3. How much time has elapsed since the declaration of independence of the United States?

4. How many years, months, and days from your birthday to this date; or what is your age?

5. How long from the battle of Bunker Hill, June 17, 1775, to the battle of Waterloo, June 18, 1815? Ans. 40 yr. 1 da.

6. What length of time will elapse from 20 minutes past 2 o'clock, P. M., June 24, 1856, to 10 minutes before 9 o'clock, A. M., January 3, 1861? Ans. 4 yr. 6 mo. 8 da. 18 h. 30 min.

7. How many days from any day of April to the same day of August? of December? of February?

8. How many days from the 6th of November to the 15th of April? Ans. 160 days.

9. How many days from the 20th of August to the 15th of the following June?

Ans. 299 days.

2. What is the difference between rod and of a foot?

Give explanation of the process of subtracting denominate fractions.

7. Two persons, A and B, start from two places 120 miles apart, and travel toward each other; after A travels, and B &, of the distance, how far are they apart?

Ans. 41. mi. 7 fur. 9 rd. 8 ft. 71⁄2 in.

8. From a cask of brandy containing 96 gallons,

leaked

out, and of the remainder was sold; how much still remained Ans. 25 gal. 2 qt, 3 gi.

in the cask?

MULTIPLICATION.

222. 1. A farmer has 8 fields, each containing 4 A. 2 R. 27 P.; how much land in all?

OPERATION. A. R. P. 4 2 27

8

37 1 16

ANALYSIS. In 8 fields are 8 times as much land as in 1 field. We write the multiplier under the lowest denomination of the multiplicand, and proceed thus; 8 times 27 P. are 216 P., equal to 5 R. 16 P.; and we write the 16 P. under the number multiplied. Then 8 times 2 R. are 16 R., and 5 R. added make 21 R., equal to 4 A. 1 R.; and we write the 1 R. under the number multiplied. Again, 8 times 4 A are 32 A., and 4 A. added make 36 A., which we write under the same denomination in the multiplicand, and the work is done. Hence,

RULE. I. Write the multiplier under the lowest denomination of the multiplicand.

II. Multiply as in simple numbers, and carry as in addition of compound numbers.

Multiplication of compound numbers, how performed? Rule.

8. In 6 barrels of grain, each containing 2 bu. 3 pk. 5 qt., Ans. 17 bu. 1 pk. 6 qt. 9. If a druggist deal out 3 lb 43 13 29 16

how

many bushels?

6 gr. of medicine a day, how much will he deal out in 6 days? 10. If a man travel 29 mi. 3 fur. 30 rd. 15 ft. in 1 day, how far will he travel in 8 days?

11. If a woodchopper can cut 3 Cd. 48 cu. ft. of wood in 1 day, how many cords can he cut in 12 days? Ans. 401 Cd. 12. What is the weight of 48 loads of hay, each weighing 1 T. 3 cwt. 50 lb.?

ANALYSIS. When the multiplier is large, and a composite number, we may multiply by one of the factors, and that product by the other. Multiplying the weight of 1 load by 6, we obtain the weight of 6 loads, and the weight of 6 loads multiplied by 8, gives the weight of 48 loads.

13. If 1 acre of land produce 45 bu. 3 pk. 6 qt. 1 pt. of corn, how much will 64 acres produce? Ans. 2941 bu. 14. How much will 120 yards of cloth cost, at 1 £ 9 s. 81 d. per yard?

15. If $80 will buy 4 A. 3 R. 26 P. 20 sq. yd. 3 sq. ft. of land, how much will $4800 buy? Ans. 295 A. 10 sq. yd. 16. If a load of coal by the long ton weigh 1 T. 6 cwt. 2 qr. 26 lb. 10 oz., what will be the weight of 73 loads?

Ans. 97 T. 11 cwt. 3 qr. 11 lb. 10 oz.

17. The sun, on an average, changes his longitude 59′ 8.33"
per day; how much will be the change in 365 days?

18. If 1 pt. 3 gi. of wine fill 1 bottle, how much will be re-
quired to fill a great gross of bottles of the same capacity?

DIVISION.

223. 1. If 4 acres of land produce 102 bu. 3 pk. 2 qt. of
wheat, how much will 1 acre produce?

OPERATION.

pt. bu. pk. qt. pts.
4) 102

3 2

25 2 6

1

ANALYSIS. One acre will produce
as much as 4 acres. Writing the divi-
sor on the left of the dividend, we divide
102 bu. by 4, and we obtain a quotient of
25 bu., and a remainder of 2 bu. We
write the 25 bu. under the denomination of bushels, and reduce the
2 bu. to pecks, making 8 pk., and the 3 pk. of the dividend added
makes 11 pk. Dividing 11 pk. by 4, we obtain a quotient of 2 pk.
and a remainder of 3 pk.; writing the 2 pk. under the order of
pecks, we next reduce 3 pk. to quarts, adding the 2 qt. of the
dividend, making 26 qt., which divided by 4 gives a quotient of 6 qt.
and a remainder of 2 qt. Writing the 6 qt. under the order of
quarts, and reducing the remainder, 2 qt., to pints, we have 4 pt.,
which divided by 4 gives a quotient of 1 pt., which we write under
the order of pints, and the work is done.

2. A farmer put 132 bu.

1 pk. of apples into 46 barrels ;

OPERATION.

bu.

pk.

how many bu. did he put into 46) 132 1(2 bu.

a barrel?

92

Explain the process of dividing compound numbers,

RULE. I. Divide the highest denomination as in simple numbers, and each succeeding denomination in the same manner, if there be no remainder.

II. If there be a remainder after dividing any denomination, reduce it to the next lower denomination, adding in the given number of that denomination, if any, and divide as before.

III. The several partial quotients will be the quotient required.

NOTES. 1. When the divisor is large and is a composite number, we may shorten the work by dividing by the factors.

2. When the divisor and dividend are both compound numbers, they must both be reduced to the same denomination before dividing, and then the process is the same as in simple numbers.

7. Bought 6 large silver spoons, which weighed 11 oz. 3 pwt.;

what was the weight of each spoon?

8. A man traveled by railroad 1000 miles in one day; what was the average rate per hour?

Ans. 41 mi. 5 fur. 13 rd. 5 ft. 6 in. 9. If a family use 10 bbl. of flour in a year, what is the average amount each day? Ans. 5 lb. 5 oz. 1458 dr. 10. The aggregate weight of 123 hogsheads of sugar is 57 T. 19 cwt. 42 lb. 14 oz.; what is the average weight per hogshead? Ans. 9 cwt. 42 lb. 10 oz.

11. How many times are 5 £ 10 s. 10 d. contained in 537 £ 10 s. 10 d.?

Ans. 97.

Give the rule. When the divisor is a composite number, how may we proceed? When the divisor and dividend are both compound numbers, how proceed?