to a simple fraction. 10 Ans. . 6 15. Change to a simple fraction. Ans. It 81 16. Change Ans. 33 8 Ans. 217. 93 18. Reduce to a simple fraction. Ans. 19285 124 19. If 7 is the denominator of the following fraction, 91 127 what is its value when reduced to a simple fraction ? Ans. 71 8 vi hat 20. If is the numerator of the following fraction, is its value when reduced to a simple fraction? Ans. 27. Art. 166. Complex fractions, after being reduced to simple ones, may be added, subtracted, multiplied, and divided, according to the respective rules for simple fractions. QUESTIONS. - Art. 166. How do you add, subtract, multiply, and divide complex fractions ? MISCELLANEOUS EXERCISES IN VULGAR FRACTIONS. 1. What are the contents of a field 7635 rods in length and 184 rods in breadth ? Ans. 8A. 3R. 304p. 2. What are the contents of 10 boxes which are 7 feet long, 14 feet wide, and 14 feet in height? Ans. 169 17 cubic feet. 3. From 1 of an acre of land there were sold 20 poles and 200 square feet. What quantity remained ? Ans. 22075ft. 4. What cost 1} of an acre at $ 1.75 per square rod ? Ans. $236.9243. 5. What cost is of a ton at $ 15% per cwt. ? Ans. $ 49.731;. 6. What is the continued product of the following numbers: 143, 114, 5%, and 101? Ans. 9184. 7. From iz of a cwt. of sugar there was sold # of it; what is the value of the remainder at $ 0.124 per pound? Ans. $ 3.57. 8. What cost 19barrels of flour at $ 7per barrel ? Ans. $ 1434. 9. What cost 13,83 quintals of fish at $34 per quintal ? Ans. $51415 10. I have two parcels of land, one containing 710 acres, and the other 913 acres. What is their value at $ 783 per acre ? Ans. $ 1380.70%. 11. From a quarter of beef weighing 1753lb. I gave John Snow of it; of the remainder I sold to John Cloon. What is the value of the remainder at 8fcents per pound? Ans. $2.0411 12. Alexander Green bought of John Fortune a box of sugar containing 475lb. for $30. He sold { of it at 8 cents per pound, and of the remainder at 10 cents per pound. What is the value of what still remains at 124 cents per pound, and what does Green make on his bargain ? Ans. Value of what remains, $ 13.198. { Green's bargain, $ 16.973. 13. What cost u of an acre at $ 14% per acre ? Ans. $ 2.00. 14. Multiply / of 1 of 11 by B of 1of . 15. What are the contents of a board 114 inches long, and 44 inches wide ? Ans. 4913 square inches. Ans. IV. 16. How many square rods in a garden which is 18% rods in length and 91 rods wide ? Ans. 1785. rods. 17. What cost 193 acres of land at $17% per acre ? Ans. $ 350,16 18. What cost 1430 tons of coal at $ 74 per top? And. $11117 19. What cost 1317 tons of hay at $ 87 per ton ? Ans. $120.400. 20. What cost 1} bushels of corn at $ 1% per bushel ? Ans. $331. 21. What is the value of 1% of a dollar? Ans. $ 0.561 22. What is the value of j7 of a dollar? Ans. $ 0.211 23. What is the value of thy of a dollar? Ans. $ 0.25. 24. What is the value of of a dollar ? Ans. $ 0.51 25. Bought a cask of molasses, containing 874 gallons ; } of it having leaked out, the remainder was sold at 271 cents per gallon ; what was the sum received ? Ans. $15.033. 26. Bought of L. Johnson 7 yd. of broadcloth at $3% per yard, and sold it at $ 4; per yard ; what was gained ? Ans. $ 3.681 27. Bought a piece of land that was 47 rods in length and 2976 in breadth; and from this land there were sold to Abijah Atwood 5 square rods, and to Hazen Webster a piece that was 5 rods square ; how much remains unsold ? Ans. 136633 square rods. 28. Bought a tract of land that was 97 rods long and 4811 rods wide, and from this I sold to John Ayer a house-lot, 1812 rods long, and 143 rods wide; the remainder of my purchase was sold to John Morse, at $ 3.75 per square rod; what sum shall I receive ? Ans. $16717.3013. 29. What are the contents of 10 boxes, each of which is 72 feet long, 47 feet wide, and 3 feet high? Ans. 1312 47 feet. 30. Mary Brown had $17.871; half of this sum was given to the missionary society, and of the remainder she gave to the Bible society; what sum has she left ? Ans. 83.571. 31. What number shall be taken from 121, and the remain der multiplied by 10%, that the product shall be 50 ? Ans. 81 32. What number must be multiplied by 73, that the product Ans. 245. 33. Bought of John Dow 97 yards of cloth at $4.62; per yard; what was the whole cost ? Ans. $ 45.6716 may be 20 ? 34. Bought of John Appleton 47 gallons of molasses for $12.37}; what cost one gallon? What cost 127 gallons ? Ans. $ 3.33 . 35. When $15.87} are paid for 127 bushels of wheat, what costs one bushel ? What cost 11 bushels ? Ans. $ 14.11. 36. When $19.184 are paid for 33 cords of wood, what cost one cord ? What costs of a cord ? Ans. $2.1376 37. What are the contents of a box 813 feet long, 313 feet wide, and 2 ' feet high? Ans. 681424 feet, 38. On of my field, I plant corn; on of the remainder, I sow wheat; potatoes are planted on of what still remains, and I have left two small pieces, one of which is 3 rods square, and the other contains 3 square rods. How large is my field ? Ans. 1A. OR. 29p. REDUCTION OF FRACTIONS OF COMPOUND NUMBERS. Art. 167. To reduce a fraction of a higher denomination to a fraction of a lower. Ex. 1. Reduce algo of a pound to the fraction of a farthing. Ans. $qr. OPERATION BY CANCELLATION. x 20 x 12 x 4 Since 20s. make a pound, £. fr. there must be 20 times as many 2766 parts of a shilling as parts of a 9 pound; we therefore multiply zico-£. by 20, and obtain zicos. ; and since 12d. make a shilling, there will be 12 times as many parts of a penny as parts of a shilling; hence we multiply zicos. by 12, and obtain äood. Again ; since 4qr. make a penny, there will be 4 times as many parts of a farthing as parts of a penny; we therefore multiply 14 d. by 4, and obtain a = r., Ans. Rule. Multiply the given fraction by the numbers that would be employed in reduction of whole numbers to reduce the denomination of the fraction to the lower denomination required. QUESTIONS. - Art. 167. What is the rule for reducing a fraction of a higher denomination to the fraction of a lower ? Will you explain the operations ? Does this process differ in principle from reduction of whole compound num. bers ? |