42. What cost 279 barrels of salt, at $1.75 a barrel? 43. What cost 1565 acres of land, at $27 per acre?

44. What cost 758 baskets of peaches, at $2.50 a basket? 45. If a hall will seat 1250 persons, and each seat is occupied by a person weighing 135 lbs. what weight is sustained by the floor?

46. Bought 2 farms; one contained 327 acres at $83 an acre, the other 526 acres at $58 an acre. What did they both cost? What was the difference in their cost?

47. What is the value of 56 railway cars, at $9550.75 each ? 48. A man bought 31 colts at $28 apiece, and paid 10 tons of hay at $25 a ton; how much did he owe for the colts?

49. A grocer bought 21 barrels of flour at $5 per barrel, and sold 16 barrels of it at $7; finding the rest damaged, he put it at $3 a barrel. How much did he make or lose, by the operation?

50. A farmer having 75 turkeys, sold 50 of them at 86 cents apiece, and the rest at 54 cts. apiece; what did they come to? 51. A man owns 7 orchards; in each orchard there are 8 rows of apple-trees, and 29 trees in each row; how many apple-trees has he?

52. In a certain school there are 3 departments, in each department there are 11 classes, and in each class there are 48 pupils; how many pupils are there in the school?

53. If you multiply 58 by 37, and this product by 29, what will be the result?

54. If 450 is multiplied by 254, and this product by 178, what will be the result?

55. A man sent 37 loads of wheat to market; every load contained 16 bags, and each bag 3 bushels; how many bushels did he send?

56. What is the product of 378 + 342 by (763-251)? 57. What is the product of 254 + 451 by (836 - 434)? 58. Required the product of 823 - 567 by (827 +230). 59. Multiply 267 +75+ 430 by (468324).

60. Multiply 869 675 by (300 + 87 + 90).

61. What is the product of (843 — 478) × (973 + 379) ?

89. To multiply by the Factors of the Multiplier. 1. What will 15 tables cost at $7 apiece?

ANALYSIS.-The factors of 15 are 5 and 3. (Art. 80.) Now as 1 table costs $7,5 tables will cost 5 times $7 or $35. Again, since

153 x 5 ít follows that 15 tables will cost 3 times as much as 5 tables, and 3 times $35 are $105. Hence, the

$105

RULE.-Multiply the multiplicand by one of the factors of the multiplier, then this product by another, and so on, till all the factors have been used. The last product will be the answer.

2. What will 27 sofas cost, at $85 apiece?
3. What will 24 wagons cost, at $37 apiece?
4. What will 36 cows cost, at $19 per head?

5. If a man travels at the rate of 42 miles a day, how far can he travel in 205 days?

6. What cost 45 acres of land, at 110 dollars per acre?

7. At $6 per week, how much will it cost a person to board 52 weeks?

8. At the rate of 56 bushels per acre, how much corn can be raised on 460 acres of land?

9. What cost 672 pieces of cashmere, at $24 apiece?

10. What cost 1265 yoke of oxen, at $72 per yoke?

90. When the Multiplier has ciphers on the right.

1. What is the product of 56 multiplied by 10?

SOLUTION.-When a figure is moved one place to the left, its value is increased ten times. (Art. 34, 2°.) Hence, if we annex a cipher to 56 we multiply it by 10 and it becomes 560.

2. Multiply 64 by 100.

Ans. 560.

SOLUTION.-Annexing two ciphers to 64 increases its value 100 times, and therefore multiplies it by 100.

3. Multiply 87 by 1000. Ans. 87000.

Ans. 6400.

4. Multiply 316 by 40.

EXPLANATION.-Multiplying 316 by 4 ones it becomes 1264. But we are required to multiply by 4 tens instead of 4 ones; therefore 1264 is ten times less than the true product. To correct this result we annex a cipher to it, which increases it 10 times.

5. Multiply 345 by 700.

SOLUTION.-Multiplying by 7 ones only, gives a result 100 times less than the true product. To correct this we annex two ciphers to it. Hence,

91. To multiply by 10, 100, 1000, etc.

OPERATION.

316

40

Ans. 12640

OPERATION.

