RULE. Reduce the given quantity to its lowest term mentioned, for a numerator; and the integer into the same name, for a denominator; which reduce to their lowest terms. Note 1. If a fraction be given, multiply both parts by the denominator thereof, and to the numerator, add the numerator of the given fraction. 2. Case 8 and 9 prove each other. EXAMPLES." 1. Reduce 138. 4d. to the fraction of a pound. 2. Reduce 5d. to the fraction of a shilling. 3. Reduce 9 oz. troy to the fraction of a lb. 4. What part of 5l. 9s. is 4l. 13s. 54d.? Facit Facit 31 5. Reduce 3 C. 8 lb. 9 oz. 137 dr. to the fraction of a ton Facit ton 6 Reduce 2 f. 8 in. 13 b.c. to the fraction of a yard. 3 Facit yd Facityd 7. Reduce 1 yd. to the fraction of an ell English. Facit ell 8. Reduce 3 qr. 2 na. to the fraction of a yard. 9. Reduce 1 R. 30 per. to the fraction of an acre. Facit acre 10. Reduce 13 h. 30 min. to the fraction of a day. Facit CASE 10. To reduce fractions from one denomination to another the same value, having the numerator of the required fractio given. RULE. As the numerator of the given fraction, Is to the denominator, So is the numerator of the intended fraction, To its denominator. Note. As the tenth, eleventh, and twelfth cases are seldom useful, they may be taught or omitted, at the option of the teacher. EXAMPLES. 1. Reduce to a fraction of the same value, whose numerator shall be fifteen. 2. Reduce to a fraction of the same value, the numerator of which shall be 42. Facit 43 3. Reduce to a fraction of the same value, the numerator of which shall be 34. Facit 4. Reduce to a fraction of the same value, the numerator of which shall be 73. Facit 73 CASE 11. To reduce fractions from one denomination to another of the same value, having the denominator of the required fraction given. RULE. As the denominator of the given fraction, Is to its numerator; So is the denominator of the intended fraction, Note. Case 10 and 11 prove each other. EXAMPLES. 1. Reduce to a fraction of the same value, whose denominator shall be 20. As 4 3:20.. 15 Facit = 2. Reduce to a fraction of the same value, the denominator of which shall be 49. Facit 28 3. Reduce & to a fraction of the same value, the denominator of which shall be 46. Facit 34 Facit 73 1312 4. Reduce & to a fraction of the same value, the denominator of which shall be 1313. CASE 12. To reduce a mixt fraction to a simple one; RULE. Multiply each term of the principal fraction by the denominator of that annexed, for the like term of the simple fraction, adding the annexed numerator to the product of the term to which it belongs. REDUCE the given fraction, if necessary, to simple fractions, and to a common denominator, (omitting integers ;) place the sum of the numerators over the common denominator; then to the value of said fractions, add the integers, (if any.) If fractions be of different integers, find their value separately, and add as in compound addition. EXAMPLES. 1. Add and together. 16 1 + 7 = 3/8 + 11 = 28=13 Facit. 2. Add, and together. 3. Add 19, 7, and of together. : 4. Add of, and 4 of 12 together. 5. Add of 95, and 7 of 14 together. 6. Add 2, and 171⁄2 together. 7. Add 12, 3, and 43 together. 8. Add 6, 7 of 5, 4 of 1, and 74 together. 9. Aid, of, and 9 10. Add 2 of a penny to 11. Add of a pound to 12. Add of a lb. troy to together. 28. 3d. 13qr. 18s. 3d. gr. Facit 6 oz. 11 dwt. 16 13. Add of a ton to of an C.wt. Facit 12 C. 1 qr. 8 lb. 12 oz. 124 dr. 14. Add 2 of a mile to of a furlong. 18. Add 3 of a yard, 2 of a foot, and 3 of a mile together. Facit 1540 yd. 2 ft. 9 in. of a shilling, and of a Ans. 3s. 1d. 11f gr. 12 dol. of of 3 of a 13 Ans. 7 dol..86 cts: of 15 dol. 3 dol. and 3 of of a cent? 21. Add of 12 dol.+4 dol.+ off of a dol.+ of of Facit 9 dol. 41 cts. 34m. a cent, into one sum. 22. If a merchant own of a ship, valued at 3600 dol. and buys another person's share of her, which is ; what part belongs to him, and what is it worth? Ans. 1, worth 2475 dol. SUBTRACTION OF VULGAR FRACTIONS. RULE. PREPARE the fractions as in addition, and subtract the lower numerator from the upper, placing the difference, over the common denominator. If the lower numerator be the greater, subtract it from the › common denominator, adding in the upper numerator, and carry one to the unit's place of the integer. If fractions be of different integers, find their values sepa~ rately, subtract as in compound subtraction. 9 From of a £. take 3 of a shilling. 10. From of a shilling, take of a penny. 11. From of an oz. troy, take ៖ 12. From of an Cwt. take 13. From of a league, take 23 14. From 1 ell English, take of a dwt. of a lb. Facit 98. 3d. 51 11 dwt. 3 gr. Facit 1 qr. 27 lb. 6 oz. 10 dr. of a mile. Facit 1m. 2 fúr. 16 pls. 15. From 7 weeks, take 97 days. Facit 5 w. 4 da. 7 hr. 12 min. 16. From 4 days, 71⁄2 hours, take 1 day, 9 hours. Facit 2 da. 221 hr. 17. Borrowed 53 £. paid of 44 £. what remains? Ans. 41. 3s. 8d. 14 gr. 18. What is the difference between § of a £. and 2 of 2 of a shilling? Ans. 108. 7d. 1} gr. 2 19. Take of a shilling from 4 of 54£. and what is left? Ans. 11. 8s. 11d. 20. If a merchant own § of a ship, valued at 2160 dol. and sells of his share; what part has he left, and what is it worth? Ans. 1, worth 450 dol. MULTIPLICATION OF VULGAR FRACTIONS.. RULE. Ir a compound fraction or mixt number be given, reduce them to single, or improper fractions; multiply the numerators together for a new numerator, and the denominators for a new denominator. |