CASE II. To divide an integer or whole number by a fraction. OPERATION 1. Divide 17 by a. 17X4=6=223 Ans. By multiplying the dividend by 4, it is reduced to fourths; and by dividing the product by 3, the quotient will be threefourths. Hence the following RULE. Multiply the whole number by the denominator of the fraction, and divide the product by the numerator. OPERATION. 3 68 1. Divided by 17. 4x 17= Ans. This case is the reverse of the last. We therefore see the propriety of the following RULE. Multiply the integer by the denominator of the fraction, and write the product under the numerator. 13 CIC 2. Divide 11 by 18. 3. Divide in by 28. 4. Divide † by 27. 5. Divide is by 128. 6. Divide 14 by 98. Ans. 158 Ans. Het Ans. ą. Ans. s Ans. 166 OPERATION 1. Divide 273 by 6. We divide the 27 by 6, and find it is contained 4 times, and that 3 remains, 6 ) 273 which we multiply by the denominator, 41=4; Ans. 5, and to the product we add the numer ator, 3, the sum of which is 18; this we write over the product of 6, the divisor, multiplied by the denominator, 5=30. Hence the following RULE. Divide the integer 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. 2. Divide 293 by 9. Ans. 349. 3. Divide 14 by 7. Ans. 214 4. Divide 133 by 8. Ans. 144. 5. Divide 143 by 6. Ans. 218. 6. Divide $ 37; between 9 men. Ans. $ 419. 7. Divide $ 963 between 11 persons. Ans. $ 835 . 8. What is į of 16711 cwt. of iron? Ans. 203) cwt. 9. Divide y of a prize, valued at $ 1723, equally between 12 seamen. Ans. $ 125.634 10. What will a barrel of flour cost, if 19 barrels can be purchased for $ 1073? Ans. $ 5.6535 11. If 15 pounds of raisins can be obtained for $ 33, what Ans. $ 0.211 will 1 pound cost? 12. If 12 quarts of wine cost $ 3.75%; what will a quart Ans. $0.311 cost? 13. If $ 19 will buy 3754 acres of land; how much can Ans. 19384 acres. be bought for $1. MISCELLANEOUS QUESTIONS. a 1. How far will a man walk in 174 hours, provided he goes at the rate of 47 miles an hour? Ans. 82m. 4fur. 8rd. 1ft. 4in. 2. How much land is there in a field, which is 291, rods square? Ans. 5A. 1R. 32p. 141ft. 1091 in. 3. How much wood in a pile, which is 174 feet long, 741 feet high, and 47 feet wide? Ans. 4cd. 66107ft. 4. What is the value of 197 barrels of flour, at $ 64, a barrel? Ans. $ 134.15%. 5. What is the value of 3764 acres of land, at $ 75% per acre? Ans. $ 28387.064. 6. What cost 1710 quintals of fish, at $ 4.75 per quintal? Ans. $ 81.55 7. What cost 167073 pounds of coffee, at 12 cents per pound? Ans. $ 212.9933. 8. What cost 281 tons of Lackawana coal, at $ 114 a ton? Ans. $333.27 9. Bought 37 hogsheads of molasses, at $17.62 a hhd.; what was the whole cost? Ans. $ 655.202. 10. What cost of a cord of wood, at $ 5.75 a cord? Ans. $5.03. 11. What are the contents of a field, which is 1394 rods long, and 384 rods wide? Ans. 33A. 3R. 151}p. 12. Bought 15 loads of wood, each containing 113 feet, cord measure. I divide it equally between 9 persons; what does each receive? Ans. 191 ft. 13. If the transportation of 182 tons of iron cost $48.153, what is it per ton? Ans. $ 2.625 14. If a hhd. of wine cost $ 98], what is the price of one gallon? Ans. $1.56133 15. If 5 bushels of wheat cost $8%; what will ä bushel be worth? Ans. $ 1.643. 16. What will 11 hogsheads and 17) gallons of wine cost, at 19 cents a gallon? Ans. $ 140.323. 17. How many bottles, each containing 14 pints, are sufficient for bottling a hhd. of cider? Ans. 288 bottles. 18. I have a shed, which is 181 feet long, 10 feet wide, and 714 feet high; how many cords of wood will it contain? Ans. 11cd. 12482.in. a square foot ? a 19. What will 63 pounds of tea cost, at 65 cents per lb. Ans. $ 4.525. 20. How many cubic feet does a box contain, that is 8 feet long, 51 feet wide, and 3 feet high? Ans. 146.ft. 21. How many feet of boards will it take to cover a side of a house, which is 46 feet long, and 172 feet high? Ans. 812 ft. 22. How many feet of boards will it take to make 7 boxes, that shall be 5. feet long, 2 feet high, 31 feet wide; and how many cubic feet will they contain? Ans. 52773ft. 2862. cub. ft. 23. A certain room is 12 feet long, 11į feet wide, and 71. feet high; how much will it cost to plaster it, at ”cents per Ans. $ 13.487. 24. A man has a garden that is 14rods long, and 104 rods wide; he wishes to have a ditch dug around it, that shall be 3 feet wide and 41 feet deep; what will be the expense if he gives 2 cents per cubic foot? Ans. $ 223.764 25. How many bushels of grain will a box contain, which is 141, feet long, 511 feet deep, and 47 feet wide, there being 2150 cubic inches in a bushel? Ans. 294347abush. 26. Which will contain the most, and by how much, - a box that is 10 feet long, 8 feet wide, and 6 feet deep; or a cubical one, whose each side measures 8 feet? Ans. The last contains 32 cubic feet most. 27. Divide $ 1112equally between 129 men. Ans. $ 8. 28. Bought 68 barrels of flour at $ 711 per barrel, what was the amount of the whole? Ans. $ 5383. 29. What cost 8% acres of land at $42; per acre? Ans. $ 369.20. 30. How shall four 3's be arranged, that their value shall be nothing? 31. From 7 take 11. 3584 SECTION XVI. DECIMAL FRACTIONS. 348 100 A DECIMAL Fraction is that whose integer is always divided into 10, 100, 1000, &c. equal parts. Its denominator is always an unit, with as many ciphers annexed, as there are places in the given decimal. There is therefore no need of having the denominator expressed ; for the value of the fraction is always known by placing a point before it, at the left hand, called the separatrix. Thus, .5 is tó, .37 is it, .348 is 1.06 Ciphers annexed to the right hand of decimals do not increase their value; for .4 or .40 or .400 are decimals having the saine value, each being equal to 16 ors; but when ciphers are placed on the left hand of a decimal, they decrease the value in a tenfold proportion. Thus .4 is id, or four tenths; but .04 is , or four hundredths; and .004 is tood, or four thousandths. The figure next the separatrix is reckoned so many tenths ; the next ; at the right, so many hundredths; the third is so many thousandths; and so on, as may be seen by the following From this table it is evident, that in decimals, as well as in whole numbers, each figure takes its value by its distance from the place of units NOTE. — If there be one figure in the decimal, it is so many tenths; if there be two figures, they express so many hundredths; if there be three figures, they are so many thousandths, &c. |