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COMPOUND

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elapsed in the given year. E. g., if the date is Feb. 22d, 1845, th write 1 in the place of months; because, it is said, 2 whole months elapsed in the year 1845. But it may be doubted whether this meth not lead to frequent mistakes.

Besides, it may be urged with equal reason, that 1 ought to be from the day of the month, and 1 from the year; for neither 22 whole 1845 whole years had elapsed at the time of the date, but the 22d day 1845th year were then passing. In this way, the subject, which in simple, becomes intricate and perplexing.

24. General Washington was born Feb. 22d, 1732, an Dec. 14th, 1799: how old was he?

25. The Independence of the United States was declared 4th, 1776: how long is it since ?

26. A note was given Aug. 25th, 1840, and paid Feb 1842 how long did it run?

27. The United States Exploring Expedition sailed from N on the 18th of Aug., 1838, and returned to New York on the of June, 1842: how long was the voyage?

COMPOUND MULTIPLICATION.

304. The process of multiplying numbers of different den inations, is called COMPOUND MULTIPLICATION.

Ex. 1. What will 6 cows cost, at £5, 2s. 73d. apiece?

Analysis. Since 1 cow costs £5, 2s. 7 d., 6 cows will cost 6 times as much. Beginning with the lowest denomination, 6 times 3 far. are 18 far., equal to 4d. and 2 far. over.

Set the

£

Operation.
S. d. far.

2 11 7 " 3

6

5

30" 15" 10" 2 Ar

6 times 7d. are 420 Set the 10d. under th

2 far. under the denomination multiplied and carry the 4d. to the next product. and 4d. make 46d., equal to 3s. and 10d. pence, and carry the 3s. to the next product. 6 times 2s. are 12s and 3s. make 15s. As the product 15s. does not make one in the next denomination, we set it under the column multiplied. Fi nally, 6 times £5 are £30. The answer is £30, 15s. 10d.

QUEST.-304. What is Compound Multiplication?

305. Hence, we deduce the following general

RULE FOR MULTIPLYING COMPOUND NUMBERS.

Multiply each denomination separately, beginning with the l and divide each product by that number which it takes of the d ination multiplied, to make ONE of the next higher; set dou remainder, and carry the quotient to the next product, as in ad of compound numbers. (Art. 300.)

OBS. 1. When the multiplier is a composite number, it is advisable to ply first by one factor and that product by the other. (Art. 97.)

2. Compound Multiplication is the same in principle as Simple Mult tion. In each we carry for that number which it takes of the order or d ination we are multiplying, to make one of the next higher order or de nation.

2. What will 28 horses cost, at £21, 3s. 74d. apiece?

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3. What cost 7 acres of land, at £35, 6s. 7d. per acre? 4. What cost 18 barrels of flour, at £1, 6s. 8d. per barre 5. A man bought 15 loads of hay, each weighing 1 T. 270 what was the weight of the whole?

6. Multiply 16 tons, 3 cwt. 10 lbs. by 25.

7. Multiply 12 lbs. 3 oz. 16 pwts. by 56.

8. If 1 dollar weighs 17 pwts. 42 grs., how much will 96 lars weigh?

9. Multiply 48 hhds. 15 gals. 2 qts. 1 pt. by 63.

10. Multiply 56 pipes, 1 hhd. 23 gals. by 100.

QUEST.-305. Where do you begin to multiply a compound number? What is with each product? Obs. When the multiplier is a compos'te number, how pro Does it differ from Simple Multiplication?

