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next higher; set down the remainder, and carry the quotient to the next product, as in addition of compound numbers. (Art. 168.)

OBS. 1. When the multiplier is a composite number, it is advisable to multiply first by one factor and that product by the other. (Art. 57.) 2. The process of multiplying different denominations is called Compound Multiplication.

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3. What will 5 horses cost, at £25, 10s. 6d. apiece? 4. A colony of 6 persons agreed to pay £31, 5s. 8d. apiece for their passage from Hamburg to New York: what was the expense of their passage?

5. What cost 9 yards of cloth, at 18s. 93d. per yard? 6. What cost 6 pipes of wine, at £9, 7s. 8d. apiece? 7. What cost 8 cows, at £5, 10s. 6d. apiece?

8. In a solar year there are 365 days, 5 hrs. 48 min. 48 sec. how many days, hours, &c., has a person lived, who is 21 years old?

9. Bought 10 silver cups, each weighing 3 oz. 15 pwts. 10 grs. what is the weight of the whole?

10. What is the weight of 72 silver dollars, each weighing 17 pwts. 8 grs.?

11. Bought 7 loads of hay, each weighing 1 T. 3 cwt. 3 qrs. 12 lbs. what is the weight of the whole ?

12. What is the weight of 20 hogsheads of inolasses, each weighing 5 cwt. 3 qrs. 17 lbs. 10 oz.?

13. A man bought 9 oxen, weighing 1123 lbs. 15 oz. apiece what was the weight of the whole?

14. A grocer bought 11 casks of brandy, each containing 54 gals. 3 qts. I pt. 2 gills: how much did they all contain?

15. If a stage-coach goes at the rate of 5 m. 2 fur. 30 r. per hour, how far will it go in 10 hours?

16. If a Railroad car goes 21 m. 2 fur. 10 r. per hour, how far will it go in 10 hours?

17. Bought 12 pieces of broadcloth, each containing 27 yds. 1 qr. 2 na.: how many yards did all contain?

18 If a man mows 3 A. 35 sq. r. per day, how many acres can he mow in 30 days?

19. How many square yards of plastering will a house which has 9 rooms require, allowing 75 yds. 18 ft. to a

room?

20. A man bought 15 loads of wood, each containing 1 C. 33 ft. how many cords did he buy?

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21. A miller constructed 7 cubical bins for grain, each containing 216 feet 152 in.: what was the contents of the whole ?

22. If a ship sails 2° 25′ 10′′ per day, how far will she sail in 20 days?

23. Multiply 56°, 42' 11" by 32.

24. If a brewer sells 33 gals. 2 qts. 1 pt. of beer a day, how much will he sell in 24 days?

25. If a milk-man sells 40 gals. 3 qts. 1 pt. of milk per day, how much will he sell in 60 days?

26. What cost 82 tons of iron, at £4, 15s. 64d. per pound?

27. If 1 acre produce 33 bu. 2 pks. 5 qts. of wheat, how much will 100 acres produce?

28. If 1 suit of clothes requires 9 yds. 3 qrs. 2 na., how much will 500 suits require ?

29. If 1 mile of Railroad require 60 T. 5 cwt. 9 lbs. of iron, how much will 50 miles require ?

30. How much wheat will it require to make 1000 barrels of flour, allowing 4 bu. 2 pks. 6 qts. to a barrel?

DIVISION OF COMPOUND NUMBERS.

Ex. 1. Divide £17, 6s. 9d. by 4.

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quotient 4 under the pounds, and reduce the remainder £1 to shillings, which added to

the 6s., make 26s. 4 in 26s., 6 times and 2s. over.Set the quotient 6 under the shillings, and reduce the remainder 2s. to pence, which added to the 9d. make 33d. 4 in 33d., 8 times and 1d. over. Set the 8 under the pence, reduce the ld. to farthings, and divide as before. Ans. £4, 6s. 8d. 1 far.

173. 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. 78) If the divisor exceeds 12, but is not a composite number, long division may be einployed. (Art. 77.)

3. The process of dividing different denominations is called Compound Division.

QUEST.-173. 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? What is the process of dividing different denominations called?

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4. Divide £7, 8s. 2d. by 3.

5. Divide £35, 10s. 8d. 3 far. by 6.

6. Divide £42, 17s. 3d. 2 far. by 8.

7. A man bought 5 cows for £23, 16s. 8d.: how much did they cost apiece?

8. A merchant sold 10 rolls of carpeting for £62, 12s. 9d. how much was that per roll?

9. Paid £25, 10s. 64d. for 12 yards of broadcloth: what was that per yard?

10. A silversmith melted up 2 lbs. 8 oz. 10 pwts. of silver, which he made into 6 spoons: what was the weight of each ?

11. The weight of 8 silver tankards is 10 lbs. 5 oz. 7 pwts. 6 grs. what is the weight of each?

12. If a family of 8 persons consume 85 lbs. 12 oz. of meat in a month, how much is that apiece?

13. A dairywoman packed 95 lbs. 8 oz. of butter in 10 boxes: how much did each box contain?

16. A tailor had 76 yds. 2 qrs. 3 na. of cloth, out of which he made 8 cloaks: how much did each cloak con

17. A man traveled 49 m. 8 fur, 32 r. in 11 hours: at what rate did he travel per hour?

18. A man had 285 bu. 3 pks. 6 qts. of grain, which he wished to carry to market in 15 equal loads: how much must he carry at a load?

19. A man had 80 A. 45 r. of land, which he laid out into 36 equal lots: how much did each lot contain?

20. A farmer had 75 C. 92 ft. of wood, which he carried to market at 63 loads: how much did he carry at a load?

SECTION VIII.

DECIMAL FRACTIONS.

ART. 175. When any thing is divided into equal parts, those parts, we have seen, are called Fractions; (Art. 105;) also, that the parts take their name from the number of parts into which the thing is divided. Thus when any number or thing is divided into 10 equal parts, 1 of those parts is called one tenth; when divided into 100 equal parts, the parts are called hundredths; when divided into 1000 equal parts, the parts are called thousandths, &c. Now if 1 tenth is subdivided into ten equal parts, the parts will be hundredths, for 1-10= 16; (Art. 138;) if is subdivided into 10 equal parts, the parts will be thousandths, for 10-10-1000, &c. Hence it appears, that a tenth is ten times less than a unit; a hundredth, ten times less than a tenth; a thousandth, ten times less than a hundredth; a ten-thousandth, ten times less than a thousandth, &c.

176. The class of fractions which arise from dividing a unit into ten equal parts, then subdividing each of

QUEST. 175. What are fractions? From what do the parts take their name? 176. What are decimal fractions? Why called decimals?

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