Ans. $1.811. Ans £26 16s. old. 5. Multiply 64 cents by 20. 6. Multiply 17s. 3 d. by. 31. 7. Multiply 11s. 34d. by 39. 8. Multiply 18s. 8d. by 46. 9. Multiply 7 pounds, 9 ounces, 3 pennyweights,. 12 grains by 47. Ans. 364lb. 11oz. 4dwt. 12gr. Ans. £42 18s. 8d. 10. Multiply 30 tons, 10 hundredweight, 3 quarters by 52. Ans. 1587 tons, 19cwt. Oqr. 11. Multiply 31 yards, 2 quarters by 53. Ans. 1669yd. 2qr. 12. Multiply 30 miles, 3 furlongs, 29 poles by 58. Ans. 1767m. Ofur. 2p. 13. Multiply 36 square feet, 120 square inches by 65. Ans. 23948q.ft. 24sq.in. 14. Multiply 37 acres, 1 rood, 10 poles by 68, Ans. 2537a. 1r. 15. Multiply 12 cubic feet, 1700 cubic inches by 69. Ans. 33c.yd. 4c.fl. 1524c.in. 16. Multiply 31 years, 302 days, 20 hours, 20 minutes by 76. Ans. 2419yr. 21dy, 9hr. 20m. 17. Multiply 13 gallons, 3 quarts, 1 pint, 2 gills by 27. Ans, 1tun, 1hhd. 61 gal. 1qt. Opt. 2 gills. 18. Multiply 30 chaldrons, 2 bushels, 20 pecks, 2 quarts by 82. Ans. 2465ch. 30b. Op. 4qt. 19. Multiply 3° 30′ 30′′ by 89. Ans. 20. Multiply $3:37 by 150. 25. Multiply £2 78. 8d. by 79. 11 signs 25° 30′ 30′′. Ans. $27.181. Ans. £47 4s. 0žd. Ans. £188 8s. 11 d. Exercises in Compound Multiplication. Ex. 1. Required the cost of a chest of tea, containing 97 pounds, at 87 cents per pound. Ans. $84.87. 2. Required the cost of a firkin of butter, weighing 72 pounds, at 182 cents per pound. Ans. $13.50. 3. Required the cost of 25 pounds of beeswax, at 12 cents per pound. Ans $3.12. 4. Required the cost of 12 chaldrons of Liverpool coal, at $12.50 per chaldron. Ans. $150.00. 5. Required the cost of 35 chaldrons of Schuylkill coal, at $11.25 per chaldron. Ans. $393.75 6. Required the cost of 22 pounds of Cocoa, at 10 cents per pound. Ans. $2.31. 7. Required the cost of 120 pounds of coffee, Porto Rico, at 15 cents per pound. Ans. $18-60. 8. Required the cost of 119 pounds of coffee, St. Domingo, at 134 cents per pound. Ans. $16.361. 9. Required the cost of 33 pounds of copper, at 27 cents per pound. Ans. $9.07. 10. Required the cost of 256 pounds of cotton, NewOrleans, at 104 cents per pound. Ans. $26.24. 11. Required the cost of 25 yards of calico, at 18 cents per yard. Ans. $4.62. 12. Required the cost of 36 yards of shirting, brown, at 8 cents per yard. Ans. $3.15. Ans. $5.77. 13. Required the cost of 42 yards of check, at 134 cents per yard. 14. Required the cost of 29 pieces of diaper, Russia, at $2.25 per piece. Ans. $65.25. 15. Required the cost of 32 pounds of figs, at 81 cents per pound. Ans. $2.72. Ans. $346-75. 16. Required the cost of 365 bushels of barley, at 95 cents per bushel. 17. Required the cost of 26 gallons of honey, Havana, at 75 cents per gallon. 18. Required the cost of 15 pounds of sugar, at 13 cents per pound. Ans. $19.50. Ans. $2:02. 19. Required the amount of a box of linen cloth containing as under: 20. From 1783 to 1793, both inclusive, the money paid for slaves, imported into the West Indies, in Liverpool ves sels, was, at an average, £1380622 16s. 44d. each year. What was the entire amount? Ans. £15186851 Os. 1d. 21. How much is the weight of 35 chests of tea, each weighing 96 pounds, 10 ounces? Ans. 3381lb. 14oz. 22. How much is the weight of 16 hogsheads of sugar, each weighing 7cwt. 3qr. 21lb. Ans. 127cwt. Oqr. Olb. 23. How much is the weight of 28 ingots of gold, each weighing 6 pounds, 7 ounces, 15 pennyweights, 20 grains? Ans. 1861b. 2oz. 3dwt. 8gr. 24. What is the weight of 1000 dollars, each weighing 17 pennyweights 6 grains? Ans. 71lb. 10oz. 10dwt. 25. In 36 pieces of linen cloth, each measuring 25 yards, 2 quarters, 1 nail: how many yards? Ans. 920yd. 1qr. 26. How many acres are there in 34 farms, each con taining 315 acres, 3 roods, 30 poles? Ans. 10741a. 3r. 20p. 27. In 17 pipes of brandy, each containing 127 gallons, 3 quarts, 1 pint, how many gallons? Ans. 2173gal. 3qt. 1pt. 28. The Moon performs her mean sidereal revolution in 27 days, 7 hours, 43 minutes, and 11 seconds. In how many days will she perform 13 revolutions? Ans. 355 dys. 4hrs. 21′ 291". 