36. Multiply 7008005 by 10008. 37. Multiply 4001100 by 40506. 38. Multiply 6716700 by 808070. 39. Multiply 987648 by 481007. 40. Multiply 18711000 by 470. 41. Multiply 10000 by 7000. Ans. 70136114040. Ans. 162068556600. Ans. 5427563769000. Ans. 475065601536. Ans. 8794170000. Ans. 70000000. 42. Multiply 101010101 by 2020202. Ans. 204060808060402. 43. Multiply 70000 by 10000. Ans. 700000000. Ans. 7207272072. Ans. 63126063000. Ans. 3394240201606. Ans. 169233130080. 48. Multiply 304050607 by 3011101. Ans. 915527086788307. 49. Multiply 908007004 by 500123. Ans. 454115186861492. 50. Multiply 2003007001 by 6007023. Ans. 12032109124168023. 51. Multiply 9000006 by 9000006. Ans. 81000108000036. 52. Multiply 1152921504606846976 by 1152921504606846976. Ans. 1329227995784915872903807060280344576. 53. What will 27 oxen cost at 35 dollars each ? Ans. $945. 54. What will 365 acres of land cost at 73 dollars per acre? Ans. $26645. 55. What will 97 tons of iron cost at 57 dollars a ton? Ans. $5529. 56. What will 397 yards of cloth cost at 7 dollars per yard? Ans. $2779. 57. What will 569 hogsheads of molasses cost at 37 dollars per hogshead? Ans. $21053. 58. If a man travel 37 miles in one day, how far will he travel in 365 days? Ans. 13505 miles. 59. If one quire of paper have 24 sheets, how many sheets are in a ream, which consists of 20 quires? Ans. 480 sheets. 60. If a vessel sails 169 miles in one day, how far will she sail in 144 days? Ans. 24336 miles. 61. What will 698 barrels of flour cost at 7 dollars a barrel? Ans. $4886. 62. What will 376 lbs. of sugar cost at 13 cents a pound? Ans. 4888 cts. 63. What will 97 lbs. of tea cost at 93 cents a pound? Ans. 9021 cts. 64. If a regiment of soldiers consists of 1128 men, how many men are there in an army of 53 regiments? Ans. 59784. 65. What will an ox weighing 569 pounds amount to at 8 cents a pound? Ans. 4552 cts. 66. If a barrel of cider can be bought for 93 cents, what will 75 barrels cost? Ans. 6975 cts. 67. If in a certain factory 786 yards of cloth are made in one day, how many will be made in 313 days? Ans. 246018 yds. 68. A certain house contains 87 windows, and each window has 32 squares of glass; how many squares are there in the whole house? Ans. 2784 squares. 69. There are 407 wagons each loaded with 30009 pounds of coal; how many pounds are there in the whole? Ans. 12213663 pounds. 70. Multiply three hundred and seventy-five millions two hundred and ninety-six thousand three hundred and twenty-one, by seventy-nine thousand and twenty-four. Ans. 29657416470704. 71. What would be the cost of 687 fothers of lead at 73 dollars a fother? Ans. $50151. SECTION V. DIVISION. THE object of Division is to find how many times one number is contained in another. Division consists of three principal parts; the Dividend, or number to be divided; the Divisor, or number by which we divide; and the Quotient, which shows how many times the dividend contains the divisor. When the dividend contains the divisor an exact number of times, the quotient is expressed by a whole number. But when this is not the case, there will be a remainder, when the division has reached its limit, and this remainder placed above the divisor, with a horizontal line between them, will form a fraction, and should be written at the right hand of the quotient, and will be a part of it. See Example 2d, and note. 1. The Remainder may be considered a fourth term in Division, and it will always be of the same denomination with the dividend. For the sake of convenience, Division has been divided into two kinds, Long and Short. 2. All questions in which the divisor is not more than 12 may be conveniently performed by Short Division; all others are better performed by Long Division. SHORT DIVISION. EXAMPLE. 1. Divide 948 dollars equally among Dividend. Divisor 4)948 4 men. In performing this question, inquire how many times 4, the divisor, is contained in 9, which is 2 times, and 1 remaining; write the 2 under the 9 and suppose 1, the remainder, to be placed before the next figure of the dividend, 4, and the number will be 14. Then inquire how many times 4, the divisor, is contained in 14. It is found to be 3 times and 2 remaining. Write the 3 under the 4, and suppose the remainder, 2, to be placed before the next figure of the dividend, 8, and the number will be 28. Inquire again how many times 28 will contain the divisor. It is found to be 7 times, which we place under the 8. Thus we find each man receives 237 dollars. From the above illustration, we deduce the following RULE. Write down the dividend and place the divisor on the left, with a curved or perpendicular line drawn between them. Draw also a horizontal line under the dividend, then observe how many times the divisor is contained in the first figure or figures of the dividend (beginning at the left hand), and place the quotient figure directly under the right-hand figure of the part of the dividend that was taken. If there be no remainder, proceed to inquire how many times the divisor is contained in the next figure* of the dividend, and set down the result at the right hand of the quotient figure already obtained, or directly under the figure of the dividend, and continue the work in this manner until the whole dividend is divided. But if there be a remainder either in the first or any subsequent division, imagine the number denoting it to be placed directly before the next figure of the dividend, and ascertain the number of times the divisor is contained in the number thus formed, and place the *If this figure be smaller than the divisor, it cannot contain it, and the figure to be placed in the quotient will be a cipher. Sometimes, as when we divide by 11 or 12, we may have two successive ciphers in the quotient, as when the divisor is 12 and the next two figures are 1's or 1 and 0. We are then obliged to proceed to a third figure in the dividend, before we can effect a proper division. quotient figure underneath, as before. Proceed in this way until every part of the dividend is thus divided, and the result will be the quotient sought. From this and subsequent examples it will be seen that fractions arise from division, and are parts of a unit; that the denominator of the fraction represents the divisor, and shows into how many parts the given number or quantity is divided, and the numerator, being the remainder, shows how many units of the given quantity or dividend remain undivided. By writing the numerator over the denominator in the form of a fraction, we signify that it is to be divided by the denominator; and when placed at the right hand of the whole number in the quotient, the fraction becomes a part of the quotient, and, as such, is as much less than a unit, as the numerator is less than the denominator. |