10. Multiply 52 by 83. 11. Multiply 76 by 113. 14. Multiply 156 by . 12. Multiply 135 by 26. 13. Multiply 258 by 4211. 15. If a railroad train runs 36 miles an hour, how far will it run in 153 hours? 16. If a mill is worth $2650 and B owns of it, how much is B's share worth? 17. What will 216 barrels of pork cost at $63 per barrel? 18. At $2 a cord, what will 18 cords of wood cost? 104. To multiply a fraction by a fraction. 1. What will of a yard of flannel cost at § of a dollar per a. Reduce mixed numbers to improper fractions. b. Multiply the numerators together and multiply the denominators together. Under the product of the numerators, write the product of the denominators. c. Reduce to its simplest form. NOTE. Cancel all factors common to numerators and denominators. 8. Multiply 34 by 18. 9. Multiply 18% by 10. 10. What is the product of, 1 and ? 11. What is the product of 29, †, 3 and 8? 12. What is the product of, §, 14 and 31? 13. What is the product of 41, 51, 63 and 7}? NOTE.-Fractions with the word of between them are sometimes called compound fractions. The word of is simply an equivalent for the sign of multiplication, ×, and signifies that the numbers between which it is placed are to be multiplied together. 16. What is the product of 8, of 71⁄2, 1, 16 and 3? 17. What is the value of of # of 1 of ? of of of ? 18. What is the value of of $? of 20. A man owning of a store sold of his share. What part of the whole store did he sell? 21. What will of a pound of tea cost at of a dollar per pound? Find the value of the following expressions: Where the mixed numbers are large, instead of reducing them to improper fractions they may be multiplied by the following method: Or, 36} × 9}=} × } = 354° or 3541%. 10 33. Multiply 323 by 7%. 34. Multiply 86% by 93. 35. What cost 1283 barrels of pork at $83 per barrel? 36. A farmer sold 17 bushels of corn at $3 per bushel. How much did he receive? 37. I bought 23 barrels of salt at $2 each. What did it cost me? 38. A farmer sold a quarter of a beef that weighed 523 pounds at 53c per pound. How much did he receive for the quarter? 39. At 6 c per pound, what sum would be received for 3 hogs that weighed respectively 316§, 411% and 374 pounds? 40. A grain dealer bought 283 bushels of rye from one man and 47 bushels from another. He paid $13 per bushel. What did the rye cost the dealer? 41. In 1 rod there are 16 feet. How many feet are there around a field that is 18% rods on each side and 14 rods on each end? 42. A who owned of a mill worth $7200, sold of his share to B. How much did B pay A, and what part of the mill did he buy? 43. L. J. Camp sold 24 hogs that averaged 368 pounds at 8 c per pound. How much did he receive for the hogs? 44. If a boy earns $1 per day, how much would he earn in of 4 weeks, allowing 4 days for time lost by sickness? 45. A. K. Case bought of J. M. Sims 2 dozen eggs at 11c per dozen, 11⁄2 pounds of Rio coffee at 32c per pound, 4 pounds A sugar at 9c per pound, 33 bushels of potatoes at 30c per bushel, 4 cans of tomatoes at 12c per can, 3 gallons kerosene at 11 c per gallon, dozen lemons at 20c per dozen. Find the total amount of the purchase. 46. M. N. Oliver bought of P. S. Rawson 3 pounds of pork at 9c per pound, 5 pounds ham at 12c per pound, 8 pounds beef at 8c per pound, 16 pounds chicken at 73c per pound, 3 quarts oysters at 131c per quart, 41 pounds bacon at 101c per pound, 2 pounds sausage at Sc per pound, 12 pounds mutton at 81c per pound. What was the total cost? 47. Mrs. E. M. Cooper bought of Cook Bros. 4 yards of rib bon at 10c per yard, 33 yards of muslin at 6c per yard, 9 yards drilling at 8c per yard, 7 yards calico at 53c per yard, 114 yards flannel at 24c per yard, 93 yards carpet at 30c per yard, 16 yards linen at 10c per yard, 121 yards silk at $3 per yard. much should Mrs. Cooper pay Cook Bros.? How 48. I bought 2 cords of wood at $5 per cord, and 3 tons of coal at $7 per ton. I gave the merchant two 20-dollar gold pieces. How much change should I receive? 49. If 173 yards of broadcloth are bought at of 7 dollars per yard and sold at of $5 per yard, what is the gain or loss? DIVISION OF FRACTIONS 105. A Fraction is divided by dividing the numerator or multiplying the denominator. (See Sec. 92.) 106. To divide a fraction by a whole number. ORAL PROBLEMS 1. If 3 pounds of butter cost $3, what will 1 pound cost? 2. If 6 pounds of cheese cost $1 what will 1 pound cost? 3. Find the value of the following: 3 x; } ÷ 6 = x; ÷ 9 = x; } ÷ 9 = x; & § ÷ 5 = x; 25 4. If 3 yards of calico cost $1, what will 1 yard cost? 5. If 5 dozen eggs cost $16, what will 1 dozen cost? 6. Find the value of the following: = x; ÷ 9 = x. 4x; } ÷ 3 = x; 7. A paid $63 for 5 bushels of clover seed, what did he pay per bushel? (6.) 8. I paid $5 for 3 turkeys, find the cost of each. 9. Find the value of the following: 335 = x; 163 ÷ 10 x; 53 ÷ 6 = x ; 83 ÷ 6 = x. WRITTEN PROBLEMS 1. If 3 bushels of timothy cost of a dollar, what will 1 bushel cost? NOTE. We divide the numerator when it is exactly divisible by the divisor; otherwise we multiply the denominator. 10. If 6 pounds of cheese cost of a dollar, what will 1 pound cost? 11. At $4 a yard what part of a yard of broadcloth can be bought for fr of a dollar? 12. If 7 dozen eggs cost of a dollar, what will one dozen cost? 13. If 7 bushels of wheat cost $63 what will one bushel cost? NOTE.-Reduce the mixed number to an improper fraction and divide as before. 14. If dozen hammers cost $234, what will one dozen cost? 15. A farmer paid $563 for 4 horses. How much did he pay for each? 16. If 9 men consume of 5 pounds of meat in a day, how much does each man consume? 107. To divide by a fraction. ORAL PROBLEMS 1. If coffee can be bought at the rate of $1 per pound, how many pounds can be bought for $1? $4? $4? $1? $? $3? $1? $!? $11? $21? 6 2. Find the value of the following: ; 3 ÷ 1; 8 ÷ }; 3 ÷ }; } ÷ }? 7 8 3. Find the value of the following: ; 3÷4;8÷}; 4. If 2 bushels of oats cost $1 what is the cost of one bushel? 5. Find the value of the following: 33 21; 13 1; 32 ÷ 17; 5 ÷ 21. 108. The Reciprocal of a number is 1 divided by the number; thus the reciprocal of 3 is 3. 109. Since the reciprocal of a number is 1 divided by that number the reclprocal of a fraction is that fraction inverted. Inverting a fraction shows how many times it is contained in 1. |