125. What is the product of five thousand four hundred fourteen, and fifteen thousandths, multiplied by 38 ? 131. $617.43 × 355 = what? 132. How many bushels of wheat can be raised on 5634 acres at the rate of 47 bushels per acre? 133. Multiply nine hundred sixty-five, and thirteen hundredths, by three thousand seven hundred five ? The multiplier a number of tens, hundreds, etc. 134. Multiply 48 by 10; by 100. 135. Multiply 427 by 10, by 100, and by 1000, and add the results. 136. How many are a thousand times 7854? 138? What is the product of $ 55.56 multiplied by 100? $55.56 100 $5556.00 Solution. The removal of a figure one place to the left in a number increases the value expressed ten-fold (Art. 18). Hence, we multiply $55.56 by 10 by removing the decimal point one place to the right, and by 10 × 10, or by 100, by removing the point two places to the right. 137. Multiply 97 by 600. 97 58200 Solution. 600 is 100 times 6; 600 times 97 is the same as 100 times 6 times 97. 6 times 97 are 582, and 100 times 6 times 97 are 100 times 582, or 58200. That is, 61. To multiply by a number of tens, hundreds, etc. Multiply without regard to the ciphers at the right of the multiplier, annex that number of ciphers to the product, and give it as many decimal figures as the multiplicand has. 148. If the earth moves about the sun at the rate of 68000 miles an hour, how far does it move in 240 hours? 149. A square mile is 640 acres. How many acres has a State whose area is 7800 square miles? MISCELLANEOUS EXERCISES. 150. Bought 20 barrels of flour at $8.50 a barrel, 8 tons of fine feed at $19.50 a ton, and oats for $ 63.25, and gave in payment a $ 500 bank-bill. How much should be paid back? 151. In a certain battle an army lost 416 killed and 3 times as many wounded. The enemy's loss was 5 times as many. What was the entire loss of killed and wounded in the battle? 152. A clerk had a salary of $1500 for a year of 52 weeks. His board cost him $4.25 a week; he wasted for cigars and liquor $1.30 a week; and his other expenses were for the year $150. How much did he save? How much could he have saved if he had avoided the cigars and liquor? 153. Two trains of cars leave Boston at the same time on the same railroad for the West. One goes at the rate of 31.50 miles an hour, and the other at the rate of 16.25 miles an hour. How far apart will the two trains be at the end of 48 hours? 154. A drover has bought 120 fat oxen, each weighing on an average 1360 pounds. What is the weight of the whole? 155. In a school of 56 pupils there are 29 boys whose average weight is 85 pounds. The girls average 79 pounds each. What is the weight of the school? 156. A merchant bought 130 yards of cloth at $ 3.75 a yard, and sold the whole for $ 573.95. How much did he make? 157. Multiply the sum of 842 and 796 by twice their differ ence. 158. When boards are $31.50 a thousand feet, and shingles $4.25 a thousand, what will 40 thousand feet of boards and 22 thousand of shingles cost? 159. James Hudson has a house worth $2500, another worth $1900, and 60 acres of land worth $75 an acre. How much more is the land worth than the two houses? 160. Bought 17 yards of silk at $ 2.75 a yard, 114 yards of carpeting at $1.80 a yard, and $ 17 worth of lining. What was the amount of the bill? 161. A drover bought 60 oxen at $ 50 a head, 120 sheep at $4.25 a head, and 28 cows at $45.50 a head. He returned 20 of the oxen at cost and bought 5 horses at $125 each. What was the cost of the whole to him? 162. Bought 24 car-loads of wheat, each car holding 325 bushels, at $1.48 a bushel. I sold the wheat at $1.65 a bushel. How much did I gain? QUESTIONS. 50. What is multiplication? 51. What is the multiplicand? 52. The multiplier? 53. The product? The factors of the product? 54. What is the sign of multiplication? 55. What is a concrete number? 56. An abstract number? 58. What are principles of multiplication? 59. How are numbers written for multiplying? How do you multiply? 60. What is the proof? 61. How do you multiply by a number of tens, hundreds, etc? DIVISION. 62. 1. James has 32 books. How many times 8 books has he? 2. How many quarts of nuts, at 9 cents a quart, can be bought for 54 cents? 3. How many times 9 cents are 54 cents? How many times 9 cents in 54 cents? 4. If 7 men share 42 pounds of tea, how many pounds will each man have? 5. Ella has 27 cents. How many pencils at 5 cents each can she buy, and how many cents left? 63. Division is finding how many times one number is contained in another; or, finding one of the equal parts of a number. 64. The Dividend is the number divided. 65. The Divisor is the number by which we divide. 66. The Quotient is the result of a division. 67. The Remainder is the part of the dividend left, when the latter does not contain the divisor an exact number of times. 68. The Sign of Division,÷, or, means divided by. Thus, 168, or 16: 8, is read, sixteen divided by eight. Division is also indicated by writing the divisor at the left of the dividend, with a curve, ), between, or by writing the divisor under the dividend, with a horizontal line between. Thus, 2) 6, or §, may be read, six divided by two. 69. A Parenthesis, (), or Vinculum, , is used to include such numbers as are to be considered together. Thus, 6+82 + 5 = 15, but (6 +8) ÷ (2 + 5) = 2. NOTE. The signs X and have no force in either direction beyond a + or a- unless a parenthesis is used. Operations indicated by them must be performed first. 70. The Equal Parts into which a number may be divided are named, according to their size. Thus, — One of two equal parts, written, is called one half ; ORAL EXERCISES. 6. John has 84 cents. How many times 7 cents has he? 7. How many times 12 cents in 84 cents? 8. Ellen has 49 peaches. Should she divide them equally among 7 of her playmates, how many would each receive? 9. What number is one of the 7 equal parts of 49? What is ? 10. If $96 be equally divided among 12 men, what sum would each receive? How much is 11. In 84 days how many weeks? What is of 84? 84? of $ 96 ? How many times 7 in |