4) 3579 OPERATION. 12) 894 d. +3 qr. 20) 74 s. 6 d. ing. 3 £ 14 s. 6 d. 3 qr., Ans. As 4 qr.=1 d., we shall have Į as many pence as farthings, or 894 d. and 3 qr. remaining; as 12 d.1 8., we shall have as many shillings as pence, or 74 s. and 6 d. remain Hence As 20 s. 1 £, we shall have as many £ as s., or 3£ and 14 s. remaining, making the entire result 3 £ 14 s. 6 d. 3 qr. the RULE FOR REDUCTION ASCENDING. Divide the given number by the number which it takes of its denomination to equal one of the next higher, and note the remainder. Divide the quotient thus obtained as before, and thus proceed till the required denomination is attained. The last quotient, with the several remainders, will be the required result. PROOF. As reduction ascending is the converse of reduction descending, either process may be proved by the other. EXAMPLES. 1. Reduce 3681 farthings to an equivalent value in higher denominations. In the same manner reduce, 2. 36875 farthings. 3. 4328 pence. Ans. 3 £ 16 s. 8d. 1 qr. Ans. 38 £ 8 s. 2 d. 3 far. WEIGHT. 162. TROY Weight. Gold, silver, and precious stones are weighed by this system. The denominations are pounds, ounces, pennyweights, and grains. 24 grains (gr.)=1 pennyweight, marked pwt. 20 pwt. TABLE. 1. Reduce 18 lb. 11 oz. 5 pwt. 17 gr. to grains. 2. Reduce 48 lb. 2 oz. 0 pwt. 3 gr. to grains. 3. Reduce 1 oz. 23 gr. to grains. Ans. 109097 gr. 4. Reduce 3681 lb. 9 oz. 1 pwt. to pennyweights. Reduce to equivalent values in higher denominations, 5. 928641 pwts. 6. 3786541 grs. 7. 9042028 grs. Ans. 3869 lb. 4 oz. 1 pwt. 8. What is the value of 2 lb. 8 oz. of gold, at $16.00 an ounce ? 9. What is the value of 1 lb. 3 oz. 7 pwt. of gold, at 4 cents per grain ? 10. What will 20 silver dollars weigh, each dollar weighing $12 grains? 163. APOTHECARIES' Weight. Apothecaries use this weight for mixing medicines; but they buy, and generally sell, by Avoirdupois weight. The denominations are pounds, ounces, drachms, scruples, and grains. TABLE. 20 grains (gr.)=1 scruple, marked sc. or . 1. Reduce 5 lb. 7 3, 73, 29, 12 gr. to grains. 2. Reduce 3 fb. 0 3, 7 3, 19, 9 gr. to grains. Ans. 32632 gr, Ans. 44 b. 10 3, 4 3,0 9,1 gr 4. Reduce 36845 D to pounds, ounces, &c. 5. Reduce 987326 gr. to pounds, ounces, &c. 6. Reduce 28 lb. 3 3, 1 3, 2 D, 5 gr. to grains. 164. AVOIRDUPOIS Weight. This weight is used for weighing almost all articles, except gold, silver, and precious stones. The denominations are tons, hundred weight, quarters, pounds, ounces, and drams. NOTE. The long ton of 2240 lbs., which gives 28 lbs. to the qr., is sometimes used for weighing gross articles, as iron and coal, and is the ton recognized by the United States Government. 8. Reduce 4 T. 3 cwt. 2 qr. 0 lb. 8 oz. to ounces. 9. How many ounces in 1 cwt.? in 1 T.? 10. How many pounds in one ton? 11. How many more pounds in a long ton than in a short ton? 12. At the rate of 3 lb. a day, how many hundred weight of flour will a family consume in a year, or 365 days? 165. COMPARISON OF WEIGHTS. 1. Reduce 364 lbs. Troy to Avoirdupois weight. Ans. 299 lbs. Av. 2. Reduce 36 lbs. Troy to Avoirdupois weight. 3. Reduce 5 lbs. Avoirdupois to grains in Apothecaries' weight; Ans. 6 lb. 0 3, 7 3, 1 9. te units of higher denominations. 4. Reduce 375 lbs. Avoirdupois to Apothecaries' weight. 5. Reduce 73 lbs. Avoirdupois to Troy weight. MEASURES OF EXTENSION. 166. LONG MEASURE. The denominations are miles, furlongs, rods, yards, feet, inches and lines. 360 of which degrees the distance round the earth. |