EXAMPLES FOR PRACTICE.

1. Multiply 3 T. 10 cwt. 1 qr. 12 lb. 11 oz. by 9. 2. How much grain in 15 bins, each containing 122 bu. 3 pk. 1 qt.?

3. What distance can a man walk in 13 hours, at the rate of 3 mi. 5 fur. 25 rd. an hour?

4. A sold 6 loads of wood, each containing 1 C. 21 cu. ft. 576 cu. in.: how much did he sell?

5. How much land in 12 farms, each containing 140 A. 3 R. 30 P.?

6. What are the contents of 32 boxes, each holding 3 bu. 2 qt.?

7. If 1 load of hay weighs 1 T. 23 lb., what is the weight of 30 loads?

8. If one silver spoon weighs 1 oz. 10 gr., what is the weight of 2 dozen?

9. Multiply 13° 18′ 35′′ by 16.

10. If a barrel of flour will support a family 3 wk. 5 da., how long will 12 barrels support them?

11. If 1 keg holds 5 gal. 1 qt. 1 gi. of wine, how much will 24 kegs hold?

12. Find the weight of 100 barrels of sugar, each weighing 1 cwt. 2 qr. 10 lb.

13. Multiply 10 t. 103 73 15 gr. by 62.

14. If a man sleeps 7 hr. 45 min. 20 sec. each day, how long will he sleep in 24 days?

15. A man walks 5 ft. 10 in. a second: how far will he walk in 10 minutes?

16. A brewer fills 5 dozen ale bottles, each containing 1 qt. 1 pt.: how much will they contain?

17. A hotel uses daily 3 doz. and 6 eggs: how many will it use in a month?

DIVISION OF COMPOUND NUMBERS

81. Division of Compound Numbers is the process of finding how many times one number is contained in another of different denominations.

MODEL SOLUTION.

EXAMPLE.-What is the quotient of 17 bu. 3 pk. 2

qt. divided by 5?

SOLUTION.-Divide the highest denomina

tion first, so that, if there be a remainder, it

may be reduced to the next lower denomina- 5)17 3 2 tion, and added to it.

3 2 2

One-fifth of 17 bu. is 3 bu., with 2 bu. remaining; place the 3 bu. under bu., and reduce the 2 bu. to pk.; 2 bu. = 8 pk.; 8 pk. + 3 pk. = 11 pk.

One-fifth of 11 pk. is 2 pk., with 1 pk. remaining; place the 2 pk. under pk., and reduce the 1 pk. to qt.; 1 pk. = 8 qt.; 8 qt. + 2 qt.

=

10 qt.

One-fifth of 10 qt. is 2 qt., which write under qt.

CONCLUSION.-Therefore, the quotient of 17 bu. 3 pk. 2 qt. divided by 5, is 3 bu. 2 pk. 2 qt. Hence, the

Rule for Division of Compound Numbers.-Beginning with the highest denomination, divide each number separately, and write the quotient beneath.

If a remainder occurs after dividing any denomination, reduce and add it to the next lower denomination, and divide as before.

PROOF.-The same as in Simple Numbers.

NOTE.-In dividing one compound number by another, as in example 20, reduce both quantities to the same denomination.

EXAMPLES FOR PRACTICE.