345

700

Ans. 241500

Annex as many ciphers to the multiplicand as there are ciphers in the multiplier.

When the significant figures have ciphers on the right.

Multiply by the significant figures, and to the result annex as many ciphers as are on the right of both factors. (See Art. 864, Appendix.)

6. What will 100 bales of cotton weigh, at 468 lbs. to a bale? 7. How many pages in 2300 books, of 352 pages each?

ORAL PROBLEMS FOR REVIEW.

92. 1. If 4 men can do a job of work in 6 days, how long will it take 1 man to do it?

ANALYSIS.-It will take 1 man 4 times as many days as it takes 4 men; and 4 times 6 days are 24 days, Ans.

2. In 1 peck are 8 quarts; how many quarts in 6 pecks ? 3. How many quarts are 7 pecks and 3 quarts

4. In 1 bushel are 4 pecks; how many pecks in 15 bushels? 5. How many pecks in 20 bushels and 3 pecks?

6. If 9 men can build a wall in 20 days, how long will it take 1 man to do it?

7. In 1 pound are 16 ounces; how many ounces in 4 pounds? 8. How many ounces in 5 lbs. 7 ounces?

9. If a barrel of flour will last 8 persons 12 days, how long will it last 1 person?

10. What will 8 lbs. of maple sugar cost, at 9 cts. a pound? 11. How many inches in 11 feet?

12. How many feet in 12 yds. and 2 feet?

13. How many quarts in 25 gallons of milk?

14. How many quarts in 30 gallons and 5 quarts?

15. If two men start from the same place and travel in opposite directions, one at the rate of 4 miles per hour, the other, 3 miles, how far apart will they be in 6 hours?

WRITTEN PROBLEMS FOR REVIEW.

93. 17. George has 27 cents, and Henry has 3 times as many cents as George lacking 5; how many cents has Henry? How many have both?

18. At a military parade there were 5 regiments, in each regiment 8 companies, in each company 9 platoons, and in each platoon 10 soldiers; how many soldiers were on parade?

19. If 325 men can grade a street in 28 days, how long will it take 1 man to do it? How much will he receive for it, if he has $2 per day?

20. A and B are 20 miles apart, and travel in opposite directions, A goes 4 miles an hour and B 5 miles; how far apart will they be in 48 hours?

21. If I hire a carpenter at $28 a month, and his apprentice at $14, how much will be due them in 12 months?

22. A man bought a drove of 1560 sheep, at $4 a head; it cost him $68 to send them to market, and they brought him $5 apiece; how much did he make on them?

23. A drover bought 360 head of cattle and 96 horses; he afterwards sold the former at a profit of $19 a head, and the latter at a loss of 23 dollars a head; did he gain or lose by the operation, and how much?

24. A grocer bought 585 barrels of flour at $6 a barrel, and 117 barrels at $7; he then sold the whole at $6.50. What was the result of his speculation?

25. In music, two minims equal a semibreve; two crotchets a minim; two quavers a crotchet; two semi-quavers a quaver; and two demi-semiquavers a semi-quaver; how many demisemiquavers are equal to 259 semi-breves?

26. Two persons start from the same place, and travel in the same direction ; one at the rate of 33 miles per day, and the other at the rate of 37 miles per day; how far apart will they be at the end of a year?

27. Multiply two thousand seven, by one thousand four.

28. Multiply four thousand forty, by two thousand one hundred three.

29. Multiply forty thousand, four hundred four, by ten thousand ten.

30. Multiply one hundred five thousand seven, by sixty thousand, four hundred three.

31. Multiply five millions, two hundred six, by seventy thousand, two hundred five.

QUESTIONS.

76. What is Multiplication? 77. The Multiplicand? 78. The Multiplier? What does the Multiplier show? 79. What is the Answer called? 80. The numbers which produce the product called? 81. Make the Sign of Multiplication. What does it show? How read?

85. How proceed when the multiplicand or multiplier has decimals ? 88. Give the general rule? How prove multiplication? 89. How multiply by the factors of a number?

91. How multiply by 10, 100, 1000, etc.? When there are ciphers on the right, how proceed?