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.
[See Section IX. Part I.]

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
12. What is
What is 4
13. Divide of by 4. Divide of
14. Multiply of 37 by 194.
15. What is the value of 324

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.?
16. What part of a bush. is 7 qts.?
17. What part of a week is 4 hours?
18. What part of a week is 74 hours?
19. What part of 3 hours is 12 minutes?

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?
25. Value of of a gal.? Value of
26. How many oz., dwt. and grs. in
27. What is the value in oz., dwt. and grs. of
28. How many square rods in of an acre?
29. How many square feet and inches in

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.?
16. What part of a month of 31 days, is 17 h. 181 m.?
17. What part of an ell Eng. is 2 n. 1 in.?

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?
14. What part of a sq. rod is 3 sq. yards?
15. What part of a sq. rod is 5 sq. 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?