9

11. Bought 72 pieces of cloth, each containing 323 yards: how much did they all contain?

12. If 1 cloak requires 10 yds. 3 qrs., how muck will 500 cloaks require?

13. Multiply 175 miles, 7 fur. 18 rods by 84.

14. Multiply 40 leagues, 2 m. 5 fur. 15 r. by 50.

15. Multiply 149 bu. 12 qts. by 60.

16. Multiply 26 qrs. 7 bu. 3 pks. 5 qts. by 110. 17. Multiply 150 acres, 65 rods by 52.

18. Multiply 310 acres, 3 roods, 3 rods by 81. 19. Multiply 265 cu. ft. 10 in. by 93.

20. Multiply 148 cords, 29 ft. by 650.

21. Multiply 365 d. 5 hrs. 48 min. 48 sec. by 35.

22. Multiply 70 yrs. 6 mo. 3 wks. 5 d. by 17.

23. Multiply 75° 40' 21" by 210.

24. If a ship sails 3° 24′ 10′′ per day, how far will she sail in 60 days?

25. If 1 acre produce 45 bu. 26 qts., how much will 100 acres produce?

26. If 1 barrel of flour requires 4 bu. 3 pks. 5 qts. of wheat, how much will 500 barrels require ?

27. What cost a chest of tea containing 17 lbs., at 6s. 10 d. per pound?

28. What is the duty on 1000 gals. of brandy, at 13s. 7d. per gallon?

29. What is the duty on 10560 lbs. of sugar, at 6d. 3 far. per pound?

30. What is the duty on 1500 yards of broadcloth, at 6s. 91d. per yd.?

31. If 1 load of wood measures 117 ft. 110 in., how much will 40 loads of the same size measure?

32. If 1 quarter of beef weighs 216 lbs. 7 oz., how much will 4 quarters weigh?

33. If 1 bushel of salt weighs 72 lbs. 10 oz., how much will 350 bushels weigh?

34. If 1 cask of oil contains 86 gals. 2 qts. 1 pt., how much wil 100 casks of the same size contain?

COMPOUND DIVISION.

306. The process of dividing numbers of different denominations, is called COMPOUND DIVISION.

Ex. 1. Divide £25, 3s. 4d. 2 far. by 6.

£

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Operation.
S. d. far.

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6)25 3 4 "1 2

4 3 " 10" 3 Ans.

Beginning with the pounds, we find

6 is contained in £25, 4 times and 1 over. Set the 4 under the pounds, and reduce the remainder £1 to shillings, which added to the 3s. make 23s. 6 in 23s. 3 times and 5s. over. Set the 3 under the shillings, and reduce the remainder 5s. to pence, which added to the 4d. make 64d. 6 in 64d., 10 times and 4d. over. Set the 10 under the pence, reduce the 4d. to farthings, and divide as before. Ans. £4, 3s. 10d. 3 far.

307. Hence, we deduce the following general

RULE FOR DIVIDING COMPOUND NUMBERS.

Begin with the highest denomination, and divide each separately. Reduce the remainder, if any, to the next lower denomination, to which add the number of that denomination contained in the given example, and divide the sum as before. Proceed in this manner through all the denominations.

OBS. 1. Each partial quotient will be of the same denomination, as that part of the dividend from which it arose.

2. When the divisor exceeds 12, and is a composite number, it is advisable to divide first by one factor and that quotient by the other. (Art. 129.) If the divisor exceeds 12, but is not a composite number, long division may be employed. (Art. 120. II.)

3. Compound Division is the same in principle, as Simple Division. Prefixing the remainder to the next figure of the dividend in simple division, is the same as reducing it to the next lower order or denomination, and adding the next figure to it.

QUEST.-306. What is Compound Division? 307. Where do you begin to divide a compound number? What is done with the remainder? Obs. Of what denomination is each partial quotient? When the divisor is a composite number, how proceed? Does it differ from Simple Division ?

2. A man wished to divide 75 cwt. 2 qrs. 10 lbs. of beef equally among 35 families: how much could he give to each?

Operation. cwt. qrs. lbs.

7)75" 2" 10

5)10 3 5

2 11 0" 16 Ans.

We divide by the factors of 35, which are 7 and 5, and set down each result as above.

3. Divide 312 lbs. 9 oz. 18 pwts. by 43.

Ans. 7 lbs. 3 oz. 6 pwts.

4. Divide 410 lbs. 4 oz. 5 pwts. 6 grs. by 8.

5. Divide 786 bu. 18 qts. by 25.

6. A farmer raised 1000 bu. 3 pks. 16 qts. of wheat on 40 acres: how much was that per acre?

7. A man bought 10 horses for £200, 15s.: how much did he give apiece?

8. Divide £87, 10s. 74d. by 18.

9. A merchant tailor put 216 yds. 3 qrs. of cloth into 20 cloaks: how much cloth did each cloak contain?

10. Divide 500 yds. 3 qrs. 2 na. by 54.

11. A man traveled 1000 miles in 12 days: at what rate did

he travel per day?

12. Divide 1500 m. 2 fur. 30 r. 12 ft. by 7.

13. Divide 120 gals. 3 qts. 1 pt. by 72.

14. Divide 400 hhds. 10 gals. 2 qts. 1 pt. by 9.

15. Divide 365 d. 10 hr. 40 min. by 15.

16. Divide 111 yrs. 20 d. 13 hrs. 25 min. 10 sec. by 11.

17. Divide 45° 17′ 10′′ by 25.

18. Divide 65 signs 12° 47′ by 41.

19. Divide 164 cords, 30 ft. by 17.

20. Divide 410 cords, 10 ft. 21 in. by 61.

21. If a chest of tea weighing 96 pounds cost £33, what will 1 pound cost?

22. If the duty on a pipe of wine is £50, 6s. 6d., what is the duty per gallon?

23. If a person spends £200 a year, what are his expenses per day?

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