41. Bought of a coal-mine for $3675, and having sold of my share, I gave of the remainder to a charitable society, and divided the residue among 7 poor persons; what was the share of each? Ans. $50 for each poor person. 42. Of an estate valued at $5000, the widow receives, the oldest son of the remainder; the residue is equally divided among 7 daughters; what is the share of each daughter? Ans. $158. 240. When the dividend is a mixed number, and the divisor a whole number, we may Divide the integral part of the mixed number as in division of whole numbers, and the remainder divide as in Art. 239; and add together the results for the quotient required. 9. Divide of a prize, valued at $1723, equally between 12 seamen. 10. What will a barrel of flour cost, if 19 barrels can be purchased for $107 } ? Ans. $5.65g. 11. If 15 pounds of raisins can be obtained for $32, what will 1 pound cost? Ans. $0.21. 12. If 12 quarts of wine cost $3.75%, what will a quart cost? 13. If $19 will buy 3751 acres of land, how much can be bought for $1? Ans. 1933 acres. REDUCTION OF COMPLEX FRACTIONS. 21 241. A COMPLEX fraction is one having a fraction in its 3 numerator or denominator, or in both. Thus, and complex fractions. 242. To reduce complex to simple fractions. are Ans. 18. Since the numerator of a fraction is the dividend, and the denominator the divisor (Art. 216), we divide the numerator,, by the denomi nator, ğ, as in division of fractions (Art. 239). and then proceed as in Ex. 1. Hence, to reduce complex to simple fractions, Consider the denominator as a divisor, and the numerator as a dividend, and proceed as in division of fractions (Art. 239). NOTE. Another and often a ready method of reducing a complex fraction is to multiply both its terms by the least common multiple of their denomi nators. = z, Ans Or, multiply by the least common multiple of the denominators, 17. If 7 were to be the denominator of the fraction whose numerator is 77 11 what would be its value? 18. If is the numerator of the fraction whose denominator is what is its value? Ans. 61. 243. Complex fractions, after being reduced to simple ones, may be added, subtracted, multiplied, and divided, according to the respective rules for simple fractions. 4. What is the continued product of the following numbers: 27 87급 공 3798 21 5. Divide of 73 by of 11. Ans. 341 6. Divide of 91 by of 87. Ans. $649. MISCELLANEOUS EXAMPLES IN MULTIPLICATION AND DIVISION OF FRACTIONS. 1. At 2 bushels to an acre, how many bushels of wheat will be required to sow 7 acres? Ans. 174. Ans. $0.574. 2. Bought 8 bushels of apples for $4.684; what did they cost per bushel? 3. Bought a bale of cloth for $963; I dispose of it for of the cost, and by so doing I lose $2 on a yard; required the number of yards in the bale. Ans. 18 yd. 4. If a dividend be 18 times and a quotient 6 times, what was the divisor? 5. By what number must 11 be multiplied, that the product shall just equal 1? Ans. . 6. Bought a horse and chaise for $250, and paid for the harness of what I paid for the horse. The chaise cost the value of the horse. What was the price of each? Ans. Horse, $13042; chaise, $11913; harness, $833 7. S. Walker has engaged to work at yearly wages of $200 and a suit of clothes. At the end of 9 months, falling sick, and being unable to labor longer, he receives the suit of clothes and $144, as the amount justly due. What was the cost of the clothes? Ans. $24. 8. What will be the result if of 2 of 3 be multiplied by of itself, and the product divided by ? 9. Bought 137 acres of land at $25 it in wheat at $23 per bushel. require? per acre, and paid for How many bushels did it Ans. 137 bushels. 10. How long will it take a man to travel 553 miles, provided he travels 3 miles per hour, and 97 hours per day? 11. If $ per cord is paid E. Holmes for sawing into three pieces wood that is 4 feet long, how much more should he receive per cord for sawing into pieces of the same length wood that is 8 feet long? Ans. $0.22. 12. A steamboat leaves New Orleans, January 1st, bound up the river to a place distant 23174 miles. Her forward motion is at the rate of 94 miles per hour for 162 hours each day, and she lies at anchor in the night for fear of running upon a snag. But having lost her anchor on the fifth day, she each succeeding night drifts backward, at the rate of 2 miles per hour. On what day of January will she reach her point of destination? Ans. 15th day. A PROPOSED NUMERATOR, OR DENOMINATOR. 244. To reduce one fraction to another of equal value, having a proposed numerator, or denominator. Ex. 1. Reduce to an equivalent fraction having 4 for a 4 numerator. 418415 OPERATION. 4 Ans. Ans. ៦៖ The proposed numerator, 4, is such a part of the given numerator as 4 divided by 5, or . Now, as the numerator proposed is only as large as the given numerator, in order that the value of the two fractions be the same, the denominator of the proposed fraction should be only as large as the denominator of the given fraction. Taking of the given denominator, 7, we obtain X 7 53 |