This is a case of Reduction Descending. Multiply the £5 by 20, to reduce them to shillings, because 20 shillings make a pound. Add in the 19 shillings. £5 19s. 3 far. 20 119s. 12 1428d. 4 Multiply 119s., thus obtained, by 12, to reduce them to pence, because 12 pence make a shilling. There are no pence in the given number to add in. Multiply the 1428d., thus obtained, by 4, to reduce them to farthings, because 4 farthings make a penny. Add in the 3 farthings. Ans. 5715 far. EXAMPLE 2.-Reduce 15383 far. to pounds, shillings, &c. 4) 15383 far. 20) 320s. 5d. £16 Ans. £16 5d. 5715 far. Ans. This is a case of Reduction Ascending. Divide 15383 far. by 4, to reduce them to pence, because 4 farthings make a penny. Divide the quotient, 3845d., by 12, to reduce it to shillings, because 12 pence make a shilling. Divide the quotient, 320s., by 20, to reduce it to pounds, because 20 shillings make a pound. The last quotient and the several remainders form the answer. Always mark the denominations throughout, as in these examples. EXAMPLE 3.-Reduce £457 to farthings. We may here proceed as above, or we may somewhat shorten the operation. Looking under the Table on : 960 far. page 133, we find £1: Then in £457 there are 960 times 457 farthings. When, then, the number to be reduced has but one denomination, we may multiply at once by the number that connects it with the denomination required. 9140s. £457 £1960 far. 20 £457 12 960 9. Reduce 1 to farthings. Reduce / to pence. Prove by reducing the answers obtained back to shillings. 10. In £8000 how many pence? 11. How many farthings in 2/? In 11-? In 8s. 31d.? 12. How many sovereigns are 12480 pennies worth? 13. How many pence are 840 sovereigns worth? 14. Reduce 560 guineas to farthings. Ans. 564480 far 15. Reduce 118567 far. to pounds, &c. Ans. £123 10s. 1ąd. 16. Reduce £3 10s. to pence. Reduce 18s. 9d. to pence. 17. How many pounds, &c., in 15199 pence? In 189s.? 18. How many crowns are £25 equal to? 1 crown = 5s. How many crowns in £1, or 20s.? How many in £25? 19. How many pounds are 100 guineas equal to? 20. Reduce 7643s. to pounds; to guineas. 21. Reduce £1000 to farthings. 22. Reduce 4800000 far. to pounds, &c. 23. In 24000 far. how many crowns? Ans. 100 crowns. 24. A subscribes £500 for the poor; B, 500 guineas. Which subscribes the most, and how much? TROY WEIGHT. Ans. B £25. 231. To express weight, three different scales are used, called Troy, Apothecaries', and Avoirdupois Weight. 232. Troy Weight is used in weighing gold, silver, coins, and precious stones; also in philosophical experi ments. TABLE. 24 grains (gr.) make 1 pennyweight, . = 20 = 480 12 = 240 = 5760 The Troy pound is the standard unit of weight of the United States and Great Britain. It is equal to the weight of 22.794377 cubic inches of distilled water, at its greatest density. 233. The denominations grain and pennyweight take their name from the fact that silver pennies were once coined, required by law to equal in weight 32 grains of wheat from the middle of the ear, well dried. The value of the penny being afterwards reduced, the number of grains in the 231. Name the different scales used to express weight.-232. For what is Troy Weight used? Recite the Table of Troy Weight. What is the standard unit of weight of the United States? To what is the Troy pound equal?-238. Why are the grain and pennyweight so called? pennyweight was also reduced to 24.-Oz. stands for the Spanish word onza, an ounce. 234, Troy Weight takes its name from Troyes, a town of France, whence it was carried to England by goldsmiths; or, according to others, from Troy Novant, an old name applied to London. 