13. Three merchants A, B, and C, have a ship in company. A hath, B, 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 0s. 5d C's share £28 12s. 1d. B's share £57 4s. 2d. 7 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 midshipmen, 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 $342 50cts. a midshipman's $137, and a sailor's $35 88cts." 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.-This is done by Multiplication. Ascending is when small names are brought into great, as shillings into pounds, hours into days, &c. This is performed by Division. REDUCTION DESCENDING. RULE. Multiply 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 order of the question, and divide your last product by the last multiplier, and so on. EXAMPLES. 1. In 25l. 158. 9d. 2qrs. how many farthings? NOTE. In multiplying by 20, I added in the 15s.-by 12 the 9d.-and by 4 the 2qrs. which must always be done in like cases. 2. In 317. 11s. 10d. 1qr. now many farthings? Ans. 30329 3. In 46l. 5s. 11d. 3qrs. how many farthings? Ans. 44447 4. In 611. 12s. how many shillings, pence and ferthings? Ans. 1232s. 14784d. 59136 qrs. 5. In 841. how many shillings and pence? Ans. 1680s. 20160d. 6. In 18s. 9d. how many pence and farthings? Ans. 225d. 900grs. 7. In 312l. 8s. 5d. how many half-pence? Ans. 149962 8. In 846 dollars at 6s. each, how many farthings? Ans. 243648 9. In 41 guineas at 28s. each, how many pence? Ans. 13776 10. In 59 pistoles, at 228. how many shillings, pence, and farthings? Ans. 1298s. 15576d. 62304grs. 11. In 37 half-johannes, at 48s. how many shillings, six-pences, and three-pences? Ans. 1776s. 3552 six-pences, 7104 three-pences. 12. In 121 French Crowns, at 6s. 8d. each, how many pence and farthings? Ans. 9680d38720grs. 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. PROOF. Multiply inversely by the several divisors. EXAMPLES. 1. In 224765 farthings, how many pence, shillings and pounds? Farthings in a penny-4)224765 NOTE. The remainder is always of the same name as the dividend. 2 Bring 30329 farthings into pounds? Ans. £31 11s. 10d. 1qr. Ans. £46 5s. 11d. 3qrs 3. In 44447 farthings, how many pounds? 4. In 50136 farthings, how many pence, shillings, and pounds? Ans. 14784d. 1232s. £61 12s. 5. In 20160 pence, how many shillings and pounds? Ans. 1680s. or £84. 6. In 900 farthings, how many pounds? Ans. £0 183. 9d. 7. Bring 74981 half-pence into pounds? Ans. £156 4s. 24d. 8. In 243648 farthings, how many dollars at 6s. each? Ans. $846. 9. Reduce 13776 pence to guineas, at 28s. per guinea. Ans. 41. 10. In 62304 farthings, how many pistoles, at 22s, each ? Ans. 59. 11. In 7104 three pences, how many half-johannes, Ans. 37. at 48s? 12. In 38720 farthings, how many French crowns, at 6s. 8d.? Ans. 121. Reduction Ascending and Descending. 1. In 1211. Os. 91d. how many half-pence? Ans. 58099. 2. In 58099 half-pence, how many pounds? Ans. 1211. Os. 9 d. 3. Bring 23760 half-pence into pounds. Ans.£49 10s. 4. In 2147. 1s. 3d. how many shillings, six-pences, three-pences, and farthings? Ans. 4281s. 8562 sixpences, 17125 three-pences, and 205500 farthings. 5. In 1371. how many pence, and English or French crowns at 6s. 8d. each? Ans. 32880d. 411 crowns. 6. In 249 English half-crowns, how many pence, and pounds? Ans. 9960d. and £41 10s. 7. In 346 guineas, at 21s. each, how many shillings, groats and pence? Ans. 7266s. 21798gr'ts. and 87192d. S. In 48 guineas, at 28s. each, how many 41d. pieces? Ans. 3584. 9. In 81 guineas, at 27s. 4d. each, how many pounds? Ans. £ 110 14s. 10. In 24396 pence how many shillings, pounds and pistoles ? Ans. 2033s. £101 13s. and 92 pistoles. 9s. over. Ans. 324. 11. In 252 moidores, at 36s. each, how many guineas at 28s. each ? 12. In 1680 Dutch guilders, at 2s. 4d. each, how many pistoles at 22s. each? Ans. 178 pistoles, 4s. 13. Borrowed 1248 English crowns, at 6s. 8d. each, how many pistareens, at 141d. each, will pay the debt? Ans. 6885 pistareens and 7d. 14. In 50l. how many shillings, nine-pences, six-pences, four-pences, and pence, and of each an equal num12d.+9d.+6d+4d.+1d.=32d. and £50 = 120004.32=375 Ans. ber? REDUCTION OF FEDERAL MONEY. 1. Reduce 2745 dollars into cents. 2745 dollars Ans. 274500 Here I multiply by 100, the cents in a dollar; but dollars are readily brought into cents by annexing 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 show how many cents the given sum contains; and when dollars, cents, and mills are so joined together, they will show the whole number of mills in the given sum.Hence, properly speaking, there is no reduction of this money; 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, are dollars; and the figures cut off are cents, or cents and mills. 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 dols. 8 cts. into cents. Ans. 2508. 5. Reduce 54 dols. 36 cts. 5m. into mills. Ans. 54265* 6. Reduce 9'dols. 9 cts. 9m. into mills. Ans. 9039 1. How many grains in a silver tankard, that weighs 1 lb. 11 oz. 15 pwt. ? |