29. The mean daily motion of the planet Venus in her orbit, is 1 degree, 36 minutes, 8 seconds, per day. many degrees, &c. does she describe in 224 days? How Ans. 358° 53′ 52". 30. The mean daily motion of the Earth in its orbit, is 59 minutes, 8 seconds. How many degrees will the Earth describe in 365 days? Ans. 359° 43. 40". When is compound multiplication used? When the multiplier does not exceed 12, how is the operation performed? When the multiplier exceeds 12, but is the product of two or more known factors, each less than 13, how is the . operation performed? Repeat the rules of operation, when the multiplier is not produced by factors below 13.* *Compound Multiplication is seldom employed except in relation to money; but if it be necessary to use it in cases not illustrated here, no difficulty can arise, as the method is similar in all cases. It may perhaps be proper to caution learners against the absurdity of attempting to multiply money by money. This caution will not appear unnecessary, if it be considered, that whole pages have been filled with instructions how to perform this problem; and it has been attempted to be shown, even with the semblance of geometrical demonstration, that if 2s. 6d. be multiplied by 2s. 6d. the product will be 31. or 6s. 3d. Let it be considered, however, that in multiplication a quantity is simply repeated a given number of times: thus, if 2s. 6d. be repeated 4 times, the amount is 10s.; if 5 times, 12s. 6d. To talk, therefore, of multiplying 2s. 6d., by 2s. 6d, or, which amounts to the same thing, repeating 2s. 6d., 2s. 6d. times, is absolute nonsense. In the rule of propor tion, indeed, we sometimes appear to multiply such quantities. Thus, in finding the interest of a sum at a given rate, for a year, we multiply by the rate and divide by 100. In this case, however, both 100 and the rate are divested of their characters as expressions for money, and are merely to be regarded as abstract numbers, used as the terms of a ratio. By multiplying by the rate, suppose 5, we merely repeat the principal COMPOUND DIVISION. 56. When the dividend expresses a quantity of the same kind, but of different denominations, the process is termed Compound Division. Problem 1. To divide a number of more denominations than one, by a number not exceeding 12. 57. RULE. Divide the highest denomination by the given divisor by short division. Reduce the remainder, if there be any, to the denomination next lower, and add to the result what was given of that denomination. Divide the sum by the divisor; and thus proceed to the lowest denomination or till nothing remains. * Ex. 1. Divide $ 17.35 by 2. Here the division is performed as in whole numbers; but it may be observed that the mark of dollars being prefixed, the cents must be separated from the dollars by a point. £ s. d. 10)14 16 71 2. Divide £ 14 16s. 71d. by 10. In this example, after dividing £ 14 by 10, we have £4, or 80 shillings; which, increased by 16, becomes 968. Hence we find the next part of the quotient to be 9s. and the remainder 1 9 72 14 16 7 proof. $cls. 2) 17 35 $8.67 far, or 1d. This is 6s. or 72d. which, increased by 7, becomes 79. being divided by 10, we have the remainder 9d. or 36 far 5 times, or find a principal 5 times as great; and then, as there must be one pound of interest for each hundred pounds in this increased principal, we try by division how often it contains one hundred pounds; and we thus find the pounds of the interest. In like manner, the multiplication of 200 cents by 200 cents, is complete nonsense, except there be a given term of comparison; for instance, one dollar or one cent; that is, if one dollar gain two hundred cents or two dollars, two dollars or two hundred cents would gain four dollars. But, if one cent would gain 200 cents, then 200 cents would gain 40000 cents, or 400 dollars. |
