13. What must be given for 235 barrels of cider, at $2,35 the barrel? Ans. $552,25. CASE FOURTH. Q. When the quantity given consists of several denomina. tions, as hundreds, quarters, &c. what is the RULE ? A. Multiply the given price by the integers in the given quantity, and for the other denominations, take parts from the price of an integer: the several quotients, added together, will form the answer. EXAMPLES. 1. What cost 7 cwt. 3 qrs. 14 lbs. of sugar, at $9,50 per hundred weight? Ans. $74,814. 2. What cost 12 tons, 16 cwt. 3 qrs. 21 lbs. of hemp, at $35, 75 cents a ton ? Ans. $459,273 cents. 3. What must be given for 125 bush. 3 pks. 6 qts. of clover seed, at $6,37 a bushel? Ans. $802,85 cts. 4. What cost 7 yds. 3 qrs. 2 na. of lace, at $34 a yard? Ans. $25,59 cts. 5. A lady bought 1 yd. 3 qrs. of satin, at 873 cents a yard; what did it cost? Ans. $1,64 cts. 6. What will 2 ounces of tea cost, at the rate of 92 cents the pound? Ans. 11,5 mills, or 11 cts. 7. What must you give for 4 gals. 3 qts. 1 pt. of molasses, at 33 cents a gallon? Ans. $1,60,8 mills. 8. What will 3 qrs. of lace cost, at $14 a yd.? Ans. $1,53. 9. What must be given for 36 rods of land, at $25 an acre? Ans. 5 dollars, 79 cts. and 3 na. of silk, at 75 cts. Ans. 32 cents, 8 mills. 10. What must I give for 1 qr. a yard? 11. What must be given for 5 oz. of sewing silk, at 8 dollars, 25 cts. a pound? Ans. 2 dollars, 57 cts. 8 mills. 12. What cost 2 qrs. 3 n. of silk, at $1,75 a yd.? Ans. $1,20. 13. What will 24 yards, 3 quarters of broadcloth, come to, at $5 a yard? Ans. 145 dollars, 40 cts. 6 mills. CASE FIFTH. Q. What are you taught by the Fifth Case? A. By this case, we are taught to apply the rules of Practice to the multiplication of Compound Numbers, as of weights, measures, &c. Q. When one of the terms, to be multiplied, is a whole number, and the other, a compound number, what is the RULE? A. Multiply the whole number, given, by the integers in the compound number, and for the smaller denominations, divide the whole number by the greatest even part of an integer, contained in the smaller denominations, and for the residue, take even parts of the quotients, as in former cases, and the sum of these quotients and product will be the answer. Q. What if all the denominations, given, in the compound number, be less than an integer; how will you then proceed? A. As in that case, we have nothing to multiply by, we have therefore, only to divide the whole number by the greatest even part of an integer, contained in the given denominations, of the compound number, and take parts of the quotient for the residue, as before, and the sum of all the quotients will be the answer. . EXAMPLES. 1. What is the weight of 12 ingots of silver, each weighing 2 lbs. 8 oz. 12 pwts. 16 Operation. 6 oz. is grs. ? 12 ingots. 3. How many yards in a bale of cloth, containing 48 pieces, and each piece, 31 yds. 3 qrs. 3 na.? Ans. 1533 yards. 4. How many bushels of apples, in 18 barrels, each containing 2 bushels, 3 pecks? Ans. 51 bushels, 3 pecks. 5. How many square feet in a stock of boards, 24 in number, measuring, 12 feet in length, and 1 foot 103 inches in width? Ans. 540 feet. 6. How many solid feet, in a load of wood, measuring 8 feet in length, 3 feet in width, and 3 feet 10 inches in height? Ans. 92 solid feet. 7. In 16 drums of figs, each weighing 9 lbs. 14 oz., how many pounds? and what will they amount to at 16 cents a pound? The whole weight, 158 lbs. Will amount to $25,28. Ans. { 8. How many acres in 6 lots of land, each containing 24 acres, 3 roods, and 35 rods? And what must I give for the whole, at 46 dollars an acro? Ans. { Whole number of acres, 149, 3 roods, 10 rods. 9. How many square feet, in a board 14 feet long, and 10 inches wide? Ans. 11 feet, 8 inches. 10. How many gallons in 150 junk bottles, each containing 1 pint, and 3 gills. Ans. 32 galls. 3 quarts, 0 pint, 2 gills. 11. How many square yards in a piece of cloth measuring 36 yds. in length, and 3 qrs. 1 n. in width. Ans. 29 yds. 1 qr. 12. There is a strip of land measuring 36 yards in length, and 24 feet in width, and is so connected with my lot, that I am willing to give 50 cents the square yard; how many square yards in the strip, and what must I give for it? Ans. 27 square yards. I must give for it, $13,50. 