13. Three mercnants, A, B, and C, have a ship in company. A hath $, B i, and C }, and they receive for freight 2281. 16s. 8d. It is required to divide it among the owners according to their respective shares Ans. A's share £ 143 Os. 5d. B's share £57 4s. 2d. C's share £:28 12s. ld. 14. A privateer having taken a prize worth $6850, it is divided into one hundred shares; of which the captain is to have 11 ; 2 lieutenants, each 5; 12 midshipinen, each 2; and the remainder is to be divided equally among the sailors, who are 105 in number. Ans. Captain's share $753 50cts. lieut's. 8342 50cts. a midshipman's 8157, and a sailor's 835 88cts ܪܐ REDUCTION, TEACHES to bring or change numbers from one name to another, without altering their value. Reduction is either Descending or Ascending. Descending is when great names are brought into small, as pounds into shillings, days into hours, &c.Thris is done by Multiplication. Ascending is when sınall names are brought into great, as shillings into pounds, hours into days, &c. This is performed by Division. REDUCTION DESCENDING. RULE. Mùltiply the highest denomination given, by so many of the next less as make one of that greater, and thus continue till you have brought it down as low as your question requires. PROOF. Change the oruer of the question, and divide your last product by the last multiplier, and so on, EXAMPLES. 1. In 251. 15s. 9d. aqr's how many farthings? Notz. In multiplying oy 20, I added in the 155.by 12 the 91.and by 4 the eqrs. which must always be done in like cases. %. In s1l. 11s. 10d. 1gr. how miny farthings ? Ans. 30329 3. In 46l. 5s. 11d. Sqrs. how many farthings ? Ans. 44447 4. In 61l. 128. how many shillings, pence and far things? Ans. 12325. 14784d. 59156qrs. 5. In 841. how many shillings and pence? Ans. 1680s, 20160d. 6. In 188. 9d. how many pence and farthings ? Ans. 225d. 900grs. 7. In $121. 8s. 5d. how many half-pence ? Ans. 149962 8. In 846 dollars at 68. each, how many farthings ? 6s Ans. 243648 9. In 41 guineas at 286. each, how many pence? Ans. 13776 10. In 59 pistoles, at 22s. how many shillings, pence, and farthings? Ans. 1298s. 15576d. 62504grs. 11. In 37' half-johannes, at 48s. how many shillings, six-pences, aml three-pences ? Ans. 1776. 5552 six-penres. 7104 three-pences. 12. In 121 French crowns, at 6s. 8d. each, how many pence and farthings? Ans. 9680d. 38720grs. REDUCTION ASCENDING. RULE. Divide the lowest denomination given, by so many of that name as make one of the next higher, and so on through all the denominations, as far as your question requires. Proor. Multiply inversely by the several divisors. EXAMPLES. 1. In 224765 farthings, how many pence, shillings and pounds ? Farthings in a penný= 4)224765 12)56191 1 Shillings in a pound 210)468|2 7d. £234 2s. id. Igr. Ans. 56191d. 46828. 2541. Nore. The remainder is always of the same name as the dividend. 2. Bring 30529 farthings into pounds : Ans. £31 11s. 10d. Igr. 3. In 44447 farthings, how many pounds ? Ans. £46 58. 1.1d. Syrs. 4. In 59136 farthings, how many pence, shillings, and pounds ? Ans. 14784d. 1232s. £61 125, 5. In 20160 pence, how many shillings and pounds! ? Ans. 1680s. or £ 84. 6. In 900 farthings, how many pounds ? uns. £0 18s. 9d. 7. Bring 74981 half-pence into pounds? Ans. £156 4s. 21d. 8. In 245648 farthings, how many dollars at 6s. each : Ans. 6846. 9. Reduce 13776 pence to guineas, at 28s. per guiner. Ans. 41 10. In 62304 farthings, how many pistoles, at 299. tach Ans. 59. 11. In 7104 three-pences, how many hall-johannes, at 48s. ? Ans. 57. 12. In 38720 farthings, how many French crowns, at 68. 8d. ? Ans. 121. Reduction Ascending and Descending. 1. MONEY. 1. In 1211. 0s. 9fd. low many balf-pence? Ans. 58099 2. In 58099 half-pence, how many pounds? Ans. 1211. (s. 9 d. 3. Bring 23760 half-pence into pounds. Ans. £,49 10%. 4. In 2141. 15. 30. how many shillings, six-perces, three pences, and farthings! Ans. 47815. 8562 si.ro pences, 17125 three-pences, and 205500 farthings. 5. I» 1571. how many pence, and English or French crowns at 6s. 81. each ; Aus. 32880d. 411 croirns. 6. In 249. English half-crowns, how many pence and pounds! Ans. 9960d. and 141 10s. 7. In 346 guineas, at 21s. each, how many shillings, groats and pence? Ans. 7266s. 21798 grits and 871921. 8. In 48 yuineas, at 28s. each, how many thil. pieces? Ans. 3584 9. In 81 guineas, at 27s. 4d. cach how many pounds ? Ans. £110 145. 10. In 24596 pence, how many shillings, pounds and pistoles ? Äns. 20335. £101 13s. and 9:2. pistoles. 9s. Olpro, 11. In 252 moidores, at 36s each, how many yuineas at 28s. each? dis. 324. 12. In 1680 Dutch guilders, at 2s. 411. each, how many pistoles at 22s. cach: Ans. 178 pistoles, 4s. 13. Borrowed 1248 English crowns, at 6s. 80l. each, how inany pistareens, at 11 d. cach will pay the debt ? Ans. 6885 pistarrpns and 14. In 501. how many shillings, nine-pences, si ces, four-pences, and pence, and of each an equal in 12d.+9d.+6d.+1d.+ id. =321. and ! 120000-S2-575 1 EXAMPLES IN REDUCTION OF FEDERAL MONEY. 1. Reduce 2745 dollars into cent3. flere I multiply by 100, the 100 cents in a dollar; but dollars are readily brought into cents by anAns. 274500 nexing two cyphers, and into mills by annexing three cyphers. Also, any sum in Federal money may be written down as a whole number and expressed in its lowest denomination ; for, when dollars and cents are joined together as a whole number, without a separatrix, they will shew how many cents the given sum contains; and when dollars, cents, and mills are so joined together, they will shew the whole nuniber ou mills in the given sum.--Hence, properly speaking, there is no reduction of this monry; for cents are readily turned into dollars by cutting off the two right hand figures, and mills by pointing off three figures with a dot ; the figures to the left hand of the dot, ar? dollars ; and the figures cut of are cents, or cents and milis. 2. In 345 dollars, how many cents and mills ? Ans. 34500cts. 345000 mills. 3. Reduce 48 dols. 78 cts. into cents. Ans. 4878 4. Reduce 25 dels. 8 cts, into cents. Ans. 2508 5. Reduce 54 dols. 36 cts. 5m. into mills. Ans 54365 6. Reduce 9 dols. 9 cts. Im. into mills. Ars, 2099 $. cts. 7. Reduce 41925 cents into dollars. Ans. 419 25 8. Change 4896 cents into dollars. 48 96 9. Change 45009 cents into dollars. 450 09 10. Bring 4625 mills into dollars. 4 62 5 2 2. TROY WEIGHT res, py How many grains in a silver sankard, that reichs 11 0% 15 pwt. ? |