how much will it consume in 100 days? In 365 days, or 1 year? In 4 years? 83. A house contains 4 stories of 6 rooms each, what will the papering cost at $17 a room? 84. A man sold 41 barrels of vinegar, each containing 35 gallons, at 44 cents a gallon: how much did he receive for it? EXAMPLES COMBINING ADDITION, SUBTRACTION, AND MULTIPLICATION.. 85. Multiply the sum of 402 and 940, by the dif ference of 102 and 47. 86. Multiply the sum of 5080 and 6890, by the difference of 739 and 1806. 87. Multiply the difference between 1004 and 806, by the sum of 87 and 263. 88. A man having 207 hogs, bought 65 more; and then sold all at $14 apiece: what was the amount realized? 89. A man bought 45 acres of land at $375 an acre, and sold the entire piece for $15000: how much did he lose? 90. At $507 apiece, how much more will 297 carriages cost than 133? 91. A had 57 horses worth $129 apiece, which he traded for 77 mules at $77 apiece, and the balance in money: how much money did he receive? 92. Bought 491 yards of cloth at 81 cents a yard; used 29 yards, and sold the rest at 95 cents a yard: how much did I gain? 93. By selling an acre of land for $47, I lose $17: how much did 208 acres cost? 94. If 237 days of a year are pleasant, and the others disagreeable, how many more pleasant than unpleasant days ir 3 years? 95. If a ship sail at the rate of 236 miles each day of 24 hours, how many more miles will it sail in 13 days than in 7 days? 96. In a division of 3 brigades, each brigade containing 4 regiments of 10 companies each, 3 men from each company volunteer for special service: how many volunteer? 97. Find the number of words in a dictionary of 460 pages of double columns, containing 45 words in each column. 98. If 24 trains of 9 cars each, each car containing 64 passengers, run daily on a railway, how many persons will be conveyed in 16 days? 99. A bought 475 barrels of flour at $16 a barrel; he sold 280 barrels at $17 a barrel, and the rest at $14: what did he gain or lose? 100. The sum of two numbers is 234, and the greater is 182: what is their product? 101. The sum of three numbers is 800; the least is 100, and the greatest 400: what is the product of the three numbers? 102. What is the value of 87 cords of wood at $9 a cord, 240 bushels of apples at $2 a bushel, 869 barrels of flour at $7 a barrel, and 250 acres of land at $63 an acre? 103. If a man earns $11 a week, how much more will 84 men earn in 69 weeks, than 27 men will in 53 weeks? 104. Sold 540 acres of land at $108 an acre, and with the proceeds bought 23 horses at $95 each, 13 mules at $76 each, and 396 sheep at $3 each, and paid the balance for a farm: what did the farm cost? 105. A cow, a horse, 3 mules, and 15 sheep are worth $764; the cow is worth $34, the horse $230, the mules $120 apiece: what are the sheep worth? QUESTIONS FOR REVIEW. What is Multiplication? What is the Multiplicand? The Multiplier? The Product? The Factors? The sign of multiplication? What does the Sign of Multiplication denote? Give the rule for multiplication. What is the proof? What do you understand by partial product? (Teacher explain.) How do you multiply when the multiplier is 10, 100, or 1000, etc.? Why? How, when the multiplier has any number of ciphers at the right? What is Addition? What is the sum or amount? What is the sign of addition? What does it show? What is the sign of equality? What does it show? What numbers can be added? Of what denomination is the sum or amount? What is a problem? A solution? An operation? A conclusion? A rule? Give the rule for addition. What the method of proof? What is meant by proof? Ans. It is a second operation to ascertain the correctness of the first. What is subtraction? What the minuend? The subtrahend? The remainder? The sign of subtraction? What does the sign of subtraction show? Give the rule for subtraction. What the method of proof? What is Arithmetic? What is a number? What are the fundamental rules? What does "fundamental" mean? What is notation? Numeration? How many kinds of notation are there? Where is the Roman notation used? (Teacher explain.) What characters are used in the Arabic notation? What are figures? What is the smallest number expressed by one figure? The largest? The smallest expressed by two figures? The largest? In the number 365, what is the value expressed by the figure 3? By 6? By 5? What is meant by the local value of a figure? What is the square of a number? The cube? DIVISION. 40. Division is the process of finding how many times one number is contained in another. 41. The Dividend is the number to be divided. 42. The Divisor is the number by which we divide. 43. The Quotient is the number of times the divisor is contained in the dividend. 44. The Remainder is the number left after di. viding. NOTE. Since the remainder is a part of the dividend, it must be of the same kind, or denomination; that is, if the dividend be dollars, the remainder will be dollars; if pounds, the remainder will be pounds. Placed between 45. The Sign of Division is two numbers, it denotes that the one on the left is to be divided by the one on the right. read, 12 divided by 3 equals 4. Thus, 12÷÷3=4, NOTE.-Division is also expressed by writing the dividend above, and the divisor below a horizontal line; thus, 12, read 12 divided by 3, or 12 thirds. There are two methods of division, Long Division and Short Division. 46. In Short Division, the work of dividing is performed mentally, and the results only are written. In Long Division, each step of the operation is written. Short division is generally used when the divisor does not exceed 12; long division, when it does exceed 12. |