13. How many solid feet in a load of wood measuring 4 feet in length, 1 foot, 6 inches in width, and 1 foot, 11 inches in height? Ans. 11 feet, 6 inches. CASE SIXTH. Q. What is the Sixth Case? A. When two terms are to be multiplied together, both of which are Compound Numbers; as yards, feet, inches, &c.. Q. What is the RULE in this Case? A. Multiply one of the given terms, by the integers in the other given term, as in Compound Multiplication, then divide the multiplicand by the even or aliquot parts of an integer, contained in the smaller denominations of the multiplier, as in the former case, and the sum of the quotients and product will be the answer. EXAMPLES. 1. Multiply 9 yds. 3 qrs. 2 nails, by 4 yds. 3 qrs. 3 nails. NOTE. In dividing feet and inches by aliquot parts, it is most convenient to carry the remainders into seconds, (") thirds, ("") &c. calling 12 thirds 1 second, and 12 seconds inch, and add them as in Compound Addition. 2. How many square feet in a room measuring 14 feet, 10 inches in length, and 9 feet, 9 inches wide? Ans. 144 ft. 7 in. 3. How many square feet in a board 13 feet, 8 inches long, and 2 feet, 7 inches wide? Ans. 35 feet, 3 inches. 4. How many solid feet in a stick of timber 24 feet long, 1 foot, 5 inches broad, and 10 inches in depth or thickness? Ans. 28 feet. 5. How many solid feet of stone in a wall 40 feet, 9 inches in length, 7 feet, 10 inches in height, and 1 foot, 8 inches in thickness? Ans. 532 solid feet. 6. How many square yards of plastering in a room measuring 16 feet, 9 inches in length, 12 feet, 8 inches in width, and 7 feet, 10 inches in height, and including the ceiling over head? Ans. 208 yards, 2 feet, 1 inch, 8". NOTE. In computing the plastering of a room, you must recollect to add the length and breadth together, and multiply their sum by 2, to get the distance round the room, then mul tiply this product by the height of the wall, which will give the superficial measure of the sides and ends; then if the ceiling over head is to be reckoned, cast that separately, and add its measurement to that of the walls, and the sum will be the answer. 7. How many feet of plastering in a hall 44 feet long, 24 feet, 9 inches wide, and 10 feet, 8 inches high, not including Ans. 1466 square feet, 8 inches. long, and the ceiling, overhead? 8. How many yards in a carpet 6 yds. 2 qrs. 3 na.. 5 yds. 3 qrs. 2 na. wide? Ans. 39 yds. 1 qr. 0 na. L 9. How many feet of boards will cover the sides of a building, 32 feet, 6 inches long, 22 feet, 9 inches wide, and 16 feet, 10 inches high, making no allowance for doors or windows; and how many feet will lay the floor? Ans. It will require 1860 feet, 1 inch, to cover the sides. 739 ft. 4 in. to lay the floor. 10. How many feet in a load of wood, measuring 8 feet long,. 3 feet, 9 in. wide, and 3 feet, 8 in. high? Ans. 6 ft. 10 in. NOTE.-In measuring wood on a wagon or sled, if the wood be of customary length, (that is 8 feet,) you must multiply the average width, by the height, and half the product will be the number of cord feet, 8 of which make a cord of wood. NOTE 2.-If the load be more or less than 8 feet long, multiply the length and width together, and that product by the height; then divide this last product by 16, and the quotient will be the number of cord feet, as before. 11. Bought a load of wood, measuring 7 ft. 8 in. in length, 4 ft. 3 in. wide, and 5 ft. 7 in. high; how many cord feet, in the load, and what will it come to, at $6,75 the cord. It measured 11 feet, 4 in. 5", 3"", 9/ Will come to $9,59,2+. Ans. } 12. How many cords of wood, in a pile, 29 ft. 9 in. long, 3 ft. 10 in. wide, and 4 ft. 3 in. high; and to how much will it amount, at $5,62 the cord? It measures 3 cd. 6 ft. 3 in.+ Ans. Amount, $21,29,8 m.+ 13. How many cubic feet, in a block of marble, 6 ft. 10 in. long, 4 ft. 7 in. wide, and 3 ft. 4 in. thick? Ans. 104 ft. 4 in. 9" 4". 14. What quantity of wood, in a load, measuring, 8 ft. long, 2 ft. 9 in. wide, and 3 ft. 7 in. high; and what will it be worth, at 75 cents a foot? Ans. It measures 9 ft. 10 in. 3". Will be worth $7,39. ft. 15. How many square feet, in 32 windows, each measuring 6 ft. 4 in. in height, and 3 ft. 9 in. in width? Ans. 760 sq.: 16. What amount of duties must be paid on a piece of broadcloth, measuring 36 yds. 3 qrs. 2 na. in length, and 1 yd. 2 qrs, 3 na. in width, at 37 cents the square yd.? Ans. $23,33+. MISCELLANEOUS QUESTIONS. 1. What cost 123 yards of satinet, at 5s. 6d. a yard? Ans. 112 dollars, 75 cts. 2. What must I give for 375. barrels of beef, at 73 dollars a barrel ? Ans. 2765 dollars, 62 cents. 3. Bought half a pint of high wine, at $4,50 a gallon; what did it cost? Ans. 28 cents, 1 mill. |