by the 2 tens. 2 tens times 6 units, or 6 times 2 tens, are 12 tens, equal to 1 hundred and 2 tens; place the 2 tens under the tens figure in the product already obtained, and add the 1 hundred to the next hundreds produced. 2 tens times 4 tens are 8 hundreds, and the 1 hundred of the last product added are 9 hundreds; write the 9 in hundreds' place in the product. 2 tens times 7 hundreds are 14 thousands, equal to 1 ten thousand and 4 thousands, which we write in their appropriate places in the product. Then adding the two partial products, we have for the entire product, 17158. Hence the following general RULE. I. Write the multiplier under the multiplicand, placing units of the same order under each other. II. Multiply the multiplicand by each figure of the multiplier successively, beginning with the unit figure, and write the first figure of each partial product under the figure of the multiplier used, writing down and carrying as in addition. III. If there are partial products, add them, and their sum will be the product required. PROOF. Multiply the multiplier by the multiplicand, and if the product is the same as the first result, the work is correct. When the multiplier contains two or more figures, the several results obtained by multiplying by each figure are called partial products, 15. There are 52 weeks in a year; how many weeks in 1861 years? Ans. 96772 weeks. 16. An army of 5746 men having plundered a city, took so much money that each man received 37 dollars; how much money was taken? Ans. 212602 dollars. 17. If it cost 47346 dollars to build one mile of railroad, what will it cost to build 76 miles? Ans. 3598296 dollars. 27. A gentleman bought 307 horses for shipping, at the rate of 105 dollars each; how much did he pay for the whole? 28. What will 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; what did they all cost him? Ans. 59328 dollars. 30. How many yards of broadcloth in 487 pieces, each piece containing 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 tons. 32. How many oranges in 356 boxes, each box containing 264 oranges? Ans. 93984 oranges. 33. If it require 6894 shingles for the roof of a house, how many shingles will be required for 19 such houses? 34. 37896 × 149=how many? 35. 8567 x 462=how many? Ans. 5646504. Ans. 3957954. 36. 6793 × 842=how many? 41. Multiply 40930 by 779. 46. Multiply twelve thousand thirteen, by twelve hundred four. Ans. 14463652. 47. Multiply thirty-seven thousand seven hundred ninety-six, 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; what will be the entire cost of the road? Ans. 9661680 dollars. 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 6×3=18; or, 9×2=18; or, 3×3×2=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, (4 x 5=20); or, 2 and 2 and 5, (2x2x5=20). 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, (4×3-12); 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? 8 times 4 horses, or 32 horses, the number bought. 61. Hence the following RULE. I. Separate the composite number into two or more factors. II. Multiply the multiplicand by one of these factors, and the product by another, and so on until all the factors have been used; the last product will be the product required. The product of any number of factors will be the same in whatever order they are multiplied. Thus, 4×3× 5-60, and 5× 4×3=60. |
