dollars, and at another 49 dollars; how much had he remaining in bank? Ans. 1807 dollars. 4. A man bought a farm for 4765 dollars, and paid 750 dollars for fencing and other improvements; he then sold it for 384 dollars less than it cost him; what did he receive for it? Ans. 5131 dollars. 5. A forwarding merchant had in his warehouse 7520 bar rels of flour; he shipped at one time 1224 barrels, at another time 1500 barrels, and at another time 1805 barrels; how many barrels remained? 6. A had 450 sheep, B had 175 more than A, and C had as many as A and B together minus 114; how many sheep had C? Ans. 961 sheep. 7. A farmer raised 1575 bushels of wheat, and 900 bushels of corn. He sold 807 bushels of wheat, and 391 bushels of corn to A, and the remainder to B; how much of each did he sell to B? Ans. 768 bushels of wheat, and 509 of corn. 8. A man traveled 6784 miles; 2324 miles by railroad, 1570 miles in a stage coach, 450 miles on horseback, 175 miles on foot, and the remainder by steamboat; how many miles did he travel by steamboat? Ans. 2265 miles. 9. Three persons bought a hotel valued at 35680 dollars. The first agreed to pay 7375 dollars, the second agreed to pay twice as much, and the third the remainder; what was the third to pay? Ans. 13555 dollars. 10. Borrowed of my neighbor at one time 750 dollars, at another time 379 dollars, and at another 450 dollars. Having paid him 1000 dollars, how much do I still owe him? Ans. 579 dollars. 11. A man worth 6709 dollars received a legacy of 3000 dollars. He spent 4379 dollars in traveling; how much had he left? 12. In 1850 the number of white males in the United States was 10026402, and of white females 9526666; of these, 8786968 males, and 8525565 females were native born; how many of both were foreign born? Ans. 2240535. MULTIPLICATION. MENTAL EXERCISES. 53. 1. What will 4 pounds of sugar cost, at 8 cents a pound? ANALYSIS. Four pounds will cost as much as the price, 8 cents taken 4 times; thus, 8+8+8+8=32. But instead of adding, we may say,-since one pound cost 8 cents, 4 pounds will cost 4 times 8 cents, or 32 cents. 2. If a ream of paper cost 3 dollars, what will 2 reams cost? 3. At 7 cents a quart, what will 4 quarts of cherries cost? 4. At 12 dollars a ton, what will 3 tons of hay cost? 4 tons? 5 tons? 5. There are 7 days in 1 week; how many days in 6 weeks? In 8 weeks? 6. What will 9 chairs cost, at 10 shillings apiece? 7. If Henry earn 12 dollars in 1 month, how much can he earn in 5 months? in 7 months? in 9 months? 8. What will 11 dozen of eggs cost, at 9 cents a dozen? At 10 cents? At 12 cents? 9. When flour is 7 dollars a barrel, what must be paid for 7 barrels? for 9 barrels ? for 12 barrels ? 10. At 9 dollars a week, what will 4 weeks' board cost? 7 weeks'? 9 weeks'? 11. If I deposit 12 dollars in a savings bank every month, how many dollars will I deposit in 6 months? In 8 months? In 9 months? 12. At 9 cents a foot, what will 4 feet of lead pipe cost? 7 feet? 10 feet? 13. When hay is 8 dollars a ton, how much will 3 tons cost? 4 tons? 7 tons? 9 tons? 11 tons? 14. What will be the cost of 11 barrels of apples, at 2 dollars a barrel? at 3 dollars? 15. At 10 cents a pound, what will 9 pounds of sugar cost? 11 pounds? 12 pounds? 54. Multiplication is the process of taking one of two given numbers as many times as there are units in the other. 55. The Multiplicand is the number to be multiplied. 56. The Multiplier is the number by which to multiply, and shows how many times the multiplicand is to be taken. 57. The Product is the result obtained by the process of multiplication. 58. The Factors are the multiplicand and multiplier. 1. Factors are producers, and the multiplicand and multiplier are called factors because they produce the product. 2. Multiplication is a short method of performing addition when the numbers to be added are equal. 59. The sign, x, placed between two numbers, denotes that they are to be multiplied together; thus, 9×6=54, is read 9 times 6 equals 54. Define multiplication. Multiplicand. Multiplier. Product. Factor. Multiplication is a short method of what? What is the sign of multiplication? OPERATION. Multiplicand, Hunds. Tens. Units. 374 Units, 24 Tens, • 42 Hundreds, Product, 18 ANALYSIS. In this example it is required to take 374 six times. If we take the units of each order 6 times, we shall take the entire number 6 times. Therefore, writing the multiplier under the unit figure of the multiplicand, we proceed as follows: 6 times 4 units are 24 units; 6 umes 7 tens are 42 tens; 6 times 3 hundreds are 18 hundreds; and adding these partial products, we obtain the entire product, 2244. Case I is what? Give explanation. The operation in this example may be performed in another way, which is the one in common use. OPERATION. 374 6 2244 ANALYSIS. Writing the numbers as before, begin at the right hand or unit figure, and say: 6 times 4 units are 24 units, which is 2 tens and 4 units; write the 4 units in the product in units' place, and reserve the 2 tens to add to the next product; 6 times 7 tens are 42 tens, and the two tens reserved in the last product added, are 44 tens, which is 4 hundreds and 4 tens; write the 4 tens in the product in tens' place, and reserve the 4 hundreds to add to the next product; 6 times 3 hundreds are 18 hundreds, and 4 hundreds added are 22 hundreds, which being written in the product in the places of hundreds and thousands, gives, for the entire product, 2244. 61. The unit value of a number is not changed by repeating the number. As the multiplier always expresses times, the product must have the same unit value as the multiplicand. But since the product of any two numbers will be the same, whichever factor is taken as a multiplier, either factor may be taken for the multiplier or multiplicand. In multiplying, learn to pronounce the partial results, as in addition, without naming the numbers separately; thus, in the last example, instead of saying 6 times 4 are 24, 6 times 7 are 42 and 2 to carry are 44, 6 times 3 are 18 and 4 to carry are 22, pronounce only the results, 24, 44, 22, performing the operations mentally. This will greatly facilitate the process of multiplying. Second explanation. Repeating a number has what effect on the unit value? The product must be of the same kind as what? |