9. Reduce of a pint to the fraction of a hlid. Ans. 10. Reduce of a pound to the fraction of a guinea. Compounded thus, 4 of 2 of As.4 Ans. 11. Express 5 furlongs in the fraction of a mile. Thus 51 of 1=1↓ Ans. 12. Reduce of an English crown, at 6s. 8d. to the fraction 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 inferfor denomination, and divide the product by the denomi nator; and if any thing remains, multiply it by the neat Inferior denomination, and divide by the denominator aş before, and so 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 75 and 76; but for the scholar's exercise, I shall give a few more examples in each. EXAMPLES. 1. What is the value of of a pound? 2. Find the value of 7 of a cwt. Ans. 88. Gja Ans. 3qrs. 3lb. 1oz. 124dr. 3. Find the value of 4 of 3s. 6d. 4. How much is of a pound avoirdupois ? 5. How much is of a hhd. of wine? 6. What is the value of 11⁄2 of a dollar? 7. What is the value of of a guinoa Ans. 7oz. 10dr. 8. Required the value of 107 of a pound apothecaries. Ans. 2oz. 3grs. Ans. £4 13s. 54d. of of of a hhd. of wine? Ans. 15gals. Sqts. 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 75.] EXAMPLES FOR EXERCISE. 1. Reduce 12 lb. 3 oz. to the fraction of a cwt. 2. Reduce 13 cwt. 3 qrs. 20 lb. to the fraction of a ton. 32 Ans. 3 Ans. 3. Reduce 16. to the fraction of a guinca. 4. Reduce 1 hhd. 49 gals. of wine to the fraction of a Lun. Ans. $ 5. What part of 4 cwt. 1 qr. 24 lb. is 5 cwt. 3 qrs. 17 lb. BOL. Ans. ADDITION OF VULGAR FRACTIONS. RULE. REDUCE compound fractions to single ones; mixed numbers to improper fractions; and all of them to their east common denominator (by Case VI Rule II.) then the sum of the nume.ators written over the common denominator will be the sum of the fractions required. Then reduced to their least common denominator by Case VI. Rule 11. will become 132 13 Then 132+18+146 or 6 Answer. 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 rumbers of the given mixed numbers. 6. Find the sum of 52 73 and 15. I find the sum of 2 and to be 21=1} 7. Addard 17 together. 8. Add 25, 81 and 1 of 2 of 1% Ans. 332 NOTE 2.-To add fractions of inoney, weight, &c. reduce fractions of different integers to those of the saine. 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 of a puund. 1st method. 4 of 24 £. Then +£ Whole value by Case VIII. is os. Od. 3 qrs. Ans. 2ú Method. 10. Add lb. Troy, to § of a pwt. Ans 7oz. 4pnot. 131gr. 11. Add 4 of a ton, to of a cwt. 12. Add of a mile to 13. Add of a yard, gether. Ans. 12cwt. 1gr. 8lb. 12-az. 14. Add of a week, of a minute together. Ans. 6fur. 28po. of a foot, and of a mile toAns. 1540yds. 2ft. 9in. of a day, of an hour, and Ans. 2da. 2ho, 30min. 45sec. 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. 7. From 14 take of 19 8. From 3 37 take 9. From of a pound, take of £. Then from 1 140 of a shilling, take. Ans. 37£. 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 £. take 3 shilling. Ans. 5s. 6d. 23grs. of an oz. take of a pwt. Ans.11pwt. Sgr. Ans. 1gr. 27b. 6oz. 10, dr. 13. From 33 weeks, take 4 of a day, and of 2 of & of an hour. 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 denomina tor, 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 ro mainder 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. 6. Multiply of 8 by 7 of 5 7. Multiply 7 by 91 8. Multiply of 3 by of S Ans. 4 9. What is the continued product of of 3, 7, 51 and of? DIVISION OF VULGAR FRACTIONS. RULE. PREPARE the fractions as before; then, invert the di visor and proceed exactly as in Multiplication :-The pr ducts will be the quotient required. |