To reduce the fraction of one denomination to a fraction of nother, but greater denomination, retaining the same value. RULE. Make a fraction a compound one, by multiplying it by all the enominations between it and that to which it is to be reduced; hich fraction reduce to a single one. EXAMPLES. 37. Reduce of a penny to the fraction of a pound. Ans. T 38. Reduce of a penny to the fraction of a pound. Ans. zi 39. Keduce of a farthing to the fraction of a shilling. Ans. . 40. Reduce of a cent to the fraction of a dollar. 41. Reduce & of an ounce troy, to the fraction of a pound. Ans. of a pound avoirdupois, to the fraction of a cwt. 42. Reduce Ans. zz. 392 43. Reduce of a pint of wine, to the fraction of a hogshead. Ans. hhd. 44. Reduce of a minute, to the fraction of a day. Ans. 1585 CASE 9. To reduce a fraction of one denomination to a fraction of other, but less, retaining the same value. RULE! Multiply the given numerator by the parts of the denominations tween it and that to which it is to be reduced, for a new nuerator, and place it over the given denominator; which reduce its lowest terms. Vole. This case and case 6th prove each other. 45. Reduce T440 46. Reduce EXAMPLES. of a pound to the fraction of a penny. 5×20×12=128=d. Ans. of a pound to the fraction of a penny. *Ans ¡d. of a shilling to the fraction of a forthing, Ans. qr. of a dollar to the fraction of a cent. Ans. ct. of a lb troy, to the fraction of an ounce. Ans. of a cwt. to the fraction of a lb. avoirdupois. 180 47. Reduce 48. Reduce 49. Reduce 50. Reduce gla 51. Reduce 52 Reduce of a hhd. to the fraction of a pint. Ans. gib. Aus. 3 CASE 10. To reduce the value or proper quantity of a fraction to th known parts of the integer. RULE. Multiply the numerator by the known parts of the integer, and divide by the denominator. EXAMPLES. 53. Reduce of an acre to its proper quantity. Ans. 1R. 30per. $4. Reduce of a dollar to its proper quantity. 55. Reduce ៖ Ans. 60cts. of a shilling to its proper quantity. Ans. 5d. 56. Reduce of £5 9s. to its proper quantity. Ans. £4 13s. 54d. of a ton weight to its proper quantity. 57. Reduce 58. Reduce 59. Reduce Ans. 3cwt. Oqr. 8lb. 9oz. 1342dr. of 10cwt. 1qr. 12lb. to its proper quantity. Ans. 8cwt. 1qr. 25lb. 1oz. 7, dr. of a mile to its proper quantity. Ans. 4fur. 125yd. 2ft. 1in. 24b.c. 60. Reduce of a month to its proper quantity. Ans. 3 weeks 1 day 9 hours 36 minutes. Note. See more examples in this case, page 65. CASE 11. To reduce any given value, or quantity, to a fraction of any greater denomination of the same kind. RULE. Reduce the given quantity to the lowest denomination mentioned for a numerator; and the integer (or whole number) to the same denomination for a denominator. Note-If a fraction be given, multiply both parts by the nominator thereof, and to the numerator add the numerator of the given fraction. EXAMPLES. 61. Reduce 13s. 4d. to the fraction of a pound. 13s. 4d. 160d. 2 ----=-£. Ans. £1 20s. 240d. 3 62. Reduce 10s. 6d. to the fraction of a pound. 63. Reduce 41d. to the fraction of a shilling. 64. Reduce 9oz. 2dr. to the fraction of a lb. Ans. £21. Ans. 3s. avoirdupois. Ans. 4lb. 65. Reduce 3qr. 3lb. 1oz. 12dr. to the fraction of an cwt. Ans. cwt. 66. Reduce 1 rood 30 poles to the fraction of an acre. Ans. acre. 67. Reduce 2qr. 3 nails to the fraction of an English ell. Ans. & E. E. 68. Reduce 6 furlongs 16 poles, to the fraction of a mile. Ans. 4 mile. 69. Reduce 3 weeks 1 day 9 hours 36 minutes, to the fraction of a month. Ans. month. PROMISCUOUS EXAMPLES. Ans. 1912* 70. Reduce 354 to its proper terms. 71. Reduce,,, and 7, to a common denominator. Ans. 144, 183, 848, and 253.; 2889 288" ។ 288 192 240, 72. Reduce 12lb. 3oz. to the fraction of a cwt. 25 Ans. 195 1792 Ans. Ans. 1fur. 28po. 34yd. Ans. 115. 76. Reduce 12 to an improper fraction. 3969 Ans. day. 78. Reduce to its lowest terms. 79. Reduce of a pound to the fraction of a penny. Ans. d. 80. Reduce, 23 and 4 to fractions of a common denominator. Ans. 35, 38, 81. Reduce 1382 to its equivalent or proper number. Ans. 541. 82. Reduce of 5s. to the fraction of 21 shillings Ans. 25 83. Reduce of a lb. Avoirdupois to the fraction of an cwt. Ans. 1cwt. 84. Reduce of 4 of 4 of 5 of 1 of 1 to a simple fraction. 85. Reduce of a shilling to its proper quantity. 86. Reduce 13 to an improper fraction. G Ans. Ans. 4d. 3 qr. 87. Reduce of 785 an cwt. to the fraction of a lb. Ans. 4lb. 88. Reduce,, 3, and 4 to fractions having the least common denominator. Ans. 8, 8, 4, and 8. ADDITION OF VULGAR FRACTIONS. RULE. 1. Reduce compound fractions to single ones, mixed numbers to improper fractions, and all to a common denominator. 2. Add all the numerators together, and place the sum over the common denominator, and it will be the sum of the fraction required. 3. When fractions are united with whole numbers, the sum of the fractions may be found and added to the whole numbers. Note. If the fractions be of different denominations, find their value separately, and add as in compound addition: of ? 1. What is the sum of 23, 4, and Ans. 3. 61 120 The fractions are now prepared for adding, and should stand 8 (hus-1, 3.4. 7X8X5=280) 3x3x5= 45 Numerators. 4,13, or thus, 4X3X8= =96 421 Sum of numer. 3x3x5=45 Then 3×8X5x120 Denominator. 39 59 1X5X8=40 2 181=1, 3x5x3=120 3, Ans. Which, placed together, stand thus 413, the Ans. 2. Add and together. 3. Add 1, 4, and §, together. 4. Add 1, 41, and 2, together. Ans. 18 21 Ans. 17. 84 5. Add 2, and 3 of 2, together. 7. Add 124 32 and 43 together. 8. Add, 7, and of, together. Ans. 411. Ans. 11. Ans. 431. Ans. 20 Ans. 83. Ans. 131 of a shilling. s. 15 10,4 d. Ans. Add and 1. 11 Add of a pound to 2 of a shilling. Ans. 18s. 34 Prepare the given fractions as in addition, then subtract the less numerator from the greater, and place the difference over the common denominator. NOTE. When the given fractions are of different denominations, reduce them to their proper values, and then subtract as in compound subtraction. 8. From of a pound take 9. From of a shilling take 10. From of an oz. take 11. From of a league take of a mile. Ans. 1m. 2fur. 16p, 12. From 7 weeks take 9,7 days. Ans. 5w. 4d. 7h. 12m. 13. Borrowed £53 paid 4 of £44 what remains? Ans. £4 0s. 10d. MULTIPLICATION OF VULGAR FRACTIONS. RULE. Reduce compound fractions to single ones, and mixed number to improper fractions; then multiply the numerators together for a new numerator, and the denominators for a new denominator: A |