87. Miscellaneous Examples. 63. I have four bins, containing severally 63 bushels, 54 bushels, 37 bushels, and 29 bushels. If there are 60 pounds of corn in a bushel, how many pounds of corn will they all hold ? 64. What is the height of an iceberg which is 375 feet above the surface of the water and 7 times as many feet below ? 65. Myron walks 847 steps of 2 feet each in going to school. How many more feet must he take to walk a mile, or 5280 feet ? 66. What do I save a year, my income being $ 1600 a year, and my expenses $ 24 a week, 52 weeks making the year ? 67. Mr. Fiske receives a salary of $ 1500 a year, pays $ 130 for clothing, $ 275 for other expenses, also $6 a week for his board. How much money has he left at the end of the year ? 68. If 768 be one factor, and 861 – 237 the other factor, what is the product ? 69. Smith & Co. consume 74 tons of coal in a year. How much more did they pay for their coal in 1864, when coal was $ 14 a ton, than in 1877, when it was $7 ton ? 70. If in one yard of cloth there are 580 fibres of warp and 432 of filling, and each fibre of warp contains 32 strands, and each of filling 48, how many strands are there in the yard ? 71. One house is valued at $ 6750, and another at three times as much. How much will pay for both houses ? 72. Mr. Gould had $ 2500 with which he bought 17 acres of land at $ 42 an acre, a house for $ 1500, 2 cows at $45 apiece, and a horse for $75. How much money had he left ? 73. Mr. Bodwell paid for labor and use of oxen on his land, the following sums : $ 135, $ 128, and $ 90; he also paid $ 64 for fertilizers and $ 10 for seed, and raised on the land 23 tons of hay which he sold at $ 25 a ton. What was his gain above his expenses ? 74. Add 284, 1752, 45, and 846; subtract 2731 from the sum; multiply the remainder by 208; and find the difference between the product and 40801. SECTION V. DIVISION. 88. Mr. Rice has 24 bushels of sand to bring from the beach. If he brings 8 bushels at each load, how many loads must he bring ? He must bring as many loads as there are 8's in 24. We have already seen by multiplication that three 8's are 24, so we know that he must bring 3 loads. If a cheese weighing 54 pounds be divided equally among 6 persons, how many pounds will each receive? Each person will receive one of the 6 equal parts into which the 54 pounds is to be divided. We have seen by multiplication that 6 nines are 54; hence one of the 6 equal parts of 54 is 9, and each person will receive 9 pounds. It will be noticed in the first example that we find how many equal numbers, one of which is given, there are in another number (that is, how many times one number is contained in another); and in the second that we find one of the equal parts of a number. 89. The process of finding how many times one number is contained in another or of finding one of the equal parts of a number is division. 90. The number to be divided is the dividend. 91. The number by which we divide is the divisor. 92. The result obtained by division is the quotient. NOTE 1. When the divisor is one of the given equal numbers, the quotient will tell how many such numbers there are in the dividend. NOTE II. When the divisor tells how many equal parts the dividend is to be separated into, the quotient will tell how great one of those equal parts is. NOTE III. By comparing the first process with multiplication (Arts. 69-72), we see that the product and multiplicand are given, and the multiplier is to be found. By comparing the second process with multiplication, we see that the product and multiplier are given, and the multiplicand is to be found. In either case the product and one of the factors are given, and the other factor is required. 