REDUCTION Teaches to change numbers of one name into others of another name, without altering their value. RULE 1.–Great names are brought into small, by multiplying by as many of the small as make one of the great. RULE 2.-Small names are brought into great, by dividing by as many of the small as make one of the great. Erample. Reduce £3246. 18s. 7d. into shillings and pence. d. To reduce pounds into shillings and pence, 3246 18 7 is to change great names (pounds) into small 20 (shillings and pence). 64938 shillings.* because 20 shillings=1 pound, taking in 18 By Rule 1. Multiply the pounds by 20, 12 shillings. Next, multiply the shillings by 779263 12, because 12 pence=1 shilling, taking in pence.* 7 pence. Answer, 64938 shillings, and 779263 pence. Example. lb. oz. dwts. grs. In 17 lb. 5 oz. 13 dwts. 17 grs. of silver, how 17 5 13 17 12 many grains ? To reduce pounds into grains, is to bring 20 great names (lb.) into small (grs.) 4193 dwts.* Multiply by 12, because 12 ozs. = 1 lb.; 16789 next by 20, because 20 dwts. =1 oz.; lastly, by 24, because 24 grs. =1 dwt. 100649 grains.* Answer, 100649 grains. 209 ozs.* 24 8386 EXERCISES. 1. Reduce £62. 13s. 9d. into shillings and pence. Answer, 1253 sgs. 15045 pence. In £2735 how many crowns and shillings? Answer, 10940 crowns. 54700 sgs. 3. Reduce 427 guineas into shillings, pence, and farthings. Answer, 8967 sgs. 107604 pence. 430416 farthings * Always affix the names to the several products. 4. In £5027 how many crowns and half-crowns ? Answer, 20108 crowns. 40216 half-crowns. 5. Reduce £265. 17s. 104d. into farthings. Answer, 255257 farthings. 6. In £372. 18s. 6d. how many sixpences ?* Answer, 14917 sixpences. Example. In 12214 farthings how many pence, shillings, and pounds ? Farthings. 4 ) 12214 To reduce farthings into pence, shillings, and pounds, is to change small names (farthings) 12 ) 3053) into great (pence, shillings, and pounds). By Rule 2. Divide by 4, because 4 farthings 20 ) 25,4 5 =1 penny. Divide the pence by 12, because £12 14 51 12 pence=1 shilling. Divide the shillings by 20, because 20 shillings=1 pound. Answer, 3053} pence, 254 shillings 54d., and £12. 14s. 5}d. Example. Reduce 12843499 drams into tons. Drams. To reduce drams 16 into tons, is to 4) 3210874+3 change small names (drams) into great (8) 802718+2=11 drs. (tons). 16 2) 100339+6 Divide by 16, be cause 16 drs.=1 oz. 7) 50169+1=14 ozs. Again, by 16, be28 cause 16 oz. 1 lb. | 4)7167 Next, by 28, because 28 lb. =l qr. 4) 1791+3=21 lb. Next, by 4, because 4 qrs. .=1 cwt. Last20) 44. 7+3 qrs. ly, by 20, because 20 cwt.=1 ton. Tons. 22. 7 cwt. 3 qrs. 21 lb. 14oz. 11 drs. Answer, 22 tons. 7 cwt. 3 qrs. 21 lb. 14 ozs. 11 drs. EXERCISES. 7. In 71854 pence how many shillings and pounds ? Answer, 5987 sgs.+10d. £299. 7s. 10d. 8. Reduce 207563 farthings into pence, shillings, and pounds. Answer, 51890, pence, 4324 sgs. 2 d. £216. 4s. 2 d. 9. Reduce 29560 sixpences into half-crowns and pounds. Answer, 5912 half-crowns, 739 pounds. * Multiply by the number of sixpences in a pound. 10. In 25643 twopences how many shillings and pounds ? Answer, 4273 sgs. 10d. £213. 13s. 10d. 11. Reduce 38716 half-crowns into crowns and pounds. Answer, 19358 crowns. £4839. 10s. 12. In 283526 farthings how many pounds? Answer, £295. 6s. 9 d. Examples, combining Rule 1st and Rule 2d. Reduce 5178 guineas into shillings and pounds. Guineas. To reduce guineas into shillings, is to 5178 21* change great names into smail. By Rule 1st, multiply by 21, because 21 shillings= 2,0) 10873,8 shillings. 1 guinea. Again, to reduce shillings into pounds, is to change small names into great. £5436,18 By Rule 2d, divide by 20, because 20 shillings = 1 pound. Answer, 108738 sgs. and £5436. 18s. In £8205. 14s. how many pieces, each £3. 12s. ? £ s. £ 3 12 8205 14 The pounds are brought into 20 20 shillings, and then divided by 72 shillings, the value of each piece. 72 ) 164114(2279 N. B. Two numbers cannot be 201 divided, unless in the same name. 26 shillings over,as the Remainder 571 is always of the same name as the Dividend. 