86. To reduce from a lower to a higher denomination. Ex. 2. How many pounds in 16743 farthings? OPERATION. 4) 167 4 3 far. 20) 3 48 s. 9d. 17 £ 8s. Ans. 17£ 8s. 9d. 3far. all the remainders to the last 8s. 9d. 3far. We divide by 4, because 4 farthings make 1 penny, and the result is 4185 pence, and the remainder, 3, is farthings. We divide by 12, because 12 pence make 1 shilling, and the result is 348 shillings, and the 9 remaining is pence. Lastly, we divide by 20, because 20 shillings make 1 pound, and the result is 17£ 8s.; and by annexing quotient, we find the answer to be 17£ RULE. Divide the lowest given denomination by the number which it takes of that denomination to make one of the denomination next higher. The quotient thus obtained divide in like manner, and so proceed until it is brought to the denomination required. The last quotient, with the remainders connected, will be the answer. 3. In 9£ 18s. 7d. how many pence? 4. In 2383d. how many pounds, &c.? 5. How many farthings in 14£ 11s. 5d. 2far.? 6. How many pounds in 13990far.? TROY WEIGHT. 87. Troy Weight is the weight used in weighing gold, silver, and jewels. 86. How do you reduce farthings to pence? Why divide by 4? How do you reduce pence to shillings? Why? Shillings to pounds? Why? Shillings to guineas? What is the general rule for reduction ascending? What is Troy Weight used for? Repeat the table. The oz. stands for onza, the Spanish for ounce. NOTE 1.. NOTE 2. A grain or corn of wheat, gathered out of the middle of the ear, was the origin of all the weights used in England. Of these grains, 32, well dried, were to make one pennyweight. But in later times it was thought sufficient to divide the same pennyweight into 24 equal parts, still called grains. NOTE 3. - Diamonds and other precious stones are weighed by what is called Diamond Weight, of which 16 parts make 1 grain; 4 grains, 1 carat. 1 grain Diamond Weight is equal to of a grain Troy. NOTE 4. The Troy pound is the standard unit of weight adopted by the United States Mint, and is the same as the Imperial Troy pound of Great Britain. MENTAL EXERCISES. 1. How many gr. in 2pwt.? In 10pwt.? 2. How many pennyweights in 4oz.? In 20oz.? EXERCISES FOR THE SLATE. In 120oz.? 1. How many grains in 721b. 10oz. 15pwt. 7gr.? 2. In 419887 grains, how many pounds? OPERATION. OPERATION. 7 2 lb. 10oz. 15pwt. 7gr. 24) 4 1 9 8 8 7 gr. 87. What was the original of all weights in England? grains did it take to make a pennyweight? How many weight now? By what weight are diamonds weighed? ard at the mint? How do you reduce pounds to grains? of the operation. How do you reduce grains to pounds? How many of these grains in a pennyWhat is the stand Give the reason 3. How many grains in 76pwt. 12gr.? 6. In 440160 grains how many pounds? 9. How many pounds in 17895gr.? 10. In 3lb. 1oz. 5pwt. 15gr. how many grains? 11. A valuable gem weighing 2oz. 18pwt. 12gr. was sold for $1.37 per grain; what was the sum paid? Ans. $1923.48. APOTHECARIES' WEIGHT. 88. Apothecaries' Weight is used in mixing medicines. NOTE 1 - In this weight the pound, ounce, and grain are the same as in Troy Weight. NOTE 2. Medicines are usually bought and sold by Avoirdupois Weight. Of fluids, 45 drops, or a common tea-spoonful, make about 1 fluid dram; 2 common table-spoonfuls, about 1 fluid ounce. 1 3 = 8 24 = 96 = 288 60 480 5760 MENTAL EXERCISES. 1. In 40 grains how many scruples? In 60gr.? In 120gr.? 2. In 5 scruples how many grains? In 10sc.? In 40sc.? 3. In 3 drams how many scruples? In 10dr.? In 17dr.? 4. How many pounds in 48 ounces? In 96oz.? 5. How many ounces in 24 drams? In 64dr.? In 144oz.? In 96dr.? 88. For what is Apothecaries' Weight used? What denominations of this weight are the same as those of Troy Weight? By what weight are medi. cines usually bought and sold? Repeat the table. EXERCISES FOR THE SLATE. 1. In 40lb. 8oz. 5dr. 1sc. 7gr. how many grains? OPERATION. 2. How many pounds in 234567 grains? OPERATION. 40 lb. 8oz. 5dr. 1sc. 7gr. 20) 2 3 4 5 6 7 gr. 6. How many pounds in 829440gr.? 7. In 12tb 83 33 19 18gr. how many grains? 8. In 73178 grains how many pounds? 9. In 73 63 29 of tartar emetic, how many doses of 20gr. each? AVOIRDUPOIS WEIGHT. Ans. 188. 89. Avoirdupois Weight is used in weighing almost every kind of goods, and all metals except gold and silver. 88 How do you reduce pounds to grains? The reason for the operation? How do you reduce grains to pounds? The reason for the operation ? 89. For what is Avoirdupois Weight used? Recite the table. NOTE 1.. wt. for weight. -In cut. the c stands for centum, the Latin for one hundred, and NOTE 2. The laws of most of the States, and common practice at the present time, make 25 pounds a quarter. But formerly, 28 pounds were allowed to make a quarter, 112 pounds a hundred, and 2240 pounds a ton, as is still the standard of the United States government at the custom-houses NOTE 3.-Avoirdupois is from the French avoir du poid, to have weight. -1 pound Avoirdupois = 1lb. 2oz. 11 pwt. 16 = 7000 gr. Troy = = = 13oz. 21 dr. loz. 1 dr. Av.; 60gr. Troy 1pwt. Troy = NOTE 4.gr. Troy; 1lb. Troy, or Apothecary Avoirdupois; 1oz. Troy, or Apoth. loz. Av. 4374gr. Troy = 18pwt. 54gr. Troy; 1dr. Apoth. 2dr. Av.; 1dr. Av. 2711gr. Troy = 1pwt. 31gr. Troy; 24gr. Troy of a dr. Av.; 1sc. Apoth. 20 gr. Troy of a dr. Av. = 768 H = MENTAL EXERCISES. = = = = 1. How many drams in 3oz.? In 7oz.? In 10oz.? In 12oz.? 2. How many ounces in 10lb.? In 15lb.? In 12lb.? In 100lb.? 3. How many pounds in 2 quarters? In 3qr.? In 20qr.? 4. How many quarters in 10cwt.? In 16cwt.? In 17cwt.? 5. How many tons in 80cwt.? In 100cwt.? In 600cwt.? 6. How many hundred weight in 16qr.? In 48qr.? In 96qr.? 89. How many pounds are now allowed for a cwt., and how many for a quar ter of a cwt., in most of the United States, in buying and selling articles by weight? How many at the custom-houses? How do you reduce tons to drams? The reason for the operation? How do you reduce drams to tons? The reason for the operation? |