62. What cost 194 barrels of flour at $73 per barrel ? Ans. $ 1433. ΤΙΣ 448 63. What cost 1383 quintals of fish at $3 per quintal? Ans. $51237. 64. I have two parcels of land, one containing 7 acres, and the other 911 acres. What is their value at $783 per acre? Ans. 1380.70§. 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 82 cents per lb. ? Ans. $2.0448. 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 12 cents per lb., and what does Green make on his bargain? S Value of what remains $13.19§. Ans. Green's bargain, 8 16.973. 67. What cost of an acre at $14 per acre? Ans. $2.00. 68. D. Sanborn's garden is 234 rods long and 13 rods wide, and is surrounded by a good fence 74 feet high. Now if he shall make a walk around his garden within the fence 75 feet wide, how much will remain for cultivation? Ans. 1A. 3R. 7p, 851481ft. 69. 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. 70. Multiply of of by of 13 of 19. Ans. . Section 24. DIVISION OF VULGAR FRACTIONS. I. To divide a fraction by a whole number. 1. How many times will OPERATION. x Ans. contain 9 ? To understand this question, of an apple we will suppose were to be divided equally among 9 persons. Now, if. we divide of an apple into 9 equal parts, there would be 63 parts, and each person would receive; but there being, each man will receive 5 times = 3 Ans. Hence we see the propriety of the following RULE. Multiply the whole number by the denominator of the fraction, and write the product under the numerator. Ans. 112 • Ans. Ans. Tog 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? Ans.. Ans. zg 8. James Page's estate is valued at $10,000, and he has given 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. $6804. II. To divide a whole number by a fraction. 9. How many times will 13 contain ? OPERATION. ¥X}== 301 Ans. Ans. 30. It is evident, that 13 will contain, as many times as there are sevenths in 13, which are 7 X 1391 times. Again, if 13 contain 1 seventh 91 times, it will contain 3 sevenths as many times as 91 will contain 3 = 30 Ans. Hence the following RULE. Multiply the whole number by the denominator of the fraction, and divide the product by the numerator. 10. Divide 18 by 7. 11. Divide 27 by Ans. 204. Ans. 295. 17. I have 50 square yards of cloth, how many yards, of a yard wide, will be sufficient to line it? Ans. 83 yards. 18. A. Poor can walk 37 miles in 60 minutes; Benjamin can walk as fast as Poor. How long will it take Benjamin to walk the same distance? Ans. 733 minutes. III. To divide a mixed number by an integer. 19. Divide 173 by 6. OPERATION. 6) 17 248 Ans. 248. We divide 17 by 6, and find it is contained 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. 7 men. 27. Divide $ 173 among 29. What is the value of of a dollar? Ans. $22. Ans. $1325. Ans. $0.341%. 30. Divide $1077 among 4 boys and 3 girls, and give the girls twice as much as the boys. Ans. boy's share $104. Girl's share $212. 31. If $14 will purchase 7 of a ton of copperas, what quantity will $ I purchase? Ans. lcwt. Oqr. 24lbs. IV. To divide one fraction by another. To understand the rationale of this process, we find the two factors of, multiplied by are, as is evident from a preceding rule. We now divide by 1, which, by case I. of this section, will be 7 × 1 = 2. Again, we wish to divide by . It is evident, that will contain nine times as often, as it will a unit, and it contains a unit times, therefore it contains nine times 2=fX 2 == 18 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 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 by 4. OPERATION. 7 × 7=18=1}} Ans. 34. Divide 7 by 33. 35. Divide by 1. OPERATION. 72 = 21, 33 = 4, 4× Z=217=283 Ans. Ans. 31 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 113 inches long, and 44 inches wide? Ans. 4915 square inches. 3. How many square rods in a garden, which is 189 rods in length and 9 rods wide? 4. What cost 192 acres of land, at $17 5. What cost 14 6. What cost 13 tons of coal at $7 Ans. 1783 rods. per acre? tons of hay at $87 Ans. $350. of a dollar? Ans. $ 0.561. of a dollar? Ans. $0.25§. 7. What cost 17 bushels of corn at $17 T6 160 of a dollar? of a dollar? Ans. $0.51%. 8. What is the value of 9. What is the value of 1 10. What is the value of 11. What is the value of 12. Bought a cask of molasses, containing 87 gallons; of it having leaked out, the remainder was sold at 271 cents per gallon; what was the sum received? Ans. $15.0332. |