674 Answer, 2279 pieces+£1. 6s. Remainder 26 sgs.=£1. 6s. EXERCISES. 13. Reduce £8701. 15s. into shillings and guineas. Answer, 174035 shillings, 8287 guineas, 8s. 14. In 7254 moidores, each 27 shillings, how many shillings and pounds ? Answer, 195858 shillings. £9792. 18s. 15. Reduce 1874 pieces, each 5s. 6d., into sixpences and pounds. Answer, 20614 sixpences. £515. 7s. 16. In 21587. guineas how many shillings and moidores ? Answer, 453327 shillings. 16789 moid. 24 sgs. 17. In £6285. 15s. how many sixpences, and pieces each 4s. 6d. ? Answer, 251430 sixpences. 27936 pieces, 3s. 18. How many pounds are in 25070 dollars, each 4s. 2d. ? Answer, £5222. 18s. 4d. Multiplied in one line, as taught in the Contractions of Simple Multiplication, page 11. Exercises in MONEY, WEIGHTS, AND MEASURES. Answer, 19. Reduce 8739 half-guineas into pence and farthings. Answer, 1101114 pence, 4404456 farthings. 20. In £213. 14s. how many ducats, each 4s. 9d. ? Answer, 899 ducats, 3s. 9d. 21. Reduce 59 lb. 9 oz. 13 dwts. of silver into grains. Answer, 344472 grains. 22. In 37 cwt. 2 qrs. 17 lb. how many pounds ? Answer, 4217 pounds. 23. In 26173 crowns how many shillings and guineas? Answer, 130865 shillings. 6231 guineas, 14s. 24. Reduce 20571500 drams into tons. Answer, 35 tons. 17 Cwt. 1 qr. 25 lb. 6 oz. 12 drs. 25. Reduce 37 miles. 3 fur. 28 poles. 2 yds. 2 ft. 9 in. into inches. Answer, 2373729. 26. In 17 pieces of Cloth, each containing 24 Flemish ells, how many yards ? Answer, 306 yards. 27. In 26 Cwt. 2 qr. 17 lb. of Tobacco, how many parcels, each 15 lb. ? 199 parcels. 28. How many spoons can be made, each to weigh 31 ounces, from 215 lb. 8 oz. of Silver ? Answer, 739 spoons, 1} oz. 29. In 75 hogsheads of Wine how many gallons and pints ? Answer, 4725 gallons, 37800 pints. 30. From the 7th of May, 1843, to the 19th February, 1844, both days inclusive, how many days? Answer, 289 days. 31. Reduce 41729 farthings into pence and dollars, each 4s. 5d. Answer, 104324 pence. 196 dollars, 3s. 81d. 32. Reduce 97 yards, 3 qrs. into ells English. Answer. 78 ells, 1 qr. 33. How many seconds are in a solar year, or 365 days, 5 hours. 48 min. 55 sec. ? Answer, 31556935 seconds. 34. Reduce £4079 into shillings, and pieces each £3. 12s. Answer, 81580 sgs. 1133 pieces. 4s. 35. In 13 hogsheads of Sugar, each 18 Cwt. 2 qrs. 17 lb., how many pounds? Answer, 27157 lb. 36. If a person step at an average 21 feet, how many steps will he take in walking 15 miles? Answer, 31680 steps. 37. In 17 hogsheads of Tobacco, each weighing 15 Cwt. 2 qrs. 14 lb. how many parcels, each 172 lb. ? 38. How many hours have elapsed since the birth of Christ to the present day inclusive, allowing the year to consist of 3651 days? 39. Bought 23 pockets of Hops, each weighing 1 Cwt. 2 qr. 17 lb., how many pounds? 40. Required the number of days and hours from the 17th of October, 1831, to the 8th of April, 1844, both days exclusive. THE RULE OF THREE,* * OR SIMPLE PROPORTION, Teaches to find a number that shall have the same proportion to one of the three given numbers, as there is between the other two. RULE. 1st. Ascertain, from the question, whether the fourth term, or answer, is to be money, weight, or measure, &c., and put the number of the same kind for the third term. 2nd. Consider whether the fourth term, or answer, is to be greater or less than the third : if greater, put the greater of the two remaining terms in the second place ; but if less, the less; and, in both cases, the other for the first. 3d. Bring the first and second terms, when necessary, into the same name, and the third into the lowest denomination mentioned. 4th. Multiply the second and third terms together, and divide the product by the first, and the quotient will be the fourth term, or answer, in the same denomination the third term was left in. Note. It is often required to bring the quotient into a higher name, that the answer may be exhibited in its proper form. * This Rule was formerly divided into the Rule of Three Direct, and the Rule of Three Inverse. Now, most Arithmeticians give a |