per acre ? per lb. ? 62. What cost 194 barrels of flour at $7% per barrel ? Ans. $ 1434. 63. What cost 13,4 quintals of fish at $34 per quintal? Ans. $51331 64. I have two parcels of land, one containing 770 acres, and the other 913 acres. What is their value at $ 783 Ans. $ 1380.708. 65. From a quarter of beef weighing 175% lbs. I gave John Snow of it ; of the remainder I sold to John Cloon. What is the value of the remainder at si cents Ans. $ 2.0415 66. Alexander Green bought of John Fortune a box of sugar containing 475 lbs. for $ 30.00. He sold of it at 8 cents per lb., and of the remainder at 10 cents per lb. What is the value of what still remains at 124 cents per lb., and what does Green make on his bargain ? Value of what remains $ 13.194. А Green's bargain, $ 16.974. 67. What cost 14 of an acre at $ 144 per acre ? Ans. $2.00. 68. D. Sanborn's garden is 234 rods long and 134 rods wide, and is surrounded by a good fence 7 feet high. Now if he shall make a walk around his garden within the fence 7 feet wide, how much will remain for cultivation ? Ans. 1A. 3R. 7p. 8513&_ft. 69. On of my field, I plant corn ; on of the remainder I sow wheat; potatoes are planted on f 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 Ans. 1A. OR. 29p. 70. Multiply 1 of 1 of 11 by of 17 of 28. Ans. To. Section 24. DIVISION OF VULGAR FRACTIONS. I. To divide a fraction by a whole number. 1. How many times will contain 9 ? To understand this question, **s='s Ans. we will suppose of an apple OPERATION. were to be divided equally among 9 persons. Now, if we divide 4 of an apple into 9 equal parts, there would be 63 parts, and each person would receive os; but there being 4, each man will receive 5 times = Ans. Hence we see the propriety of the following RULE, ns. 4. Ans. zig Multiply the whole number by the denominator of the fraction, and write the product under the numerator. 2. Divide 1 by 12. Ans. 132 3. Divide 11 by 8. Ans. 4. Divide 7 by 12. Ans. . 5. John Jones owns of a share in a railroad, valued at $ 117 ; this he bequeaths to his five children. What part of a share will each receive ? 6. Divide zby 15. Ans. Tỉs 7. Divide by 28. 8. James Page's estate is valued at $ 10,000, and he has given 4 of it to the Seamen's Society ; [of the remainder he gave to his good minister ; and the remainder he divided equally among his 4 sons and 3 daughters. What sum will each of his children receive ? Ans. $ 680107 II. To divide a whole number by a fraction. 9. How many times will 13 contain ? Ans. 304. It is evident, that 13 1x}=9=30Ans. will contain 4, as many times as there are sevenths in 13, which are 7 X 13 = 91 times. Again, if 13 contain 1 seventh 91 times, it will contain 3 sevenths as many times as 91 will contain 3 = 301 Ans. Hence the following OPERATION RULE. Multiply the whole number by the denominator of the fraction, and divide the product by the numerator. 10. Divide 18 by }. Ans. 204. 11. Divide 27 by it. Ans. 2961 12. Divide 23 by 1 Ans. 92. 13. Divide 5 by š. Ans. 25. 14. Divide 12 by . Ans. 16. 15. Divide 16 by J. Ans. 32. 16. Divide 100 by 17. Ans. 11114. 17. I have 50 square yards of cloth, how many yards, f of a yard wide, will be sufficient to line it ? Ans. 83} yards. 18. A. Poor can walk 311 miles in 60 minutes ; Benjamin can walk as fast as Poor. How long will it take Benjamin to walk the same distance ? Ans. 731 minutes. OPERATION. 43 III. To divide a mixed number by an integer. 