5. A garrison of 700 soldiers are allowed of a pound of flour a day, for each man; how much would they consume in 1 day? How much in 7 days? 6. If a horse eats of a bush. of oats in a day, how many bush. will he eat in 365 days? 7. If a horse eats 2 cwt. of hay in a week, what part of a cwt. will he eat in one day? How many cwt. will he eat in a year? 8. Three men gain by an adventure 56 dollars, which they are to share equally; what is each man's share? 9. What is of 1874? What is of 913? 10. X141? X97? X140? 11. If 3 cwt. of flour be divided equally into 5 equal parts, what part of a cwt. will each share be? 12. Divide 17 by 8. 373 by 14. 184 by 9. 13. Divide 741-5. 8111÷÷7. 3811÷9. SECTION XVI. MULTIPLICATION AND DIVISION OF FRACTIONS. 1. In 63 gallons how many bottles of of a gal, each ? 2. From 7 lbs. of flour how many loaves of bread may be made, each containing 3 of a lb. of flour? 3. Divide 4. 13÷3. 14÷31. 4. A man left 5846 dollars; % of the whole to go to his wife, and the remainder to be equally divided among four children; what was each child's share? 5. From a piece of cloth 32 yds. long, how many coats can be made, each requiring 23 yds.? 6. From a stick of timber 26 feet long, how many blocks can be cut, each of a foot long? 7. If a family consume 22 lbs. of flour in a week, how much is that a day? How much will they use in a year? 8. Divide 13. 182÷÷11. 86191. 9. Multiply 25×16. 231×2. 31×194. A fraction of a fraction, as of, is called a Compound Fraction. This is reduced to a simple fraction by multiply ing the numerators together for a new numerator, and the denominators for a new denominator. It is in fact the same as the multiplication of two fractions together. of of 84? 11. What is of of 12? What is of § of 18? yard? 16. What do 17 tons of hay 17. What is the value of 21 cord? 18. What is the value of 24 a barrel ? Mult. of 4 of 34? by 81. of 18 by 194. yds. of cloth at 41⁄2 dollars a come to at 11 dolls. a ton? cords of wood at 41 dolls. a barrels of apples at 12 dolls. 19. What is the amount of 123 shares Bank stock, at 6414 dollars a share? ADDITION AND SUBTRACTION OF FRACTIONS. If the fractions have a common denominator, perform the required operation on the numerators, and place the result over the common denominator. 1. Add ++. Add ++. 2. Subtract-8. 33-33. 17—11. If the fractions have not a common denominator, reduce them to a common denominator, (Sec. IX. Pt. I.) and then add or substract, as the question requires. 3. Add 1+1+. Add 3+✩tı?. 4. Add 3. Add ++i§. 5. Subtract from 54. 84. 1-14. 6. Add 311+571+18}. In cases like the above it is easiest to add the whole numbers first. 7. Add 67 of 71+1 of 22. 8. A man spent for various articles of a dollar, of a dollar, of a dollar, of a dollar; how much did he spend in all ? 9. From 56 bushels, 11 bush. were taken; how much remained? 10. From a firkin of butter containing 42 lbs., 181 lbs. were taken; how much remained? 11. Add 124. Add 11+22. 17 13 REDUCTION OF DENOMINATE FRACTIONS. Denominate fractions, are fractions of numbers when applied to a particular denomination. See Sec. XI. Part I. Examples. 1. What part of a bush. is 2. What part of 2 bush. is of a quart? of a quart? 3. What part of 7 bush. is of a peck? 4. What part of 3£ is § of a shilling? 5. What part of a shilling is of a penny? 6. What part of a mile is half a rod? 7. What part of 3 fur. is of a rod? 8. What part of a mile is 3 fur. 19 rods? 9. What part of a mile is 1 foot? 2 feet? 10. What part of a ton is 6 cwt. 3 qrs. 7 lbs.? 11. What part of a ton is 18 cwt. 1 qr. 6 lbs.? 12. What part of a sq. rod is 17 feet? 13. What part of a cord is 12 cubic feet? 14. What part of a cord is 184 cubic feet? 15. What part of a bush. is of a qt.? 20. What is the value in shillings and pence of 4 of a £ ? If it were 3£, there would be 60 shillings; but it is not 3£, but one seventh of that; therefore it is of 60 shillings=84 shillings. To find the value in pence of of a shilling, pursue the same reasoning; if it was 4 shillings, it would be 48 pence ; but it is not 4 shillings, but of that 64 pence. The answer, then, is 8s. 6d. 21. What is the value in shillings and pence of † of a £? 22. Value in hours, minutes, and seconds, of ↓ of a week? 23. How many minutes in of a week? of a bl. of wine? of a lb. Troy? 24. How many minutes and seconds in of an hour? of a lb. Troy? of a sq. foot? SECTION XIX. CHANGE OF DENOMINATE INTEGERS TO FRACTIONS. [See Section XI. Part I.] Examples. 1. What part of a furlong is 5 feet? 2. What part of a mile is 17 feet? 3. What part of a mile is 314 feet? 4. What part of a ton is 25 lbs. ? 5. What part of a ton is 1074 lbs. ? 6. What part of a ton is 3 qrs. 9 lbs. 8 oz.? 7. What part of a ton is 4 lbs. 13 oz.? 8. What part of an acre is 4 rods, 17 feet? 9. What part of an acre is 113 rods, 51 feet? 10. What part of a hhd. of wine is 17 gals. 3 qts. 1 pt.? 11. What part of 10 gals. is 3 pints? 12. What part of a guinea is 3s. 7d. ? 13. What part of a £ is 8s. 54d.? 14. What part of a week is 31⁄2 hours? 15. What part of 5 days is 1 hour, 41 m. 15 sec.? 18. What part of 21 yards is 34 qrs.? 19. What part of 37 yards is 14 ell Eng.? 20. What part of 7 cords of wood is 21 cubic feet? 21. What part of 31£ is 5s. 3d.? SECTION XX. PRACTICAL EXAMPLES. 1. What is the cost of 13 yds. broadcloth at 4 dolls. a yd.? 2. What is the cost of 24 yds. cloth at of a doll. a yd.? 3. What is the value of 12 bbls. of flour at 4ğ dolls. a bbl.? 4. What is the value of 31 casks of lime at of a dollar a cask? 5. What is 5 cwt. of beef worth at 43 dolls. per cwt.? 6. What is the cost of 434 bush. corn at § of a doll. a bush. ? 7. If a horse eat 1 bush. of oats in a week, how much will he eat in 52 weeks? 8. What will be the cost of the oats for 52 weeks at of a doll. a bushel? 9. What part of a cwt. is 196 lbs.? 10. What is the weight of tons? of a bbl. of flour containing of a lot of hay weighing 4 11. How many cubic feet are there in 3 of of a cord of wood? 12. A man sold of a lot of wood, the whole of which was 17 cords; how much did he sell? 13. What part of 9 rods in length is 10 feet? 16. What is 36 sq. feet of land worth at 9 dolls. a sq. rod? 17. How many gallons are there is of a barrel of wine? 18. Two men bought a lot of hay for 11 dollars; one took 13 cwt.; the other, the remainder, which was 8 cwt.; what ought each to pay? |