9. Reduce of a pint to the fraction of a hhd. 10. Reduce of a pound to the fraction of a guinea. Compounded thus, of 20 ofs. 8 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 fraction of a guinea at 28s. Ans. of a guinea. CASE VIII. To find the value of the fraction in the known parts of the integer, as of coin, weight, measure, &c. RULE. Multiply the numerator by the parts in the next inferior denomination, and divide the product by the denominator; and if any thing remains, multiply it by the next mferior denomination, and divide by the denominator as 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 '% of a cwt. Ans. 8s. 94d. Ans. Sqrs. 3lb. 1oz. 124dr. 3. Find the value of 7 of 3s. 6d Ans. 3s. Uşd. 4. How much is of a pound avoirdupois ? Ans. 7oz. 10dr. 5. How much is of a hhd. of wine? Ans. 45 gals. 6. What is the value of 15 of a dollar? Ans. 5s. 7d. 7. What is the value of of a guinea ? Ans. 18s. 8. Required the value of 107 of a pound apothecaries. Ans. 2oz. Sgrs. 9. How much is § of 5l. 9s.? Ans. £4 13s. 54d. 10. How much is of of of a hhd. of wine? CASE IX. Ans. 15gals. Sqts. 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. Ans. 195 7792 2. Reduce 13 cwt. 3 qrs. 20 lb. to the fraction of a ton. Ans. 3 Ans. 3. Reduce 16s. to the fraction of a guinea. 4. Reduce 1 hhd. 49 gals. of wine to the fraction of a tun. Ans.. 5. What part of 4 cwt. 1 qr. 24 lb. is 3 cwt. 3 qrs 17 lb. 8 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 5 and of together. Then 1 5 and of 7=12 14 reduced to their least common denominator by Case VI. Rule II. will become 132 1 Then 132+18-+14-164-62 or 6 Answer. 24 2. Add and together. 3. Add and together." 4. Add 124 34 and 43 together. 5. Add of 95 and 7 of 144 together. 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 5 7 and 15. I find the sum of and to be 31=113 7. Add † and 17 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 of a shilling to of a pound. SUBTRACTION OF VULGAR FRACTIONS. RULE.* PREPARE the fractions 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 7 7 3 of 7=1472 Then and=ù ¬ Therefore 9-7=22 =} the Ans. Answers. 11 5. What is the difference of and 17 ? 6. What differs from? 7. From 144 take of 19 8. From 42 31 208 13,2 378 10 177 O remains. 9. From of a pound, take of a shilling. of. Then from 4. take. Ans. 1. NOTE. In fractions of money, weight, &c. you may, if you please, find the value of the given factions (by Case VIII. in Reduction) and then subtract them in their proper terms. 10. From take 33 shilling. Ans. 5s. 6d. 27qrs. 11. From of an oz. take of a pwt. Ans. 1iput. 3gr. 12. From of a cwt. take of a lb. Ans. 1gr. 271b. 6oz. 10dr. 13. From 33 weeks, take of a day, and of 2 of 4 of an hour. Ans. Sw. 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 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. 8. Multiply of by of 34 9. What is the continued product of of 3, 7, 5 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. |