1. Divide 33 wk. 5 da. 23 hr. 21 min. 20 sec. by 4. 2. Divide 24 bu. 1 pk. 4 qt. 1 pt. by 7.

3. Divide 109 A. 1 R. 34 P. by 6.

4. Divide 15 hhd. 28 gal. 1 pt. by 9.

5. Divide 48 cwt. 2 qr. 14 lb. 9 oz. 8 dr. by 12.
6. Divide 41 lb. 3 oz. Troy by 18.

7. Divide 28th. 103 23 19 1gr. by 9.

8. Divide 186 sq. yd. 5 sq. ft. 50 sq. in. by 13.
9. Divide 144 da. 44 min. 16 sec. by 22.

10. A farmer divided 1540 A. 3 R. 20 P. into 20 lots: how much land in each lot?

11. A man walks 35 mi. 1 fur. in 8 hours: how far did he walk in 1 hour?

12. A vessel sails 155° 10' 10" in 26 days: what distance does it sail each day?

13. A dozen silver spoons weigh 6 oz. 4 pwt.: what is the weight of one spoon?

14. A man cut 25 C. 108 cu. ft. of wood in 12 days: how much did he cut in one day?

15. The weight of ten boxes of books was 2 T. 15 cwt. 2 qr. 15 lb.: what the weight of each?

16. A vintner put a hogshead of wine in 144 bottles: how much in each bottle?

17. A barrel of flour was divided among 16 persons: how much did each receive?

18. A farm of 364 A. 2 R. 36 P. was divided equally among 6 children: how much did each receive?

19. If 43 29 12 gr. was divided into 29 equal doses, what was the weight of each?

20. How many castings weighing 2 qr. 17 lb. 4 dr. each can be made from 16 cwt. 8 lb. 6 oz. of iron?

82. PROMISCUOUS EXAMPLES.

1. A farmer sold 158 bu. 2 pk. of rye, 1040 pk. of corn, 197 bu. 1 pk. 5 qt. of wheat: how much grain did he sell?

2. A man owning 1040 A. 2 R. of land, sold 998 A 23 P.: how much had he left?

3. A has 57 bu. 1 pk. 3 qt. of oats, B has 6 times as much: how much have both?

4. If a locomotive runs 210 mi. 3 fur. 36 rd. in 9 hours, how far will it run in one hour?

5. What is the weight of 154 hhd. of sugar, each weighing 11 cwt. 3 qr. 16 lb. ?

6. A man bought 165 firkins of butter, each containing 56 lb., at 38 cents a pound: what was the cost? 7. Reduce 3 wk. 5 da. 41 sec. to seconds.

8. A man owns 156 A. 2 R. 10 P. of land, which he divides into lots, each containing 6 A. 1 R. 2 P.: how many lots are there?

9. A grocer buys 9 hhd. of molasses at 42 cents, and sells it for 51 cents a gal.: how much does he gain?

10. What cost 172 bags of coffee, each weighing 78 lb., at 32 cents a lb.?

11. How much silver will it take to make six dozen spoons, each spoon weighing 10 pwt. 14 gr.?

12. A farmer raised 1045 bu. of potatoes, which he placed in 418 barrels: how many in each barrel? 13. Reduce 14500 pints to gallons.

14. How many times will a wheel, 18 ft. 4 in. in circumference, turn in going 15 miles?

15. How many cubic feet in a block of marble 14 ft. long, 6 ft. wide, and 3 ft. high?

16. A boy lives 2 fur. 25 rd. from school, which he attends twice a day, five days in a week: how far will he travel in attending school 4 weeks?

17. How many rods of hedge are required to surround a field 2 miles square?

18. How long will 112 bu. of oats last a horse that eats 7 qt. a day?

19. At the rate of $6.50 per cord, what is the value of a pile of wood 18 ft. long, 4 ft. wide, and 16 ft. high?

20. How long will 3 barrels of flour last a family that uses 24 lb. 8 oz. a week?

21. A vintner had 2 hhd. 23 gal. 2 qt. of wine; he sold one-half of it at 4 cents a pint: how much did it bring?

22. How many stoves, each weighing 1 cwt. 1 qr. 11 lb. can be made from 17 pigs of cast iron, each weighing 1 cwt. 1 qr. 3 lb. ?

23. In a mass of ore weighing 47 lb. 8 oz. 12 pwt., one-half is silver, 1 lb. 6 oz. 8 pwt. is gold, and the rest consists of refuse: what is the weight of the refuse?

24. How many minutes in the first three months of the year 1864?

25. Five silver vases of the same size were sold for $456.75, at 35 cents a pwt.: what was the weight of each?

26. A jeweler has gold enough to make 90 rings, each weighing 8 pwt. 16 gr.: how many rings can he make, if he makes each 1 pwt. 2 gr. heavier?

27. A travels 4 mi. 3 fur. 7 rd. less per day than B, who travels 89 mi. 4 fur. 30 rd. in 10 days: how far will A travel, while B is traveling 44 mi. 6 fur. 15 rd.?