CASE X. To reduce the value or quantity of a fraction to the known parts of an integer, as of weight, measure, coin, &c. RULE. Multiply the numerator by the parts in the next lower denomination, and divide by the denominator; if there be a remainder, multiply it by the next lower denomination, and divide by the denominator as before, and so on, as far as necessary; place the quotients after each other in their regular order, for the required answer. In examples of federal money it is only neces essary to annex ciphers to the numerator, and divide by the denominator. Examples. 1. What is the value of 4 of a mile? 1x8 8 And 7)8 1 fur. 5 per. 3 yds. 2 ft. 9 in. Answer. 2. What is the value of į of a pound? Ans. 13s. 4d. 3. What is the value of of a yard? Ans. 2 ft. 64 in. 4. Reduces of a pound troy to its proper value. Ans. 8 oz. 5. Reduce 4 of a yard to its proper value. Ans. 3 qr. 1, na. 6. Reduce of an acre to its proper value. Ans. 2 R. 20 P. 7. What is the value of į of a dollar? Ans, 12 cts. 5 mills. 8. What is the value of 1 of a dollar? Ans. 25 cts. 9.' What is the value of of a dollar? Ans. 20 cts. 10. Reduce ž of a dollar to its proper value. Ans. 33} cts. 11. What is the value of 1 of a dollar? Ans. 11; cts. 12. What is the value of of a dollar? Ans. 577 cts. 13. What is the value of 1 of a dollar? Ans. 65 cts. 14. Reduce o of a dollar to its proper value. Ans. 95 cts. 15. What is the value of of a moidore? Ans. 5 dolls. 16. What is the value of į of an eagle? Ans. $3.331. 17. What is the value of is of a day? Ans. 4 h. 48 min. L 18. Reduce } of a year to its proper value. Ans. 73 d. 1 h. 12 min. 19. What is the value of of 3 days? Ans. 2 d. 6 h. 20. What is the value of £ of a ton? Ans. 5 C. CASE XI. To reduce any given value, or quantity, to the fraction of any gr er denomination of the same kind. RULE. Reduce the given quantity to its lowest term mentioned, for a numerator, then reduce the whole number into the same name for a denominator ; this fraction, reduced to its lowest terms, will be the fraction required. Note-If a fraction be given, multiply both parts by the denominator thereof, and to the numerator add the numerator of the given fraction. Examples. 1. Reduce 1 fur. 5 p. 3 yds. 2 ft. 9 in. to the fraction of a mile. Fur. P. yds. ft. in. Mile. 1 5 3 2 9 1 40 8 2. Reduce 13s. 4d. to the fraction of a pound. Ans. 3. Reduce 2 ft. 69 in. to the fraction of a yard. Ans. . 4. Reduce 8 ounces to the fraction of a pound Troy. Ans. š. 5. Reduce 3 qrs. 15 na. to the fraction of a yard. Ans. . 6. Reduce 2 R. 20 perches, to the fraction of an acre. Ans.. 17. Reduce 12 cts. 5 mills to the fraction of a dollar. Ans. ] 5 3 17. Ans. j. Ans. j. Ans. 7. 8. Reduce 20 cts. to the fraction of a dollar. Ans. 9. Reduce 30 cts. to the fraction of a dollar. Ans. 10. Reduce 33} cts. to the fraction of a dollar. 11. Reduce 11; cts. to the fraction of a dollar. 12. Reduce 574 cts. to the fraction of a dollar. 13. What part of a dollar is 65 cents ? Ans. 14. What part of a dollar is 95 cents? 15. What part of a moidore is 5 dollars? Ans. 5. 16. What part of an eagle is $3.33}? Ans, 17. What part of a day is 4 H. 48 min. ? 18. What part of a year is 73 D. 1 H. 12 min. ? Ans. 19. What part of a ton is 5 hundred? Ans. Ans. 1g Ans. } 5. ADDITION OF VULGAR FRACTIONS. RULE. Prepare the fractions, by reducing the compound ones to single; the mixed numbers to improper fractions: then reduce each of the fractions to a common denominator ; add the numerators together, and place the sum over the common denominator. If it be an improper fraction, reduce it to its equivalent whole or mixed number: if there be any whole numbers, they may be added to the sum of the fractions. Examples. 1. Add i of of of 10, 71, 4 and 5 together. of of of 1= 36 = }, value of the compound frac. 7 = 4, The mixed number reduced to an improper fraction. Then, 1, 2 and Å, the given fractions, prepared. 1 X 3 X 4 12 the numerator for . 23 X 4 X 4 368 the numerator for 23. 3 X 4 X 3 36 the numerator for 4. 4 X 3 X 4 48 the common denominator. 384 13. 11 49 60 13} Sum. Answer. 2. Add 4, and , together. Ans. 2013 : 3. Add ., į and 1s, together. . 10 24. 7. Add 43, 51 and 23, together. 8. Add of a week to Å of a day. Ans. 2 D. 12 H. 9. Add } of a dollar to į of a dollar. Ans. 70 cts. 10. Add į of a pound Troy to ź of an ounce. Ans. 6 oz. 10 dwts. 11. Add į of a yard to į of a foot. Ans. 2 feet. 12. Add of a day, 4 of an hour and 48 minutes, together. Ans. 11 H. 9 min. 13. Add io of a bushel, į of a peck and 26 quarts, together. Ans. I bushel. 14. Add of a yard, j of a foot and 1 of a mile, together. Ans. 770 yds. 1 ft. 4; inches. 15. Adds of a week, i of a day and it an hour, together. Ans. 5 D. 41 H. 16. Add of a mile to şof a yard. Ans. 1174 yards. 17. If a merchant own of a ship, valued at 5000 dollars, and buys another person's share of her, which is it, what part belongs to him, and what is it worth? Ans. 3}, worth 4200 dollars. 18. Add zo of an eagle to } of a dollar. Ans. 1 dollar. 19. What is the sum of } of four dollars, ļof two dollars and, of one dollar? Ans. 2 dolls, 20. Add of 3 pecks to of 2 bushels. Ans. 1 bu. 2 P. 63 qts. 21. What is the sum of į of a moidore, of an eagle and of a dollar ? Ans. $8.25. 22. What is the sum of of a dollar and į of a moidore? Ans. 1 dollar. 23. What is the sum of } of a day, 4 of an hour and of a week? Ans. 2 D. 20 H. 45 M. SUBTRACTION OF VULGAR FRACTIONS. RULE, Prepare the fractions as in addition ; subtract the numerator of the less from the numerator of the greater; place the common denominator under this difference--so is this new fraction the difference of the given fractions. In subtracting mixed numbers, reduce the fractional parts only to a common denominator ; place the less quantity under the greater, and the difference of the numerators will be a numerator to be placed over the common denominator-and the difference of the whole numbers will be a whole number; but if the numerator of the fraction in the lower quantity be greater than the numerator of the fraction in the upper quan: tity, then take the lower numerator from its denominator, and add the numerator of the fraction in the upper quantity to the remainder; set it down and carry one to the integer of the lower number. Examples. 1. From 9 I take 627. 2)14 22 7 11 And 2 X 7 X 11 = 154, common multiple. And 154 ; 14 x 5 55 154 • 22 x 17 - 119 137 Ri19 134 2005 - 244 Answer, , |