106. RULE.-Reduce the divisor and dividend to equivalent fractions having a common denominator, and divide the numerator of the dividend by the numerator of the divisor. Or, Invert the terms of the divisor and proceed as in multiplication. In dividing mixed numbers, multiply both divisor and dividend by the least common denominator, and divide as in simple numbers. Find the value of the following complex fractions (56) and 108. To multiply mixed numbers together.* Ex. What cost 1016 pounds of cotton, at 123 cents per pound? Instead of reducing the mixed numbers to improper fractions, use the following methods. The second method (by aliquot parts) is preferable, and is well adapted to commercial operations, in which the fractions are usually halves, fourths, eighths, etc. In business transactions, it is customary to omit the fraction in the result, if it is less than 1, and to add 1 to the cents if it is more than. Unless otherwise stated, the exact answers will be given to examples. . FIRST OPERATION. 10161 8) 30491 381 12198 125.79 SECOND OPERATION. 10161 ANALYSIS.-Multiply 1016 by the fraction by multiplying by the numerator 3 and dividing by the denominator 8 (92); then multiply 1016 by the integer 12 (88), and add the results. ANALYSIS. =+. Multiply 1016 by by diMultiply 1016 by by taking of the 254, the product by. Multiply 1016 by 12 (88), and add the results. .123 viding by 4. 2541 127 12198 125.79 * The multiplication of mixed numbers is purposely put in this connection, as it appropriately comes here, a knowledge of division of fractions being a prerequisite to a fair understanding of the process. 110. 1. Reduce to its lowest terms. 2. Reduce to forty-eighths. 3. Reduce 7273 to an improper fraction. 6. From 1728 take 8652. 7. Multiply× 3 × × 1 × 16. 9. Multiply 1727 by 1752. 10. Divide 13 by 11. Divide 1736 by 144. 12. Divide 5779 by 2754. 13. Divide 123461 by 7; by 35. 14. What is the cost of 1583 pounds sugar @ 114 cts. per pound? 15. Add ✯ of ↓ of 44, §, 1364, and 5. 16. A merchant sold a quantity of goods for $7344, which was of the cost. What was the loss? 17. Required the value of 2993 pounds of sugar @ 93 cts. per pound? 18. If of a ship is worth $424304, what is the value of the whole ? 19. Bought 47 yards of cloth at $44 per yard, and paid for it in wheat at $21 per bushel; how many bushels were required? 20. Find the value of 311 pounds snuff @ 72 cts. per pound. 21. The less of two numbers is 777 and their difference 117; what is the greater number? 22. A and B together have $1728; if A's money is equal to of B's, how much have each ? 23. A merchant having 2146 yards of cloth, sold of it at $1 a yard, and the remainder at $2 a yard; how much did he receive? 24. A number being increased by of itself, the sum is 546; what is the number? 25. A man had $5280; he bought goods with of it, and then lent of the balance to a friend; how much had he left? 26. Find the selling price of goods sold at a profit of $75, being of the cost. 27. Mr. A bought 1174 acres of land at one time, and 87% at another; after selling 1107 acres, how much remained? 28. If 8 tons of coal cost $30ğ, what will 27 tons cost? How many tons can be bought for $1273? 29. A man paid $1145 for a horse and carriage. What was the value of each, the carriage being valued at as much as the horse? 30. If of a farm is valued at $22531, what is the value of of it? 31. What is the value of 21021 yards prints at 72 cents per yard? 32. What number must be taken from 964, and the remainder multiplied by 16%, that the product shall be 770§? 33. What is the value of 1642 yards muslin at 5 cents per yard? 34. If 7 barrels of oil contain 3131 gallons, how many gallons will 2 barrels contain? 35. An executor collects $12724.84. He pays out $4096.48 and the residue he disburses to the widow and her four children as follows: The widow receives a third part, and the remainder is divided equally among the children. What was the share of each? 36. What number increased by of itself will produce 2456 ? 37. Find the selling-price of goods, bought at $144, and sold at above cost. 38. A invests of his capital in real estate, and has $1725 remaining; what is his capital? 39. Bought a barrel of sugar containing 218 lbs., at 83 cents per pound. During the sale, it dried away. Did I gain or lose, and how much, by selling it at 94 cents per pound? 40. Multiply 23751 by 81; by 101. 41. Multiply 1727 by 181; by 1073. 42. Multiply 3771 by 161; by 373. 43. Multiply 8751 by 221; by 98. 44. A merchant sold 123 yards of silk to one customer, 214 to another, 20 to another, and 28 to another; at $23 per yard, how many dollars did he receive? 45. An army loses of its number in battle and has 16042 remaining; how many did it originally contain? 46. What is the cost of 34 pieces prints, containing 16042 yards, at 51 cents per yard? 47. What is the value of 12 pieces prints containing 48, 481, 482, 48, 492, 483, 48, 493, 492, 483, 492, 483 yards respectively at 43 cents per yard? |