49. How many yards of carpeting, that is one yard in width, will be required to carpet a room 18ft. long and 15ft. wide? Ans. 30 yards. 50. A certain machine will cut 120 shingle-nails in a minute; how many will it cut in 47 days 7 hours, admitting the machine to be in operation 10 hours per day? Ans. 3434400 nails. 51. In a field 80 rods long and 50 rods wide, how many square rods? How many acres? Ans. 25 acres. 52. How long will it take to count 18 millions, counting at the rate of 90 a minute? Ans. 138da. 21h. 20m. 53. A merchant purchased 9 bales of cloth, each containing 15 pieces, each piece 23 yards, at 8 cents per yard; what was the amount paid ? Ans. $248.40. 54. Suppose a certain township is 6 miles long and 4 miles wide, how many lots of land of 90 acres each does it contain? Ans. 192 lots. 55. The pendulum of a certain clock vibrates 47 times in 1 minute; how many times will it vibrate in 196 days 49m.? Ans. 13267583 times. 56. How many shingles will it take to cover a building that is 36 feet long and 24 feet wide, with rafters 16 feet long, supposing 1 shingle to cover 27 square inches? Ans. 6144 shingles. 57. How many times will the large wheels of an engine turn round in going from Boston to Portland, a distance of 110 miles, supposing the wheels to be 12 feet and 6 inches in circumference? Ans. 46464 times. 58. In a certain house there are 25 rooms, in each room 7 bureaus, in each bureau 5 drawers, in each drawer 12 boxes, in each box 15 purses, in each purse 178 sovereigns, each sovereign valued at $4.84; what is the amount of the money? Ans. $135689400. 59. In 18rd. 5yd. 2ft. 11in. how many inches? 60. In 3779 inches how many rods? Ans. 3779 inches. Ans. 18rd. 5yd. 2ft. 11in. 61. Sold 5T. 17cwt. 3qr. 18lb. of potash for 3 cents per pound; what was the amount? Ans. $353.79. 62. A gentleman purchased a house-lot that was 25 rods long and 16 rods wide for $100,000, and sold the same for $1.25 per square foot; what did he gain by his purchase? Ans. $36,125. § XI. ADDITION OF COMPOUND NUMBERS. ART. 101. ADDITION of Compound Numbers is the process of finding the amount of two or more compound numbers. ENGLISH MONEY. Ex. 1. Paid a London tailor 7£. 13s. 6d. 2far. for a coat; 2£. 17s. 9d. 1far. for a vest; 3£. 8s. 3d. 3far. for pantaloons; 9£. 11s. 8d. 3far. for a surtout; what was the amount of the bill? Ans. 23£. 11s. 4d. 1far. OPERATION. £. S. d. far. 3 2 17 9 1 3 8 3 9 11 8 3 Having written units of the same denomination in the same column, we find the sum of farthings in the right-hand column to be 9 farthings, equal to 2d. and 1far. We write the 1far. under the column of farthings, and carry the 2d. to the column of pence; the sum of which is 28d., equal to 2s. 4d. We write the 4d. under the column of pence, and carry the 28. to the column of shillings; the sum of which is 51s., equal to 2£. 11s. Having written the 11s. under the column of shillings, we carry the 2£. to the column of pounds, and find the whole amount to be 23£. 11s. 4d. 1far. Ans. 23 11 4 1 The same result can be arrived at by reducing the numbers as they are added in their respective columns. Thus, in working the example, we can, beginning with farthings, add in this way: 3far. and 3far. are 6far., equal to 1d. 2far., and 1far. are 1d. 3far., and 2far. are 1d. 5far., equal 2d. 1far. Writing the 1far. under the column of farthings, carry the 2d. to the column of pence; add 2d. (carried) and 8d. are 10d., and 3d. are 13d., equal to 1s. 1d., and 9d. are 1s. 10d., and 6d. are ls. 16d., equal to 28. 4d. Writing the 4d. under the column of pence, carry the 2s. to the column of shillings; add 2s. (carried) and 11s. are 13s., and 8s. are 21s., equal to 1£. 1s., and 17s. are 1£. 18s., and 13s. are 1£. 31s., equal to 2£. 11s. Writing 11s. under the column of shillings, carry the 2£. to the column of pounds, and so find the whole amount to be, as before, 23£. 11s. 4d. 1far. Thus the adding of compound numbers is like that of simple numbers, except in carrying; which difference holds also in subtracting, multiplying, and dividing of compound numbers. QUESTIONS. Art. 101. What is addition of compound numbers? How do you arrange compound numbers for addition? Why? What is the difference between addition of compound and addition of simple numbers? RULE. -- Write all the given numbers so that units of the same denomination may stand in the same column. Add as in addition of simple numbers; and carry, from column to column, one for as many units as it takes of the denomination added to make a unit of the denomination next higher. PROOF. bers. lb. 2. The proof is the same as in addition of simple num EXAMPLES FOR PRACTICE. oz. pwt. gr. 15 11 19 22 71 10 13 17 |
