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cost would he one quarter () as many dollars as there are yards, 4848 :
= $1212. When one quantity is contained in another exactly 2, 3, 4, 5, &c. times, it is called an aliquot or even part of that quantity; thus, 25 cents is an aliquot part of a dollar, hecause 4 times 25 cents is just equal to 1 dollar ; and 6 pence is an aliquot part of a shilling, because 2 times 6 pence just make 1 shilling. The following table exhibits sume of the aliquot parts of a dollar :
From the illustration of the last example, Cls
it appears, that, when the price per yard, 50 - of a dollar. pound, &c. is one of these aliquot parts of a 33}=\ of a dollar. dollar, the cost may be found by dividing 25 - of a dollar. the given number of yards, pounds, &c. by 20
} of a dollar. that number which it takes of the price to 12}= of a dollar.
make 1 dollar. If the price be 50 cents, we 64=
divide by 2; if 25 cts. by 4; if 123 cts. by To of a dollar. 5
20 * This manner of calculating the cost of articles, by taking aliquot parts, is usually called Practice.
11. What is the value of 14756 yards of cotton cloth, at 125 cents, or of a dollar per yard ? By practice.
By multiplication. 8)14756
'125 Ans. $1844'50
73780 29512 14756
Fb of a dollar.
$1844'500 Ans, as before. 12. What is the cost of 18745 pounds of tea, at $'50, = $ dollar, per pound?
Ans. $9372'50. 13. What is the value of 9366 bushels of potatoes, at 33} cents, or of a dollar, per bushel ?
9366 = $3122 Ans. 14. What is the value of 48240 pounds of cheese, at $064, = it of a dollar, per pound?
Ans.$3015. 15. What cost 4870 oranges, at 5 cents, = of a dollar, apiece ?
Ans. $243'50. 16. What is the value of 151020 bushels of apples, at 20 cents, - $ of a dollar, per bushel ?
Ans. $30204. 17. What will 264 pounds of butter cost, at 12} cents per pound ?
Ans. $33. 18. What cost 3740 yards of cloth, at $1625 per yard ?
4)$3740 = cost at $1' per yard.
935 = cost at $ '25 per yard. Ans. $4675 cost at $1625 per yard.
19. What is the cost of 8460 hats, at $1'12$ apiece ?.
at #1'50 apiece ? -at $3620 apiece? at $4'06ļ apiece ?
Ans. $9517'50. $12690. $27072. $3436875. 1 30. To find the value of articles sold by the 100, or 1000. 1. What is the value of 865 feet of timber, at $5 per hundred ?
Were the price $5 per 865
foot, it is plain, the value 5
would be 865 X 85 =
$4325; but the price is $5 $4325 = value at $5 per foot. for 100 feet; conseqnently,
$4325 is 100 times the true value of the timber; and therefore, if we divide this number (84325) hy 100, we shall obtain the true value; but to divide by 100 is but to cut off the two right hand figures, or, in federal money, to remove the separatrix two figures to the left.
Ans, $43,25. It is evident, that, were the price so much per thousand, the same remarks would apply, with the exception of cutting off three-figures instead of two. Hence we derive the general Rule for finding the value of articles sold by the 100, or 1000 :- Multiply the number ny the price, and, if it be reckoned by the 100, cut off the two right hand figures, and the product will be the answer, in the same kind of denomination as the price. If the article be reckoned by the 1000, tut off the three right hand figures.
EXAMPLES FOR PRACTICE. 2. What is the value of 4250 feet of hoards, at $14 per 1000 ?
Ans. 59 dollars and 50 cents. OPERATION.
In this example, because the price is at so much 17000
per 1000 feet, we divide by 1000, or cut off three 4250
Ans. 58-187. 6. What will 38600 bricks cost, at $4675 per
1000 ? 7. What will 46590 feet of boards cost, at $10ʻ625 per 1000 ? 8. What will 75 feet of timber cost, at $4 per 100 ? 9. What is the value of 4000 bricks, at 3 dolars per 1000 ?
DIVISION OF FEDERAL MONEY.
1 31. 1. If 3 yards of cloth cost $5'25, what is that a yard?
$5-25 is 525 cents, which 3)5625
divided by 3, the quottente is
175 cents, which, reduced to Answer, 175 cents, $1,75. dollars, is $1,75, the answer.
2. Bought 4 bushels of corn for $3 ; what was that a bushel ?
4 is not contained in 3 ; we may, however, reduce the $3 to cents, by annexing two ciphers, thus : OPERATION. 4)3600
300 cents divided by 4, the quotient is 75
cents, the price of each bushel of corn. Ans. *75 cents.
