3 9. How many times is contained in 1? 10. How many barrels of flour can be bought for 38 dollars, at 4 dollars per barrel? 47 . 11. How many times is 25 contained in 912? 12. How many times is 6 contained in 42? Direction. Reduce the two fractions to a common denominator; then reduce the mixed numbers to improper fractions, and divide one numerator by the other. 13. If a barrel of cider will last a man 3 months, how many barrels will he drink in 10 months? SECTION 31. REVIEW. 1. (§ 13.) Suppose a man to earn 95 cents per day; how many days would it take him to earn $43.16? 2. (§ 14.) How many pounds of sugar can be bought for $14, when the price is of a dollar a pound? 3. (§ 15.) If 1 yard of silk cord cost of a dollar, what is the price of 75 yards, at the same rate? 4. (§ 16.) If 147 yards of cloth be cut from a piece containing 52 yards, how much will be left? 3 5. (§ 17.) If a pound of shot cost of a dollar, what will be the cost of 17 pounds, at the same rate? 6. (§ 18.) How much corn will grow on 140 acres of land; allowing each acre to produce 34 bushels? 7. (§ 19.) If a man's expenses be $46.247 for of a year, what will be his expenses for 1 year? 8. (§ 20.) of 71 is equal to what improper fraction? Then of 71 is equal to what mixed number? 9. (§ 21.) Suppose 42 men to share equally in a prize of $1000; what is the share of one man? 10. (§ 22.) If a man can cut 46 cords of wood in 14 days, how many cords can he cut in 60 days? 11. (§ 23.) Suppose a man can build a mile of wall in 310 days; in what time can he build of a mile? 12. (§ 24.) A man bought a quantity of flour, for domestic use, and in 36 days he found that of it was consumed. How long would the whole last? 13. (§ 25.) is equal to how many ninths? how many thirty-sixths? how many seventy-fifths? 14. (§ 26.) Reduce the two fractions, 7 and 8, to their lowest terms, and then add them together. 15. (§ 27.) Suppose a farm to contain 982 acres of land; how many acres are there in of the farm? 16. (§ 28.) Add together, and and 1; then subtract from the sum;- what is the remainder? 17. (§ 29.) If and of a number be subtracted from itself, what part of that number is the remainder? 18. (§ 30.) If the mail-stage run 9 miles in 1 hour, how many hours will it be in running 175 miles? RETROSPECTIVE OBSERVATIONS. A fraction is rendered greater by increasing the numerator, and smaller by increasing the denominator. To multiply a fraction by a whole number,- Either multiply the numerator, or divide the denominator. To divide a fraction by a whole number,- Either divide the numerator, or multiply the denominator. When a number is multiplied by 1, the product is equal to the multiplicand. Therefore, when a number is multiplied by a fraction, which is less than 1, the product must be less than the multiplicand. To multiply a whole number by a fraction,— Multiply by the numerator, and divide by the denominator. Dividing a number by 1, gives a quotient equal to the dividend. Therefore, dividing a number by a proper fraction, must give a quotient greater than the dividend, because, the fraction being less than 1, is contained a greater number of times in the dividend. To divide a whole number by a fraction,-Multiply by the denominator, and divide by the numerator. To multiply a fraction by a fraction,-Multiply numerator by numerator, and denominator by denominator. To divide a fraction by a fraction, Multiply the numerator of the dividend by the denominator of the divisor, for a numerator; and multiply the denominator of the dividend by the numerator of the divisor, for a denominator 19 19. Multiply the fraction, 32, by 38. 20. Divide the fraction,, by 145. " 464 21. Multiply 8706 by the fraction, 203. 22. Divide 611 by the fraction, 320. 168 . 23. Multiply the fraction, 265, by the fraction, · 24. Divide the fraction, 24, by the fraction, 25. What is the product of 608 26 What is the quotient of 45 SECTION 32. multiplied by 8 divided by 32? MISCELLANEOUS EXAMPLES. 1. Suppose a man can perform a journey in 14 days and 3 hours, travelling 9 hours a day; in what time can he perform the journey, travelling 11 hours a day? 2. A trader gave $75 for 56 gallons of wine, and lost 11 gallons by leakage. At how much per gallon must he sell the remainder, to get the whole cost? sugar, 3. Suppose a retailer to pay $165 for a ton of at what price must he sell it per pound, in order to gain 10 per cent. on the cost? 4. What quantity of salt, worth 62 cents per bushel, must be given in exchange for 258 pounds of pork, worth 9 cents per pound? 5. What is the profit on 400 hogsheads of molasses, purchased in New Orleans at 12 cents per gallon, [63 gal. in each hhd.], freighted to New York at $3.50 per hhd., and sold at 24 cents per gallon; 3gal. 2qt. having leaked from each hhd. on the passage? 6. If a pint of rum a day will kill a man in a year and a half, how many men would a cargo of 600 hogsheads kill in the same time? 7. If 11 young men can become fools by drinking 6 bottles of wine, at $3 a bottle, what would it cost a dinner party of 25, to become fools in like manner? 8. If a man's expenses be $1.40 a day, and his income $700 a year, what will he lay up in 7 years? 9 A and B are laborers-A earns $19.50 a month, and B earns $16.25; but A gives B of his earnings What will each lay up in 14 months? 10. Find the difference between of 91, and of 91 On the opposite page, 30 cities and towns are exhibited in their respective situations, relative to each other; and the number of miles, by mail-road from town to town, is noted in figures. 11. Find the distance from Washington, through the intermediate towns, to Augusta, Me....... from Washington to Detroit....... from Washington to St. Louis...... from Washington to Natchez....... from Washington to New Orleans....... from New Orleans to Augusta, Me. 12. Suppose a citizen in each of the places on the opposite page, to start for Washington, and travel 7 miles an hour, 10 hours in each day; how long will each one be in performing his journey? 13. How long would it take you to walk from your school-room to Washington; allowing that you could walk 31⁄2 miles an hour, 7 hours in each day? 14. Two men started at the same time one of them from New Orleans, and the other from Augusta, Me.and travelled towards each other, with equal speed. Between what two towns, and what distance from each of these towns did they meet? 15. Mr. A. went from Portland to Baltimore, travelling 5 miles an hour, and 10 hours a day. Mr. B. performed the same journey; but started 1 day later, and travelled 7 miles an hour. Where did B. pass A.? 16. Divide $1000 among A, B, and C, giving B twice as much as A, and C twice as much as B. 17. Gunpowder is composed of 5 parts sulphur, 7 parts charcoal, and 38 parts nitre. How many pounds of each ingredient, in 100 pounds of powder? 18. A and B purchased a cow for $16. A paid $9 of the price, and B paid $7. They sold the cow for $21. What was each one's share of the gain? Solution. Since A paid of the price, and B. A must have of the gain, and B · 19. C and D traded in partnership; C owned $450 of the stock in trade, and D $290. They gained $146 What was each one's share of the gain? 20. Suppose $1000 stock in trade to gain $230; what is the gain on $351 of that stock? |