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OPERATION 8. d.
f. 8. d. 1 ton sa
18 17 11,X3 = 5 6 13 9 = Value of 3 tons.
10 10 tons = 188 19 2,15 = 944 15 10 = Value of 50 tons
10 100 tons =
1889 11 8,X475 58 6 8 = Value of 400 tons
= Value of 453 tons.
Ans. 8 5 5 9 16 3 Since 453 is not a composite number, we cannot resolve it into factors; but we may separate it into parts, and find the value of each part separately: Thus, 453 400 + 50 + 3. In the operation, we first multiply by 10, and obtain the value of 10 tons, and this product we multiply by 10, and obtain the value of 100 tons. Then, to find the value of 400 tons, we multiply the last product by 4; and to find the value of 50 tons, we multiply the value of 10 tons by 5; and to find the value of 3 tons, we multiply the value of 1 ton by 3. Adding the several products, we obtain 8559£. 16s. 3d. for the answer. Hence,
Having resolved the multiplier into any convenient parts, as of units, tens, &c., multiply by these several parts, and add together the products thus obtained for the required result.
EXAMPLES. 2. Multiply 2hhd. 19gal. Oqt. 1 pt. by 39. 3. Multiply 3bu. 1pk. 4qt. lpt. Igi. by 53. 4. Multiply 16ch. 7bu. 2pk. Oqt. Opt. by 17. 5. What will 57 gallons of wine cost at 8s. 31d. per gallon ?
6. Bought 29 lots of wild land, each containing 117 A. 3 R. 27p. ; what were the contents of the whole ?
7. Bought 89 pieces of cloth, each containing 37yd. 3qr. 2na. 2in. ; what was the whole quantity ?
8. Bought 59 casks of wine, each containing 47gal. 3qt. 1pt.; what was the whole quantity ?
9. If a man travel 17m. 3fur. 13rd. 14ft. in one day, how far will he travel in a year?
10. If a man drink 3gal. 1qt. 1pt. of beer in a week, how much will he drink in 52 weeks ?
11. There are 17 sticks of timber, each containing 37ft. 978in.; what is the whole quantity ?
12. There are 17 piles of wood, each containing 7 cords 98 cubic feet; what is the whole quantity ?
DIVISION OF COMPOUND NUMBERS.
OPERATION. £. s.
150. Division of Compound Numbers is the process of dividing compound numbers into any proposed number of equal parts. Ex. 1. Divide 139£. 13s. 11d. 2far. equally between 5 per
Ans. 27£. 18s. 9d. 2far. Having divided 139£. by 5, we find
the quotient to be 27£., and 4£. re5) 13 9 13 11 2 maining. We place the quotient 272.
under the 139£., and the remainder 27 18 9 2
4£. reduced to shillings = 80s.; 80s.
+ the 13s. in the dividend 93s. 5 = 18s. and a remainder of 3s. We write the quotient 18s. under the shillings in the dividend ; and the remainder 3s. reduced to pence 36d. ; 36d. + 11d. in the dividend
47d.; 470. = 5 9d. and a remainder of 2d. We write the quotient 9d. under the pence in the dividend; and the remainder 2d. reduced to farthings 8far., + the 2far. in the dividend = 10far.; 10far. = 5
2far. The quotient 2far. we write under the farthings in the dividend; and thus find the answer to be 27£. 18s. 9d. 2far.
RULE. — Divide as in division of simple numbers, each denomination in its order, beginning with the highest.
If there be a remainder, reduce it to the next lower denomination, adding in the number already contained in the dividend of this denomination, if any, and divide as before.
PROOF. - The same as in simple numbers. NOTE. — When the divisor and dividend are both compound numbers, they must be reduced to the same denomination, and the division then is that of simple numbers.
Note. — The answers to the following examples are found in the corresponding numbers of examples in Multiplication of Compound Numbers.
10. Divide 54yd. 2qr. 3na. equally among 5 persons. 11. Divide 123tun 3hhd. 36gal. 3qt. by 7. 12. Divide 209hhd. 55gal. 3qt. Opt. lgi. by 7. 13. What is the value of 118bu. 1pk. 5qt. = 6 ? 14. What is the value of 110y. 343d. 3h. 41m. 12s. = 8? 15. Divide 149deg. 9m. 5fur. 13rd. 3yd. 1ft. by 9.
16. A man divides his farm of 214A. 3R. 12p. equally among his 9 sons; how much does each receive ?
17. If one man perform a certain piece of labor in 3d. 16h. 54m., how long would it take 12 men to perform the same work ?
