115. 9 19 5 919 3 17 EXAMPLES. 137. 6. Reduce 12} to an improper fraction. 7. Reduce 791; to an improper fraction. 1513. 8. Reduce 1003. to an improper fraction. III. To reduce an improper Fraction to a whole or mixed number. RULE.—Divide the numerator by the denominator, and the quotient will be the whole or mixed number. EXAMPLES. 9. Reduce ¥ to its equivalent or proper number. Ans. 21. 10. Reduce șz to its proper number. 꽃 Ans. 4. 11. Reduce 1'362 to its equivalent number. 5415 12. Reduce 2918 to its equivalent number. 17111. IV. To reduce a compound Fraction to a single one. Rule.-Multiply all the numerators together for a new numerator, and all the denominators for a new denominator. EXAMPLES. 13. Reduce 1 of off to a single fraction. 1x2x3 of of = Ans. 2X3X4 14. Reduce y of of 19 to a simple fraction. 을 15. Reduces of of 31, to a single fraction. 16. Reduce 4 of 4 of 1 of 4, to a single fraction. V. To reduce given fractions to others of a common denominator. RULE.--Multiply each numerator into all the denominators except its own, for a new numerator, and all the denomina. tors together for a common denominator, EXAMPLES. 17. Reduce }, and to a common denoininator. 3x5x7 4X4X7 6X4X5 =11%.&4= , & 4X5X7 =120 5X4X7 7X4X5 18. Reduce and to fractions of a common demominator. Ans. 19. Reduce }, , ic and } to a common denominator. , , Reduce , 2.3 and 4 to fractions of a common denominator. Ans. 140, 0, 18 140' Ans. Ans. 수 105,4 = 18 9 10 35 100 126 70 а 25 168 VI. To reduce a fraction of one denomination to the fraction of another, but greater, retaining the same value. Rule-Reduce the given fraction to a compound one, 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. EXAMPLES. 21. Reduce of a penny to the fraction of a pound. Ans. รอ 22. Reduce dwt. to the fraction of a lb. troy. Ans. 3 ਰੈਠ 23. Reduce ž of a lb. avoirdupois to the fraction of a cwt. Ans. 24. Reduces of 58. to the fraction of 21 shillings. Ans. VII. To reduce a fraction of one denomination to the fraction of another, but less, retaining the same value. Rule-Multiply the given numerator by the parts of the denominations between it and that denomination you would reduce it to, for a new numerator, which place over the given denominator. EXAMPLES. 25. Reduce of a pound to the fraction of a penny. Ans. 36. Reduce of a lb. troy to the fraction of a pennyweight. Ans. 27. Reduce iz of a cwt. to the fraction of a lb. 28. Reduce 25 of 21s. to the fraction of 5 shillings. Ans. VIII. To find the value of a fraction, in the known parts of coin, weight, measure, &c. Rule-Multiply the numerator by the integer, and divide by the denominator : if any thing remain, multiply it by the next inferior denomination, and divide as before. EXAMPLES. 29. Required the value of of a pound? Ans. 12s. 30. What is the value of of £5 9s. ? £4 13s. 57d. 31. What is the value of 6 of a ton ? Ans. 3 cwt. Oqrs. 816. 9oz. 131 dr. 32. Required the value of il of a mile ? Ans. 1 fur. 28po. 34 yds. -33. I demand the value of of an acre ? 34. What is the value of 1% of a day? 7ho. 12min. 1 307 a Ans. . : 39 14 Ans. 2 ro. 20 po IX. To reiluce any given quantity to the fraction of any greater den nomination of the same kind. RULE--Reduce the given quantity to the lowest term mentioned, for a numerator ; then reduce the integral part to the same term, for a denominator, which will be the fraction required. EXAMPLES. 35. Reduce 12s. to the fraction of a pound. Ans. 36. Reduce £4 138. 54d. to parts of £5 9s. 37. Reduce 3 cwt. O qrs. 8lb. 902. 13. dr. to the fraction of a 13 ton. Ans. 6 38. Reduce 1 fur. 28 po. 34 yds. to the fraction of a mile. Ans. 39. Reduce 2ro. 20po. to the fraction of an acre. 40. Reduce 7ho. 12min. to the fraction of a day. 10 15 1103 105 1050 ADDITION OF VULGAR FRACTIONS. RULE.