 7 oz. 10 dr. 5. Ilow much is 1⁄2 of a hhd. of wine? 6. What is the value of 1 of a dollar? What is the value of of a guinea? Ans. 45 gals Ans. 188 ,, 8. Required the value of 17 of a pound apothecaries. 9. How much is of 5l. 9s.? Ans. 2 oz. 3 grs. Ans. £4 13s. 54d. Ans. 15 gals. 3 qts 10. How much is of of of a hhd. of wine? 14 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. in. 5. What part of 4 cwt. 1 qr. 24 lb. is 3 cwt. 3 qrs. 17 lb. 3 oz. ? Ans. 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 51⁄2 2 and 3 of together. 5- and of 7=11 Then, reduced to their least common denominator by Case VI. Rule II. will become, 1, 1 Then 132+18+14='V=632 or 61⁄2 Ans. 18 4. Add 121 33 and 4 together. 201 44179 5. Add of 95 and 3 of 14 together. 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 and 171⁄2 together. 8. Add 25, 8 and 1 of 3 of 33 NOTE 2.—To add fractions of money, weight, &c. redu 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 thei roper terms. 9. Add 4 of a shilling to 3 of a pound. # of Then 1st method Whole value by Case VIII. is 8s. Od. 3 qrs. Ans. 2d method. Ans. 8 0 3 By Case VIII. Reduction. Ans. 12 cwt. I qr. 8 lb. 12 oz. 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 31 208 13/ 348 10 171 17 12 O remains. of a pound, take of a shilling. 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 11. From 5 £. take 33 shillings. Ans. 5s. 6d. 23 qrs. of an oz. take of a pwt. Ans. 11 pwt. 3 gr. 12. From of a cwt. take of a lb. dr. Ans. I 27 lb. 6 oz. 10,8% qr. 13. From 33 weeks, take 4 of a day, and of 3 of 3 of an hour. Ans. 3 w. 4 da. 12 ho. 19 min. 17 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. Redace whole and mixed numbers to the improper frac tions, mixed fractions to simple ones, and those of differen integers to the same; then multiply all the numerators to gether for a new numerator, and all the denominators to gether for a new denominator. 8. Multiply of } by § of 33 Answers. ! 311 131 6931 9. What is the continued product of of 3, 7, 5 and 1 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. |