II. When the Numbers are to be reduced from a Lower Denomination to a Higher: DIVIDE the given number by as many as of that denomi nation make I of the next higher, and set down what remains, as well as the quotient. Divide the quotient by as many as of this denomination make 1 of the next higher; setting down the new quotient, and remainder, as before. Proceed in the same manner through all the denominations, to the highest; and the quotient last found, together with the several remainders, if any, will be of the same value as the first number proposed. EXAMPLES. 2. Reduce 1185388 farthings into pounds, shillings, and pence. 4) 1185388 12) 296347 d 2,0) 2469,5 s-7d Answer 1234/ 15s d 3. Reduce 247 to farthings. 4. Reduce 337587 farthings to pounds, &c. Ans. 23040. Ans. 351/ 13s 03. Ans. 36. 5. How many farthings are in 36 guineas? 6. In 36288 farthings how many guineas?" 7. In 59 lb 13 dwts 5 gr how many grains? Ans. 340157. 8. In 8012131 grains how many pounds, &c.? Ans. 1390 lb 11 oz 18 dwt 19 gr 9. In 35 ton 17cwt 1 qr 23 lb 7oz 13 dr how many drams? Ans. 20571005. 10. How many barley-corns, will reach round the earth, supposing it, according to the best calculations, to be 25000 miles? Ans. 4752000000. 11. How many seconds are in a solar year, or 365 days 5 hrs 48 min 48 sec ? Ans. 31556928. 12. In a lunar month, or 29 ds 12 hrs 44 min 3 sec, how many seconds? Ans. 2551443. COM COMPOUND ADDITION. COMPOUND ADDITION shows how to add or collect several numbers of different denominations into one sum. RULE. Place the numbers so, that those of the same denomination may stand directly under each other, and draw a line below them. Add up the figures in the lowest denomination, and find, by Reduction, how many units, or ones, of the next higher denomination are contained in their sum.Set down the remainder below its proper column, and carry those units or ones to the next denomination, which add up in the same manner as before.-Proceed thus through all the denominations, to the highest, whose sum, together with the several remainders, will give the answer sought. The method of proof is the same as in Simple Addition. EXAM. 9. A nobleman, going out of town, is informed by his steward, that his butcher's bill comes to 197/ 13s 74d; his baker's to 591 5s 23d; his brewer's to 85; his wine-merchant's to 1037 13s; to his corn-chandler is due 75/ 3d; to his tallow-chandler and cheesemonger, 277 15s 111d; and to his tailor 551 3s 53d; also for rent, servants' wages, and other charges, 127/ 3s: Now, supposing he would take 100/ with him, to defray his charges on the road, for what sum must he send to his banker? Ans. 830/ 14s 6d. 10. The strength of a regiment of foot, of 10 companies, and the amount of their subsistence*, for a month of 30 days, according to the annexed Table, are required? * Subsistence Money, is the money paid to the soldiers weekly which is short of their full pay, because their clothes, accoutrements, &c. are to be accounted for. It is likewise the money advanced to officers till their accounts are made up, which is commonly once a year, when they are paid their arrears. The following Table shows the full pay and subsistence of each rank on the English establishment. VOL. I. D DAILY 1st Major.. Captain 1st Lieut. 2d Ditto Cornet 1 601 3 112 10 2 401 2 61 7 01 16 01 11 0 Foot Guards. Subsist. Full Pay. 1 10 01 19 0 1 * 0 O 1 0 0 0 15 11 1 33 1 11 0 1 26 1 161 8 6 0 17 0 3 0 15 0 0 14 10 19 61 601 1 6 0 11 6 0 15 00 8 5 0 0 8 6 0 11 0 0 460 5 0 0 300 0 660 8 6 54 ၁၀ 0 5 12 60 15 600 800 900 12 0 0 7 6 0 10 0 5 0 0 500 8 0000 500 5 0 IXAMPLES N. B. When a Lieutenant, Ensign, Adjutant, or Quarter-ma-ter of Foot, Militia, Fencible Infantry, or Invalids, holds two commissions, one shifting per day is to be deducted from the above rates for each commission. |