-Reduce the given fractions to a common denominator, then add all the numerators together, under which place the common denominator. EXAMPLES. 1. Add { and į together. Ans. 2. Add and and s into one sum. 3. Add and and 21 into one sum. 4. Add and off, and 9 together. When fractions are of several denominations. RULE._Reduce them to their proper values, and add as before. 5. Add 1 of a pound to be of a shilling. Ans. 158. 10d. 6. What is the sum of £..} + s.tid. 15s. 9 d. 7. What is the sum of £}+td. - 3s. 1d. 1 qrs 8. Add $ of a pound Troy to of an ounce. Ans. 902. 3 dwt. 8 grs. 9. Add 4 of a ton to of a lb. 16 cwt. 13 oz. 54 dr. 10. Add * of a mile to of a furlong: Ans. 6 fur. 28 po. 11. Add of a week, of a day, and { of an hour together. Ans. 2 days, 144 hours. 12. A grocer sold the following parcels of sugar, vız : 16{ lb. 194 Ib. 134 lb. 204 lb. 25146 15. 30% lb. and 11 lb. 1 demand how many lb, he sold in all ? Ans. 362 31 lb, . 9 12 10 48 MULTIPLICATION OF VULGAR FRACTIONS. 55 27 112* 379 SUBTRACTION OF VULGAR FRACTIONS., RULE 1.-Reduce the given fractions to a common denominator, then subtract the less numerator from the greater and place the remainder over the common denominator. 2. In mixed numbers when the lower fraction is greater than the upper, subtract the numerator of the lower from the denominator, and to that difference add the upper numerator, carrying one to the units place of the lower whole number. EXAMPLES. 1. Subtract from 111 Ans. 2. Subtract 3 from 97 옥 700' 3. Subtract 144 from 961: 8119. 4. From 2: take 4 of į: 5. From 644 take of 4. When fractions are of several denominations. RULE.-Reduce them to their proper values and subtract as before. 6. From of a pound take of a shilling. Ans. 14s. 3d. 7. From * of a lb. Troy, take of an ounce. 802. 10 dwt. 8. From of a ton, take of a lb. Ans. 15 cwt. 3 qrs. 27 lb. 2.02. 103 dr. 9. From s of a league take yo of a mile. Ans. 1 m. 2 fur. 16 po. 10. From of a chaldron take of a bushel. Ans. 17 bus. 1; pec. 21 359 a MULTIPLICATION OF VULGAR FRACTIONS. RULE.-Reduce compound fractions to single ones, and mixed numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for a new denominator. EXAMPLES. 1. Multiply by 16 Ans. 2. Multiply by 특 11 3. Multiply 8 by 9. 841. 4. Multiply 64 by 8. 54 5. Multiply 91 by 4 of . 316 6. Multiply of by 1 of of 7. Multiply of 8 by k of 5. 21. 8. Multiply 7 of 73 by 1 of 3 736 45 $ 56 RULE OF THREE INVERSE IN VULGAR FRACTIONS. RULE.—Prepare the numbers if necessary by the rules ok reduction ; and divide the numerator by the numerator, and the denominator by the denominator, if they will exactly di. vide ; but if not, then invert the terms of the divisor, and proceed as in multiplication. EXAMPLES. 1. Divide 5 by 25x3 4-==1f Ans. Or thus, *== =*=lj Ans. 9X5 2. Divide , by Ans. 3. Divide if by 4. Divide 5883 by 84. 5. Divide of by of 9. 6. Divide 7 by ; of 7}. 7. Divide of by of 7. 8. Divide of 4 by 45 ži. 1 а RULE OF THREE DIRECT IN VULGAR FRACTIONS. RULE-Make the necessary preparations as before directed; then multiply continually together, the second and third terms, and the first with its parts inverted as in division, for the answer. EXAMPLES. 1. If of a gallon cost $ what will of a tun cost ? gal. $. tun. 8X5X5X4x63 If :$ : : 5X8X9x1x1 =$140 Ans. 2. What is the purchase of $1230 bank stock, at 10es per sent? Ans. $1336 8 cts. 3. If 3 yards cost £24 what will 14+ yards cost ? Ans. £13 15. 4d. 4. If of ý cwt. sugar cost £18 what will 82 cwt. cost ? Ans. £262 10s. 5. If 4 yards of silk cost # of fire what is the price of 15} ells Flemish ? Ans. 69 155. 10d. 6. What part of 6d. is į of 2d. Ans. . RULE OF THREE INVERSE IN VULGAR FRAC. TIONS. RULE-State and prepare as in the rule of three direct, invert the third term in place of the first, and proceed as in di. vision. x x xl 2. 3x7. х2 9 |