2 3. Reduce and to their least common denominator. Ans. 12 9 16 16 24 24 24 24 4. Reduce and to their least common denominator. Ans. 8 12 10 CASE VII. To reduce the fraction of one denomination to the fraction of another, retaining the same value. RULE. Reduce the given fraction to such a compound one, as will express the value of the given fraction. by comparing it with all the denominations between it and that denomination you would reduce it to; lastly, reduce this compound fraction to a single one, by Case V. EXAMPLES. 1. Reduce & of a penny to the fraction of a pound. By comparing it, it becomes & of 12 of 440 of a pound. 2. Reduce of a pound to the fraction of a penny. Compared thus, Tao of 20 of 13 d. Then 5 X 20 X 12 440 3. Reduce of a farthing to the fraction of a shilling. Ans. s. 4. Reduce of a shilling to the fraction of a pound. 9223 Ans. 780 5. Reduce of a pwt. to the fraction of a pound troy, Ans. tr a cwt. 6. Reduce of a pound avoirdupois to the fraction of Ans.cwt. 7. What part of a pound avoirdupois is of a cwt. Compounded thus, of 4 of 28= |13 == 3 Ans. 8. What part of an hour is of a week. 6 1 227 T 12 Ans. 1 168 9. Reduce of a pint to the fraction of a hhd. Ans. 1 10. Reduce of a pound to the fraction of a guinea. Compounded thus, of 20 ofs. Ans, 11. Express 5 furlongs in the fraction of a mile. Thus, 5 of 1=11 Ans. 12. Reduce of an English crown, at 6s. 8d. to the fraction of a guinea at 28s. Ans. 1 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 inferior 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. of a pound? Ans. 8s. 91d. 1. What is the value of 2. Find the value of 3 of a cwt. Ans. Sqrs. Slb. 1oz. 124dr. 3. Find the value of 7 of 3s. 6d. Ans. 3s. Özd. of a pound avoirdupois ? 4. How much is 5. How much is 61 Ans. 7oz. 10dr. of a hhd. of wine? Ans. 45 gals. 6. What is the value of 15 of a dollar ? Ans. 5s. 74d. 7. What is the value of of a guinea? Ans. 18s. 8. Required the value of 107 of a pound apothecaries. Ans. 2oz. Sgrs. 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. Ans. 195 1792 2. Reduce 13 cwt. 3 qrs. 20 lb. to the fraction of a ton. Ans. Ans. 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. qrs. 17 lb. Ans. 7 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. 2 5 and of 7=14 18 Then 13 14 reduced to their least common denominator by Case VI. Rule II. will become 13 14 1 Then 152+18+14-16-620 or 65 Answer. 24 2. Add and together. S. Add and together. 24 4. Add 12 34 and 43 together. 5. Add 3 of 95 and 7 of 141 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 53 74 and 15. 2 I find the sum of and 4 to be = 1}} 7. Add and 17 together. 8. Add 25, 84 and 1 of 4 of 1 5 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 20-140£. Then 1+3=112%£: Whole value by Case VIII, is 8s. Od. 3 qrs. Ans. 2d Method. Ans. 8 9.33 By Case VIII. Reduction. 10. Add 3 lb. Troy, to & of a pwt. 11. Add of a ton, to 12. Add 3 of a mile to 13. Add of a yard, gether. Ans. 78z. 4pwt. 131gr. of a cwt. Ans. 12cwb. 1gr. 8lb. 12,8oz. of a furlong. Ans. Efar. 28po. of a foot, and 7 of a mile toAns. 1540yds. 2ft. Din. 14. Add of a week, 1 of a day, of an hour, and 4 of 13 a minute together. Ans. da. Chu, 20min, 45sec." SUBTRACTION OF VULGAR FRACTIONS. RULE. PREPARE the fractions as in Addition, and the dif ference of the numerators written above the common de nominator, will give the difference of the fraction required. 7. From 14 take of 19 8. From 37 take 11! 80 12 O remaina. 9. From of a pound, take of a shilling. of. Then from . take. Ans. NOTE. In fractions of money, weight, &c. you may, you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their pro per terms. 10. From 11. From 12. From 13. From S an hour. take $7 shilling. Ans. 50. 6d. 2jqrs, of an oz. take of a pwt. Ans. 11put. 3gr. of a cwt. take of a lb. Ans. 1gr. 271b. 6oz. 10 dr. weeks, take of a day, and of of of Ans. Sw. 4da. 12ho. 19min. 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. |