68 COMPOUND SUBTRACTION. to the upper figure on the right, subtract the lower figure from the sum, and set down the remainder. When you borrow one from the upper figure, why do you add one to the figure below it? NOTE.-Upon a clear conception of the principles involved in these questions, depends the pupil's correct knowledge of the science of Arithmetic. AVOIRDUPOIS WEIGHT. tons cwt.qr. tons cwt. qr. lb. From 45 11 3 Rem. 30 1 1 cwt. qr. lb. oz. dr. 17 0 0 0 0 6 3 21 15 9 28 2 2 17 10 0 6 0 17 1. Subtract 76 tons, 18 hundred weight, 3 quarters, from 195 tons, 2 hundred weight, 2 quarters. Ans. 118 tons, 3 cwt. 3 qr. 2. Subtract 14 pounds, 6 ounces, 3 drams from 20 4. Subtract 147b. 6oz. 11dwt. from 227b. 12dwt. 6 gr. Ans. 7lb. 6oz. 1dwt. 65r. 5. From 1676. take 127b. 11oz. 10dwt. 11gr. Ans. 3lb. Ooz. 9dwt. 13gr. 4. Subtract 95 yards, 3 yards, 2 quarters, 3 nails. quarters, 2 nails, from 156 Ans. 60 yds. 3 qr. 1 nail. 5. Subtract 14 English ells, 1 quarter, 2 nails, from 52 English ells, 3 quarters, 2 nails. Ans. 38 yds. 2 qr. 4. Subtract 45 miles, 5 furlongs, 20 poles, from 320 miles, 3 furlongs, 36 poles. Ans. 274 M. 6 F. 16 P. 5. Subtract 15 yards, 2 feet, 6 inches, from 36 yards, 1 foot, 11 inches. Ans. 20 yds. 2 ft. 5 inches. 4. Subtract 36 acres, 2 roods, from 900 acres, 3 roods, 16 perches. 864 A. 1 R. 16 P. 5. Subtract 72 acres, from 360 acres, 2 roods, 29 perches. 288 A. 2 R. 29 P. 1. From a pile of wood containing 432 cords, 27 feet, and 1432 inches, have been hauled 156 cords, 92 feet, 946 inches: how much remains? Ans. 275 cords, 63 feet, 486 in. 2. From a bank of earth containing 2984 yards, 18 feet, have been taken 1436 yards, 21 feet: what remains? Ans. 1547 yds. 24 feet. 3. If I purchase 2hhd. of wine, and to oblige a friend send him 29gal., what quantity have I left? Ans. 1hhd. 34gal. 4. Bought 1 pipe of wine, 4hhd. of brandy, 2 barrels of beer; I have since sold 93 gallons of wine, 29 of brandy, 1 barrel of beer: how much of each have I remaining? Ans. 33gal. of wine, 223gal. of brandy, and 1 barrel of beer. A circle being 12 sines, how far has the hand of a watch to pass, after having gone through 4 sines, 23o 2 A person residing in latitude 27° 32′ 45′′ north, wishes to visit a place 52° 24' 18' north. How many degrees, minutes, and seconds northward must he travel? Ans. 24° 51' 33'. 5. If I take 1Y. 1M. from 6Y. what space of time will still remain? Ans. 4Y. 11 M. NOTE. To ascertain the amount of time passed between two events, set down the year, month, and day of the latter event, and place those of the former below it, and subtract. 6. A bond was given 24th July, (7th month) 1809, and paid off 13th August, 1821. yrs. mo. ds. 1821 8 13 1809 7 24 12 0 20 7. The declaration of independence of the United States passed Congress, 4th July, (7th month) 1776; and the declaration of the late war with Great Britain, 18th June, (6th mo.) 1812. How many years, &c. between them? Ans. 35yr. 11mo. 14d. 4. Subtract £290 9s. from £1000 11s. 11ąd. Ans. £800 2s. 11ąd. 5. I have a purse of money containing £1000 2s. 41d. if I take out £60 7s. 84d. what sum will be left? Ans. £939 14s. 7ąd. COMPOUND MULTIPLICATION. COMPOUND MULTIPLICATION is the art of multiplying numbers composed of several denominations. CASE 1. When the multiplier does not exceed 12. RULE. Place the number to be multiplied as directed in compound addition; and set the multiplier under the lowest denomination. Multiply as in simple multiplication, and divide the product of each denomination by as many as it takes of that to make one of the next greater; set down the remainder (if any) and carry the quotient to the product of the next denomination. Proof-Double the multiplicand and multiply by half the multiplier. EXAMPLES. Bu. pe. qt. pt. 77 2 5 53 2 1 6 1 7 times 1 pint make 7 pints; 2 pt. make 1 qt.; then 7 pt. make 3 qt. and leave 1 pt. Set down the 1 pt. and carry the 3 qt. to the product of the next figure. 7 times 5 qt. make 35 qt. to which add the 3 qt. which make 38 qt.; 8 qt. make one peck; then 38 qt. make 4 pecks and leave 6 qts. Set down the six quarts and carry the 4 pecks. 7 times 2 pecks make 14 pecks; add the 4 pecks, makes 18 pe. ; 4 pecks make one bushel; then 18 pe. make 4 bushels and leave 2 pecks. Set down the 2 pecks and carry the 4 bushels. 7 times 7 bushels make 49 bushels; add the 4 bushels, makes 53 bushels, which set down, and the work is done. |