19. Divide 173 by 6. Ans. 213. We divide 17 by 6, and find it is con6) 173 tained 2 times, which we write under the 17, and we have 5 remaining, which we multiply by 8, the denominator of the fraction; and to the product we add the numerator, 3, and the amount is 43, this we write over the product of 6, the divisor, multiplied by the denominator, 8, = 48. The rationale of the above question is the same as of those in Rule I. of this section. Hence the following RULE. Divide the integers as in whole numbers, and if any thing remains, multiply it by the denominator of the fraction, and to the product add the numerator of the fraction, and write it over the product of the divisor, multiplied by the denominator. 20. Divide 17* by 7. Ans. 215 21. Divide 187 by 8. Ans. 237. 22. Divide 2711 by 9. Ans. 31us. 23. Divide 31 ) by 11. Ans. 2015 24. Divide 789 by 12. Ans. 647 25. Divide 1897} by 4. Ans. 4713 26. Divide 10711 by 3. Ans. 3536 27. Divide $ 174 among 7 men. Ans. $244. 28. Divide $ 106] among 8 boys. Ans. 8 1342. 29. What is the value of 4 of a dollar ? Ans. $0.341. 30. Divide $ 10711 among 4 boys and 3 girls, and give the girls twice as much as the boys. Ans. boy's share $ 101. Girl's share $ 214.. 31. If $ 14 will purchase of a ton of copperas, what quantity will $ 1 purchase ? Ans. lcwt. Oqr. 24lbs. IV. To divide one fraction by another. 32. Divide [ by $. Ans. 111. To understand the raXf==131 Ans. tionale of this process, we find the two factors of , which are † and ; for f multiplied by } are $, as is evident from a preceding rule. We now divide ž by i, which, by case I. of this section, will be } X1= 32 Again, we wish to divide 32 by š. It is evident, that a will contain f nine times as often, as it will a unit, and it contains a unit 3 times, therefore it contains į nine times =X 32=42= 131 Ans. In performing this question, it will be perceived, that the numerator of the dividend has been multiplied by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor. Hence the following OPERATION. RULE. Invert the divisor and proceed as in multiplication. If, however, there be mixed numbers in the question, they must be reduced to improper fractions, and compound fractions must be reduced to simple fractions. 33. Divide 7 by . OPERATION. f x1==11& Ans. 34. Divide 74 by 34. OPERATION. 7=3, 34= 24, *1 X==23 Ans. 35. Divide ; by 1. Ans. 31. 36. Divide if by 12. 37. Divide by s. 38. Divide is by . 39. Divide by it: 40. Divide 73 by 41. 41. Divide 31 by 77. 42. Divide 114 by 54. 43. Divide 4 by 17. 44. Divide 1163 by 147. 45. Divide 814 by 9}. 46. Divides of } by 1 of z. Ans. 33 Ans. 24. Ans. 6% Ans. 43. Ans. 14%. Ans. 15 Ans. 2152 Ans. 242. Ans. 893. Ans. Sit Ans. 183. Section 25. EXERCISES IN VULGAR FRACTIONS. 1. What are the contents of a board 9 inches long and 7 inches wide ? Ans. 63 square inches. 2. What are the contents of a board 114 inches long, and 44 inches wide ? Ans. 491. square inches. 3. How many square rods in a garden, which is 183 rods in length and 910 rods wide ? Ans. 17843 rods. 4. What cost 19% acres of land, at $ 174 per acre ? Ans. $35016 5. What cost 1430 tons of coal at $ 74 per ton? Ans. $ 11137. 6. What cost 1341 tons of hay at $8} per ton ? Ans. $ 12045. 7. What cost 17 bushels of corn at $ 1% per bushel? Ans. $334 8. What is the value of of a dollar ? Ans. $ 0.561. 9. What is the value of j7 of a dollar ? Ans. $ 0.214 10. What is the value of 45 of a dollar ? Ans. $0.253. 11. What is the value of xi of a dollar ? Ans. $0.5116. 12. Bought a cask of molasses, containing 874 gallons ; jf of it having leaked out, the remainder was sold at 271 cents per gallon ; what was the sum received ? Ans. $ 15.03. |