DEFINITION AND RULE.

Art. 112. Compound Subtraction is the process of finding the difference between two compound numbers of the same kind.

Art. 113. RULE.-1. Write the subtrahend under the minuend, placing terms of the same denomination in the same column.

2. Beginning at the right, subtract each successive term of the subtrahend from the corresponding term of the minuend, and write the difference beneath.

3. If any term of the subtrahend be greater than the corresponding term of the minuend, add to the term of the minuend as many units of that denomination as equal one of the next higher, and from the sum subtract the term of the subtrahend, writing the difference beneath.

4. Add one to the next term of the subtrahend, and proceed as before.

NOTE. Instead of adding one to the next term of the subtrahend, one may be subtracted from the next term of the minuend.

LESSON III.

Multiplication of Compound Numbers.

1. Multiply 34 gal. 3 qt. 1 pt. by 9.

PROCESS.

34 gal. 3 qt. 1 pt. 9

313 gal. 3 qt. 1 pt.

Write the multiplier under the lowest denomination of the multiplicand. 9 times 1 pt. are 9 pt., equal to 4 qt. 1 pt. Write the 1 pt. under pints, and reserve the 4 qt.

to add to the product of quarts. 9 times 3 qt. are 27 qt., and 4 qt. added are 31 qt., equal to 7 gal. 3 qt. Write the 3 qt. under quarts, and reserve the 7 gal. to add to the product of gallons. times 34 gal. are 306 gal., and 7 gal. added are 313 gal. Hence, 9 times 34 gal. 3 qt. 1 pt. 313 gal. 3 qt. 1 pt.

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9

8. If a barrel of sugar weighs 2 cwt. 45 lb. 8 oz., how much will 6 barrels weigh?

9. How much gold will make a dozen rings, each weighing 7 pwt. 15 gr.?

10. If a pupil studies 4 h. 30 min. each day, how many hours will he study in 12 school weeks, of 5 days each?

11. If a ship sail 3° 25′ 33′′ in one day, how far will it sail in 15 days?

12. If one man can build 5 rd. 4 yd. 2 ft. of fence in a day, how many yards can 8 men build? 13. How much wheat in 12 bins, if each bin contains 50 bu. 2 pk. 5 qt.?

14. John's age is 7 yr. 9 mo. 16 d., which is one-fifth of the age of his father: how old is his father?

15. If a load of wood contains 6 cd. ft. 12 cu. ft., how much wood will 15 loads make?

16. If a family use 2 gal. 3 qt. 1 pt. of milk a week, how much will it use in a year?

17. How much hay is there in 6 stacks, each containing 4 T. 16 cwt. 70 lb.?

18. What is the distance round a square field, each side of which is 24 rd. 3 yd. 2 ft.?

19. If a printer uses 3 reams 15 quires 12 sheets of paper each day, how much paper will he use in 4 weeks, of 6 days each?

20. If a man walk 2 mi. 7 fur. 32 rd. an hour, how far will he walk in 12 hours?

21. A field contains 25 rows of corn. If each row yield 5 bu. 3 pk., how much corn will the field yield?

DEFINITION AND RULE.

Art. 114. Compound Multiplication is the process of taking a compound number a given number of times.

Art. 115. RULE.-1. Write the multiplier under the lowest denomination of the multiplicand.

2. Beginning at the right, multiply each term of the multiplicand in order, and reduce each product to the next higher denomination, writing the remainder under the term multiplied, and adding the quotient to the next product.

NOTE.-In both simple and compound multiplication the successive products are each divided by the number of units of their denomination, which equals one of the next higher denomination.

LESSON IV.

Division of Compound Numbers.

1. Divide 15 w. 6 d. 13 h. 12 min. by 12.

PROCESS.

12) 15 w. 6 d. 13 h. 12 min.
1 w. 2 d.
6 min.

7 h.

Write the divisor at the left of the dividend, as in simple division.of 15 w. = = 1 w. with 3 w. remaining. Write the 1 w.

under weeks. The 3 w. remaining equal 21 d., and 21 d.

8) 14 lb. 12 oz. 15 dr. 10) 53 yd. 2 ft. 8 in. 5) 52 A. 3 R. 30 P.

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6) 9cwt. 731b. 12oz. 11) 65w. 1d. 1h. 58min. 7) 14M. 53 63.

8. If a man sleep 52 h. 30 min. in a week, how long does he sleep, on an average, each day?

9. A man bought a stack of hay, containing 6 T. 19 cwt. 86 lb., and drew it home in 7 equal loads. How much hay did he draw at each load?

10. If a dozen silver spoons weigh 8 oz. 15 pwt., what is the weight of each spoon?

11. A farm of 345 A. 3 R. 24 P. was divided equally between 6 heirs: how much did each receive?

12. Five equal casks of vinegar contain 218 gal. 2 qt. how much vinegar in each cask?

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13. If a man can dig a ditch 36 rd. 4 yd. 2 ft. long in 8 days, how much can he dig in 1 day? 14. If 9 men can pave 22 sq. rd. 25 sq. yd. in a day, how much can 1 man pave in a day?

15. A ship sailed 48° 24′ 45′′ in 15 days: how far did it sail each day?

16. How many goblets can be made of 5 lb. 6 oz. 12 pwt. of silver, if each goblet weighs 7 oz. 8 pwt.?

17. How many bottles, holding 3 qt. 1 pt. each, can be filled from a cask containing 45 gallons?

18. How many baskets of peaches, containing

3 pk. 4 qt. each, will make 3 bushels?

19. How many lengths of fence, each 10 ft. 4 in., will make 28 rd. 3 ft. of fence?

20. How many castings, weighing 12 lb. 8 oz. each, can be made from 5 cwt. 50 lb. of iron?

21. How many times will a wagon wheel, 11 ft. 8 in. in circumference, turn round in going 2 mi. 4 fur.?