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Ans.

15210774.

Ans.

69371964.

Ans. 4712394711.

Ans.

2472748875.

21. Multiply 45678 by 333. 22. Multiply 202842 by 342. 23. Multiply 9636799 by 489. 24. Multiply 3064125 by 807. 25. Multiply 5610327 by 2034. 26. Multiply 1900731 by 4006. 27. A gentleman bought 307 horses for shipping, at the rate of 105 dollars each; how much did he pay for the whole ?

Ans. 7614328386.

28. What would be the value of 976 shares of railroad stock, at 98 dollars a share? Ans. 95648 dollars. 29. A man bought 48 building lots, at 1236 dollars each; how much did they all cost him? Ans. 59328 dollars. 30. How many yards of broadcloth in 487 pieces, each piece containg 37 yards? Ans. 18019 yards. 31. If it require 135 tons of iron for one mile of railroad, how many tons will be required for 196 miles?

Ans. 26460. 32. How many oranges in 356 boxes, each box containing 264 oranges? Ans. 93984. 33. If it require 6894 shingles for the roof of a house, how many shingles will be required for 19 such houses?

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46. Multiply twelve thousand thirteen, by twelve hundred four. Ans. 14463652. 47. Multiply thirty-seven thousand seven hundred ninetysix, by four hundred eight.

48. Multiply one million two hundred forty-six thousand eight hundred fifty-three, by nine thousand seven.

Ans. 11230404971. 49. What will be the cost of building 128 miles of railroad, at 6375 dollars per mile? Ans. 816000 dollars. 50. A crop of cotton was put up in 126 bales, each bale containing 572 pounds; what was the weight of the entire crop? Ans. 72072 pounds. 51. Two towns, 243 miles apart, are to be connected by a railroad, at a cost of 39760 dollars a mile; how much will be the entire cost of the road? Ans. 9661680 dollars.

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52. Allowing an acre of land to produce 105 bushels, how much would 246 acres produce? Ans. 25830 bushels. 53. If a garrison of soldiers consume 5789 pounds of bread a day, how much will they consume in 287 days? Ans. 1661443 pounds

CONTRACTIONS.

CASE I.

59. When the multiplier is a composite number.

A Composite Number is one that may be produced by multiplying together two or more numbers; thus, 18 is a composite number, since 6X3=18; or, 9X2=18; or, 3X 3x2=18.

60. The Component Factors of a number are the several numbers which, multiplied together, produce the given number; thus, the component factors of 20 are 10 and 2, (10×2=20); or, 4 and 5, (4X5=20); or, 2 and 2 and 5, (2×2×5=20).

NOTE. The pupil must not confound the factors with the parts of a number. Thus, the factors of which twelve is composed, are 4 and 3, (4X3-12); while the parts of which 12 is composed are 8 and 4, (8+4=12), or 10 and 2, (10+2—12) The factors are multiplied, while the parts are added, to produce the number. 1. What will 32 horses cost, at 174 dollars apiece?

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the cost of 8 times 4 horses, or 32 horses, the number bought. 61. Hence we have the following

RULE. I. Separate the composite number into two or more factors.

II. Multiply the multiplicand by one of these factors, and that product by another, and so on until all the factors have been used; the last product will be the product required.

NOTE. The product of any number of factors will be the same in whatever order they are multiplied. Thas, 4X3X5-60, and 5X4X3-60.

EXAMPLES FOR PRACTICE.

1. Multiply 521 by 16=4X4.
2. Multiply 4350 by 25-5X5.
3. Multiply 10709 by 36=6×6.
4. Multiply 21700 by 27=3×9.
5. Multiply 783473 by 42=6×7.
6. Multiply 764131 by 48-6×8.
7. Multiply 40567 by 96=8×12.
8. Multiply 182642 by 120=4×5ק.

Ans. 8336. Ans, 108750.

Ans. 385524.

Ans. 585900. ¡Ans. 32905866. Ans. 36678288.

Ans. 3894432.

Ans. 21917040. 9. Multiply 20704 by 84-3X4X7. Ans. 1739136. 10. Multiply 564120 by 140-4X5X7.

Ans. 78976800. 11. What will 56 acres of land cost, at 147 dollars an acre? Ans. 8232 dollars. 12. What will 75 yoke of cattle cost, at 184 dollars a yoke? Ans. 13800 dollars. 13. If a ship sail 380 miles a day, how far will she sail in 45 days? Ans. 17100 miles. 14. What is the value of 3426 pounds of butter, at 18 cents a pound? Ans. 61668 cents. 15. What would be the cost of 125 horses, at 208 dollar each? Ans. 26000 dollars. 16. What would be the value of 1842 acres of land, at 28 dollars an acre?

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17. What will be the cost of 28 pieces of broadcloth, each piece containing 42 yards, at 4 dollars a yard?

Ans. 4704 dollars.

18. What will be the cost of 16 sacks of coffee, each sack containing 75 pounds, at 9 cents a pound?

Ans. 10800 cents.

CASE II.

62. When the multiplier is 10, 100, 1000, &c. If we annex a cipher to the multiplicand, each figure is removed one place toward the left, and consequently the value of the whole number is increased ten fold. If two ciphers are annexed, each figure is removed two places toward the left, and the value of the number is increased one hundred fold; and every additional cipher increases the value tenfold.

Hence the following

RULE. Annex as many ciphers to the multiplicand as there are ciphers in the multiplier; the number so formed will be the product required.

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5. At 47 dollars an acre, what will 10 acres of land cost?

Ans. 470 dollars.

6 What will be the cost of 100 horses, at 95 dollars a head? Ans. 9500 dollars. 7. What will be the cost of 1000 fruit trees, at 18 cents apiece? Ans. 18000 cents. 8. If one acre of land produce 28 bushels of wheat, how many bushels will 100 acres produce? Ans. 2800. 9. If a man save 386 dollars a year, how much will he save in 10 years? Ans. 3860 dollars.

10. If the freight on a barrel of flour from Chicago to New York be 47 cents, how much will it be on 100000 barrels? Ans. 4700000 cents.

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