93. Iỉ Mr. Rice has 31 bushels of sand to bring from the beach, and can bring but 8 bushels at a load, how many full loads can he bring and how many bushels will then remain ? The part of the dividend left after the equal numbers have been taken away is the remainder. In the example above, which is the dividend ? the divisor? What is the remainder ? 24 94. The division of numbers is indicated by the sign -. Thus, the expression 24 - 8 = 3 means that the quotient obtained by dividing 24 by 8 is 3, and is read “24 divided by 8 equals 3.” The sign : is also used for division. Thus, 24:8 3. Sometimes the dividend is expressed above a line and the divisor below, in place of the dots. Thus, = 3. This expression is called the fractional form of indicating division, and is read “ 24 divided by 8 equals 3,” or “1 eighth of 24 equals 3." 95. When a thing or a number is divided into 2 equal parts, the parts are called halves; when divided into 3 equal parts, the parts are called thirds; when into 4 equal parts, the parts are called fourths; and so on. What is one of the parts called when a number is divided into 5 equal parts ? 6? 7? 8? 10 ? 20 ? 100 ? 1000 ? 19| 2 26 34 27 30 32 36 4. 39 46 38 41 44 48 52 57 50 53 56 60 3. 25 29 35 33 28 31 42 37 43 47 40| 45 17 6. 62 71 70 66 61 64 69| 63 68 65 67 72 7.1 76 79 77 74 83 84 9.90 88 85 93 86 95 92 96 9. 99 104 100 98 97 102 106 101 107 103 105 108 10. 110 118 111 109 117 112 115 114 119 113 116 120 11. 124 130 123 125 129 121 128 122 131 126 127 132 12. 134 142 135 140 133 139|136 143 137 141 138 144 97. Oral Exercises upon the Table. Beginning at the left of the table above, divide by 2 each number expressed in the first two lines, naming quotients and remainders at sight. In the first line the numbers to be divided are 4, 7, 2, 6, 3, 8, 5, etc. The results will be given as follows: “2; 3 and 1 over; 1; 3; 1 and 1 over; 4,” etc. Divide in the same manner the numbers expressed in either* a. Of the first 3 lines by 3. f. Of lines 2 to 8 by 8. b. Of the first 4 lines by 4. g. Of lines 2 to 9 by 9. c. Of the first 5 lines by 5. h. Of lines 2 to 10 by 10. d. Of the first 6 lines by 6. i. Of lines 2 to 11 by 11. e. Of the first 7 lines by 7. j. Of lines 2 to 12 by 12. For other oral exercises in division, see pages 61 and 63. * As the teacher may indicate. SHORT DIVISION. Examples for the Slate. WRITTEN WORK. (2) (3) 98. ILLUSTRATIVE EXAMPLE I. At $5 a day for work, how many days' work can be had for $ 4730 ? Explanation. - As many days' work can be had for $ 4730 as there are 5's in 4730. Divisor, 5) 4730 Dividend. For convenience, we write the dividend and divisor as in the margin, and divide 946 Quotient. the terms of the dividend separately, as Ans. 946 days' work. far as possible, beginning with the highest. If we divide the four thousands by 5, we shall have no thousands in the quotient, so we first divide 47 hundreds by 5. 5's in 47 (hundreds), 9 (hundred), and 2 hundreds remain. We write the 9 hundred under the line in the hundreds' place, and change the 2 hundreds remaining to 20 tens, which, with the other 3 tens of the dividend, make 23 tens. 5's in 23 (tens), 4 (tens), and 3 tens remain. We write the 4 tens under the line in the tens' place, and change the 3 tens remaining to 30 units. 5's in 30 (units), 6 (units), which we write under the line in the units' place, and have 946 for the entire quotient. Ans. 946 days' work. In dividing, the pupil may simply say, “ 5's in 47, 9 and 2 over; in 23, 4 and 3 over; in 30, 6.” Or, abbreviating still more, “5's in 47, 9; in 23, 4; in 30, 6." 1. How many cords of wood at $6 a cord can be bought for $ 522 ? for $ 3804 ? 1st Ans. 87 cords. 2. How many hours will it take to ride 3216 miles at 8 miles an hour ? at 12 miles ? 1st Ans. 402 hours. 3. At 7 cents an hour for work, how many hours must I work to earn 2835 cents ? 4. How many packages of tea, 9 pounds in a package, can be made from 8847 pounds ? |