divided into one hundred shares; of which the captain is to have 11; 2 lieutenants, each 5; 12 midsipmen, each 2; and the remainder is to be divided equally among the sailors, who are 105 in number. Ans. Captain's share $753 50 cts. ; lieutenant's, $342 50 cts.; a midshipman's, $137, and a sailor's, $35 88. 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 smali, 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. I. In 25l. 15s. 9d. 2qrs. how many farthings? 24758 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. how many farthings? Ans. 30329, 3. In 46l. 5s. 11d. 3qrs. how many farthings? Ans. 44447. 4. In 617. 12s. how many shillings, pence, and farthings Ans. 1232s. 14784d. 59136qrs. 5. In 847. how many shillings and pence? Ans. 1680s. 20160d 6. In 18s. 9d. how many pence and farthings? Ans. 225d. 900grs. 7. In 3121. 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 22s. how many shillings, pence, and farthings? Ans. 1298s. 15576d. 62304 grs. 11. In 37 half-johannes, at 48s. how many shillings, sixpences, 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. 9680. 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 de nominations, 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 Pence in a shilling 12)56191 1 gr. Shillings in a pound =20)468|2 7d. £234 2s. 7d. 1 gr. Ans. 56191d. 4682s. 2347. NOTE. The remainder is always of the same naine as the dividend. 2. Bring 30329 farthings into pounds. Ans. £31 11s. 10d. 1gr. 3. In 44447 farthings, how many pounds? Ans. £46 5s. 11d. 3qrs. 4. In 59136 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 18s. 9d. 7. Bring 74931 half-pence into pounds. Ans.£156 4s.2}d. 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. Ans. 37. 11. In 7104 three-pences, how many half-johannes, at 48s. ? 12. In 38720 farthings, how many French crowns, at 6s. 8d.? Ans. 121. Reduction Ascending and Descending. 1. MONEY. 1. In 1217. Os. 91d. how many half-pence? Ans. 58099. 2. In 58099 half-p -pence, how many pounds? Ans. 1217. Os. 91d. 3. Bring 23760 half-pence into pounds. Ans. £49 10s. 4. In 214. Is. 3d. how many shillings, six-pences, threepences, and farthings? Ans. 4281s. 8562 six-pences, 17125 three-pences, and 205500 farthings. 5. In 1377. how many pence, and English or French crowns, at 6s. 8d. each? Ans. 32880d. 411 crowns. 6. In 249 English half-crowns, how many peace and pounds? Ans. 9960d. and £41 10s. 7. In 346 guineas, at 21s. each, how many shillings, groats, and pence? Ans. 7266s. 21798 gr'ts. and 87192d. 8. In 48 guineas, at 28s. each, how many 4 d. pieces? Ans. 358. 9. In 81 guineas, at 27s. 4d. each, how many pounds? 10. In 24396 pence, how many shillings, pounds, and pistoles? Ans. 2033s. £101 13s. and 92 pistoles. 9s. over. 11. In 252 moidores, at 36s. each, how many guineas at 28s. each? Ans. 324. 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 Gs. 8d. each, how many pistareens, at 144d. each, will pay the debt? . Ans. 6885 pistareens, and 7d. 14. In 50%. how many shillings, nine-pences, six-pences, four-pences, and pence, and of each, an equal number? 12d.+9d.+6d. † 4d. + 1d.=32d. and £50= 12000d.--32=375 Ans. Examples in 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 brough into cents by annexing two ciphers and into mills by annexing three ci phers. 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, o tents and mills. 2. In 345 dollars, how many cents, and mills? Ans. 34500 cts. 345000 mills. 3. Reduce 48 dols. 78 cts. into cents. 4. Reduce 25 dols. 8 cts. into cents. 5. Reduce 54 dols. 36 cts. 5m. into mills. 6. Reduce 9 dols. 9 cts. 9 m. into mills. Ans. 4878 Ans. 2508 Ans. 54365 Ans. 9099 1. How many grains in a silver tankard, that weighs. 1 lb. 11 oz. 15 pwt. lb. oz. prot. 1 11 15 12 ounces in a pound. 23 ounces. 20 pennyweights in one ounce 475 pennyweights. 24 grains in one pennyweight. 1900 950 Proof. 24)11400 grains. Ans. 2,0)47,5 12)23 15 pwt. 1 lb. 11 oz. 15 pwt. 2. In 246 oz. how many pwts. and grains? Ans. 4920 pwt. 118080 grs. 3. Bring 46080 grs. into pounds. 4. In 97397 grains of gold, how many pounds? Ans. 16 lb. 10 oz. 18 pwt. 5 grs. 5. In 15 ingots of gold, each weighing 9 oz. 5 pwt. how many grains? Ans. 66600. 6. In 4 lb. 1 oz. 1 pwt. of silver, how many table-spoons, weighing 23 pwt. each, and tea-spoons, 4 pwt. 6 grs. each, can be made, and an equal number of each sort? 23pwt. +4pwt. 6 grs.=654 grs. the divisor; and 4 lb. 1 oz. 1 pot. 23544 grs. the dividend. Therefore 23544÷65436 Ansiger. |