18. A farmer has 29 bushels of oats which he wishes to put in 8 sacks; how much must each sack contain ?
151. When the divisor is a composite number, and none of its factors exceed 12.
Ex. 1. If 35 loads of coal weigh 72T. 14cwt. 2qr. 10lb., what will 1 load weigh?
We find the fac
tors of 35 to be 5 5) 7 2
14 2 10 weight of 35 loads. and 7. We there7) 14 10 3 17
fore divide the weight of 7 loads.
weight of 35 loads 2 1 2 6= weight of 1 load. by 5, and obtain
the weight of 7 loads; and the weight of 7 loads we divide by 7, and thus find the weight of 1 load. Hence, when the divisor is a composite number,
Divide by its factors succession.
2. If 90 hogsheads of sugar weigh 56T. 14cwt. 3qr. 15lb., what is the weight of 1 hogshead ?
3. What will be the price of 1 sheep, if 18 cost 5£. 4s. 3d. ? 4. If 21 yards of cloth cost 10£. 8s. 3d., what is the price of 1 yard ?
5. What is the value of 1 hat, when 22 cost 12£. 13s. Od. ?
6. When 96 shares of a certain stock are valued at 1290£. 4s. Od., what would be the cost of 1 share ?
7. If 120 spoons weigh 321b. 9oz. 15pwt., what does 1 weigh?
8. If a man in 1 month travels 746m. 5fur., how far does he go in 1 day?
9. If the earth revolves 15° on its axis in 1 hour, how far does it revolve in 1 minute ?
10. Divide 1275A. 2R. 16p. 22yd. 8ft. 32in. equally among 32 men.
11. If a man walk round the earth in 2y. 68d. 19h. 54m., how long would it take him to walk 1 degree, allowing 365 days to a year?
152. When the divisor is not a composite number, and exceeds 12, or when a composite number one of whose factors exceeds 12, the whole operation can be written, as in the following example.
Ex. 1. Divide 360£. 8s. 4d. by 173. Ans. 2£. 13. 8d.
We divide the pounds by 173, and obtain 2£. for the quotient, and 14£. remaining, which we reduce to shillings, and add the 8s., and again divide by 173, and obtain 1s. for the quotient. The remainder, 115s., we reduce to pence, and add the 4d., and again divide by 173, and obtain 8d. for the quotient. Thus, the method is the same as by general rule (Art. 150). By uniting the several quotients, we obtain 2£. 1s. 8d. for the answer.
173) 1 3 8 4 ( 8d.
1 3 84
2. Divide 89hhd. 52 gal. 3qt. 1pt. by 39.
5. If 57 gallons of wine cost 23£. 11s. 5d., what cost 1 gallon ?
6. Divide 3419A. 2R. 23p, by 29.
7. If 89 pieces of cloth contain 3375yd. 3qr. Ina. 0fin., how much does 1 piece contain ?
8. If 59 casks contain 44hhd. 52gal. 2qt. lpt. of wine, what are the contents of 1 cask ?
9. If a man travel in 1 year (365 days) 6357m. 5fur. 14rd. 11 ft., how far is that per day ?
10. When 175gal. 2qt. of beer are drunk in 52 weeks, how much is consumed in 1 week ?
11. When 17 sticks of timber measure 15T. 38ft. 1074in., how
many feet does 1 contain ? 12. Divide 132 cords 2ft. by 17. 13. Divide 697T. 18cwt. 3qr. 141b. by 146.
Ans. 4T. 15cwt. 2qr. 1011 lb. 14. Divide 916m. 3fur. 30rd. 10ft. 6in. by 47.
Ans. 19m. 3fur. 39rd. 13ft. 23 in. 15. Divide 718A. 3R. 37p. by 29. Ans. 24A. 3R. 63 3p. 16. Divide 815A. 1R. 17p. 200ft. by 87.
Ans. 9 A. 1 R. 19p. 1398&ft. 17. Divide 144A. 3R. 18p. 3yd. 1ft. 36in. by 11.
Ans. 13A. OR. 27p. 3yd. Oft. 45° in.
PRINCIPLES AND APPLICATIONS.
DIFFERENCE BETWEEN DATES.
153. To find the time between two different dates.
Ex. 1. What is the difference of time between May 16, 1819, and March 4, 1857 ?
Ans. 37y. Imo. 18d. Commencing with January, the first month in the
and counting the months and days in Min. 1 8 5 7 2 4
the later date up to March 4th, Sub. 1819 4 16 we find that 2mo, and 4d. have
elapsed. We therefore write the Rem. 37 9 18 numbers for subtraction as in the