45. To multiply by 10, 100, 1000, &c. Annex as many ciphers to the multiplicand as there are ciphers in the multiplier, and the number thus formed will be the product required. 40. What will 10 dresses cost, at 18 dollars apiece? 51. What will 20 wagons cost, at 67 dollars apiece? Suggestion. Since multiplying by ciphers produces ciphers, we omit multiplying by the 0, and placing Operation. 67 20 the significant figure 2 under the Ans. 1340 dollars. right hand figure of the multipli cand, multiply by it in the usual way, and annex a cipher to the product. The answer is 1340 dollars. Hence, 46. When there are ciphers on the right hand of the multiplier. Multiply the multiplicand by the significant figures of the multiplier, and to this product annex as many ciphers, as are found on the right hand of the multiplier. (55.) QUEST.-46. When there are ciphers on the right of the multiplicand, how do you proceed? 60. In one hour there are 60 minutes: how many minutes are there in 125 hours? 61. What will 300 barrels of flour cost at 8 dollars per barrel? 62. What cost 400 yds. of cloth, at 17 shills. per yd.? 63. If the expenses of 1 man are 135 dollars per month, how much will be the expenses of 200 men? 64. If 1500 men can build a fort in 235 days, how long will it take one man to build it? 47. When there are ciphers on the right of the multiplicand. Multiply the significant figures of the multiplicand by the multiplier, and to the product annex as many ciphers, as are found on the right of the multiplicand. 65. What will 43 building lots cost, at 3500 dollars a lot? Having placed the multiplier under the significant figures of the multiplicand, multiply by it as usual, and to the product thus produced, annex two ciphers, because there are two ciphers on the right of the multiplicand. Operation. 3500 43 105 140 Ans. 150500 dolls. (69.) (67.) 2400 21000 25000 17 24 32 70. What is the product of 132000 multiplied by 25? 71. What is the product of 430000 multiplied by 34? 72. What is the product of 1520000 multiplied by 43? 73. What is the product of 2010000 multiplied by 52 ? 74. What is the product of 3004000 multiplied by 61? QUEST.-47. When there are ciphers on the right of the multiplicand, how do you proceed? 48. When the multiplier and multiplicand both have ciphers on the right. Multiply the significant figures of the multiplicand by the significant figures of the multiplier, and to this product annex as many ciphers, as are found on the right of both factors. 75. Multiply 16000 by 3200. Having placed the significant figures of the multiplier under those of the multiplicand, we multiply by them as usual, and to the product thus obtained, annex five ciphers, because there are five cipaers on the right of both factors. Solve the following examples: 76. 2100X200. 78. 12000X210. 100. 680539 X 80406. Operation. 16000 3200 32 48 Ans. 51200000 77. 3400X130. 79. 25000 X 2600. 97. 864325×6728. 99. 4567832 × 27324. 101. 7563057 62043. 102. Multiply seventy-three thousand and seven by twenty thousand and seven hundred. 103. Multiply six hundred thousand, two hundred and three by seventy thousand and seventeen. QUEST.-48. When there are ciphers on the right of both the multiplier and multiplicand, how proceed? SECTION V. DIVISION. ART. 49. Ex. 1. How many lead pencils, at 2 cents apiece, can I buy for 10 cents? Solution.--Since 2 cents will buy 1 pencil, 10 cents will buy as many pencils, as 2 cents are contained times in 10 cents; and 2 cents are contained in 10 cents, 5 times. I can therefore buy 5 pencils. 2. A father bought 12 pears, which he divided equally among his 3 children: how many pears did each receive? Solution.―Reasoning in a similar manner as above, it is plain that each child will receive 1 pear, as often as 3 is contained in 12; that is, each must receive as many pears, as 3 is contained times in 12. Now 3 is contained in 12, 4 times. Each child therefore received 4 pears. OBS. The object of the first example is to find how many times one given number is contained in another. The object of the second is to divide a given number into several equal parts, and to ascertain the value of these parts. The operation by which they are solved is precisely the same, and is called Division. Hence, 50. DIVISION is the process of finding how many times ore given number is contained in another. The number to be divided, is called the dividend. The number by which we divide, is called the divisor. The answer, or number obtained by division, is called the quotient, and shows how many times the divisor is contained in the dividend. QUEST.-50. What is division? The number by which we divide? the quotient show? What is the number to be divided, called? Note. The term quotient is derived from the Latin word quoties, which signifies how often, or how many times. 51. The number which is sometimes left after division, is called the remainder. Thus, when we say 4 is contained in 21, 5 times and 1 over, 4 is the divisor, 21 the dividend, 5 the quotient, and 1 the remainder. OBS. 1. The remainder is always less than the divisor; for if it were equal to, or greater than the divisor, the divisor could be contained once more in the dividend. 2. The remainder is also of the same denomination as the dividend; for it is a part of it. 52. Sign of Division (÷). The sign of Division is a horizontal line between two dots (÷), and shows that the number before it, is to be divided by the number after it. Thus, the expression 246, signifies that 24 is to be divided by 6. Division is also expressed by placing the divisor under the dividend with a short line between them. Thus the expression 35, shows that 35 is to be divided by 7, and is equivalent to 35÷7. 53. It will be perceived that division is similar in principle to subtraction, and may be performed by it. For instance, to find how many times 3 is contained in 12, subtract 3 (the divisor) continually from 12 (the dividend) until the latter is exhausted; then counting these repeated subtractions, we shall have the true quotient. Thus, 3 from 12 leaves 9; 3 from 9 leaves 6; 3 from 6 leaves 3; 3 from 3 leaves 0. Now, by counting, we find that 3 has QUEST.-51. What is the number called which is sometimes left after division? When we say 4 is in 21, 5 times and 1 over, what is the 4 called? The 21? The 5? The 1? Obs. Is the remainder greater or less than the divisor? Why? Of what denomination is it? Why? 52. What is the sign of divi sion? What does it show? In what other way is division expressed? |