3. Reduce 6 lb. 4 oz. 3pwt. 5 gr. to grains. Ans. 36557 gr. 4. How many grains in 11 oz. 19 pwt. 23 gr.? Ans. 5759 gr. 5. In 1200 lb. how many pennyweights? Ans. 288180 pwt. 6. Reduce 9999 gr. to pounds. Ans. 1 lb. 8oz. 16 pwt. 15 gr. 7. Reduce 999 pwt. to pounds, &c. Ans. 4lb. 1 oz. 19 pwt. 8. Reduce 1561 oz. to pounds, &c. 9. Reduce 18 pwt. 4 gr. to grains. Ans. 130 lb. 1 oz. Ans. 436 gr. 10. Reduce 11000 grains to lb. Ans. 1 lb. 10 oz. 18 pwt. 8 gr. 11. In 25 lb. 17 pwt. how many grains? 12. In 87 lb. 5 oz. how many pennyweights? 13. In 8543 grains, how many pounds, &c.? 14. Reduce each of the following to pounds, and add the results: 40320 gr.; 960 oz.; 6960 pwt. Ans. 116 lb. 15. Reduce the following to grains, and add the results: 5 lb. 1pwt. 18 gr.; 11 oz. 17 pwt.; 10 lb. 4 oz. 11 pwt. Ans. 94314 gr. 16. How many ounces in four lumps of gold, weighing 7 pwt., 13 pwt., 15 pwt., and 18 pwt.? Ans. 2 oz. 13 pwt. 284. From what does Troy Weight take its name? 17. What is the weight in pounds of a silver tea-pot weighing 200 pwt., and 24 table-spoons of 35 pwt. each? Ans. 4lb. 4 oz. 18. How many pounds of gold will a miner dig in a year of 365 days, if he averages 6 pwt. daily? Ans. 9 lb. 1 oz. 10 pwt. APOTHECARIES' WEIGHT. 235. Apothecaries' Weight is used by apothecaries in mixing medicines. They buy and sell their drugs, in quantities, by Avoirdupois Weight. 5760 1 = 12 = 96 = 288 = The only difference between Apothecaries' and Troy Weight lies in the division of the ounce. The grain, ounce, and pound, are the same in both. Ans. 1lb. 73 23 7 gr. 1. Reduce 9247 gr. to pounds, &c. Which kind of Reduction does this example fall under? Recite the rule (§ 222). Name the numbers in order, by which we must divide. Prove the answer by reducing it back to grains. Ans. 4707 gr. Recite the rule (§ 220). Why do we not first given, by what would 2. Reduce 93 63 10 7 gr. to grains. Which kind of Reduction does this example fall under? Name the numbers in order, by which we must multiply. multiply by 12? If drams had been the highest denomination we have multiplied first? How can you prove the answer? 3. Reduce 15648 gr. to pounds, &c. Ans. 2 lb. 83 43 20 8gr. 4. Reduce 1 lb. 113 23 5 gr. to grains. Ans. 11165 gr. 5. Reduce 4763 to pounds, &c. Ans. 16 lb. 6 oz. 3 dr. 2 sc. 235. By whom is Apothecaries' Weight used? By what do they buy and sell their drugs in quantities? Recite the Table of Apothecaries' Weight. What is the only difference between Apothecaries' and Troy Weight? 6. Reduce 9 lb. 5 dr. to scruples. 7. Reduce 843 dr. to pounds, &c. 8. Reduce 14 lb. 8 oz. to drams. 9. Reduce 30019 gr. to pounds, &c. Ans. 2607 sc. Ans. 8b. 93 33. 10. In 2 lb. 33 43 10 11 gr. how many grains? 11. Reduce the following to grains, and add the results: 1lb. 1 gr.; 103 20; 53 1gr.; 3 lb. 19. Ans. 28202 gr. 12. Reduce the following to pounds, and add the results: 11520 gr.; 960 dr.; 864 sc.; 144 oz. Ans. 27 lb. 13. How many doses of 15 gr. each will 5 dr. of calomel make? Reduce 5 dr. to grains. How many times are 15 grains contained therein? 14. How many grains in this mixture: benzoin, 23; cascarilla, 23; nitre, 13; myrrh, 20; charcoal, 83? Ans. 2650 gr. Reduce each item to grains; then add. 15. A druggist put up 24 powders of calomel, of 10 gr. each; if he had 1 oz. of calomel at first, how many grains will he have left? AVOIRDUPOIS WEIGHT. 236. Avoirdupois Weight is used for weighing all articles not named under Troy and Apothecaries' Weight; such as groceries, meat, coal, cotton, all the metals except gold and silver, and drugs when sold in quantities. 236. For what is Avoirdupois Weight used? Recite the Table. |