3. Bought 18 gallons of brandy, for $4275; what did it cost a gallon ?
18)4275(2375 mills, = $2'375, the answer. 36
$4275 is 4275 cents. After bringing down 67
the last figure in the dividend, and dividing, 54
there is a remainder of 9 cents, which, hy
annexing a cipher, is reduced to mills, (90,) 135
in which the divisor is contained 5 times, 126
which is 5 mills, and there is no remainder.
Or, we might have reduced $4275 to mills, 90
before dividing, hy ånnexing a cipher, 42750 90
mills, which, divided by 18, would have given the same result, 2375 mills, which, re
duced to dollars, is $2'375, the answer. 4. Divide $59-387 by 8.
Quotient, 7'423, that is, 7 dollars, 42 cents, 3 mills, and s of another mill. The is the remainder, after the last division, written over the divisor, and expresses such fractional part of another mill. For all purposes of business, it will be sufficiently exact to carry the quotient only to mills, as the parts of a mill are of so little value as to be disregarded. Sometimes the sign of addition (+) is annexed, to show that there is a remainder, thus, $7*423 +.
RULE. From the foregoing examples, it appears, that division of federal moneyaloes not differ from division of simple numbers. The quotient ivill be the answer in the lowest denomination in the given sum, which may then be reduced to dollars.
Note. If the sum to be divided contain only dollars, or dollars and cents, it may be reduced to mills, by annexing ciphers before dividing; or, we may first divide, annexing ciphers to the remainder, if there shall be any, till it shall be reduced to mills, and the result will be the same.
EXAMPLES FOR PRACTICE. 5. If I pay $46875 for 750 pounds of wool, what is the value of 1 pound?
Ans. $0ʻ625 ; or thus, $0,62). 6. If a piece of cloth, measuring 125 yards, cost $181625, what is Chat a yard ?
7. If 536 quintals of fish cost $1913'52, how much is that a quintal ?
Ans. $3'57. 8. Bought a farm, containing 84 acres, for $3213; what did it cost me per acre ?
Ans. 833'25. 9. At $954 for 3816 yards of flannel, what is that a yard ?
Ans. $0'25. 10. Bought 72 pounds of raisins for $8; what was that a pound ? = how much?
Ans. $0ʻ111f; or, $0.:: t. 11. Divide $12 into 200 equal parts; how much is one of the parts ? how much?
Ans. $0ʻ06. 200 12. Divide $30 hy 750. 33 : how much ? 13. Divide $60 by 1200. To = how much ? 14. Divide $215 into 86 equal parts; how much will one of the
= how much? 15. Divide $176 equally among 250 men; how much will each man receive ?
parts be ?
SUPPLEMENT TO FEDERAL MONEY.
QUESTIONS. 1. What is understood by simple numbers ?. 2. by compound numhers ? 3. by different denominations ? 4. What is federal money? 5. What are the denominations used in federal money ? 6. How are dollars distinguished from cents ? 7. Why are two places assigned for cents, while only one place is assigned for mills? 8. To what does the relative value of mills, cents, and dollars correspond ? 9. How are mills reduced to dollars ? 10.
to cents ? 11. Why? 12. How are dollars reduced to cents ? 13. to mills? 14. Why? 15. How is the addition of federal money performed ? 16. subtraction ? 17. multiplication ?' 18. division ? 19. Of what name is the product in multiplication, and the quotient in division? 20. In case dollars only are given to be divided, what is to be done? 21. When is one number or quantity said to be an aliquot part of another? 22. What are some of the aliquot parts of a dollar? 23. When the price is an aliquot part of a dollar, how may the cost be found ? 24. What is this manner of operating called? 25. How do you find the cost of articles sold hy the 100 or 1000 ?
EXERCISES. 1. Bought 23 firkins of hutter, each containing 42 pounds, for 165 cents a pound; what would that be a firkin, and how much for the whole?
Ans. $159'39 for the whole. 2. A man killed a beef, which he sold as follows, viz. the hind quarters, weighing 129 pounds each, for 5 cents a pound; the fore quarters, one weighing 123 pounds, and the other 125 pounds, for 44 cents a pound; the hide and tallow, weighing 163 pounds, for 7 cents a pound; to what did the whole ainount? Ans. 35'47.
3. A farmer bought 25 pounds of clover seed at ll cents a polind,
3 pecks of herdsgrass seed for $2'25, a barrel of four for $6'50, 1 pounds of sugar at 12} cents a pound; for which he paid 3 cheeses each weighing 27 pounds, at 81 cents a pound, and 5 barrels of cider at $1625 a barrel. The balance between the articles bought and sold is 1 cent; is it for, or against the farmer?
4. A man dies, leaving an estate of $71600; there are demande against the estate, amounting to $39876'74 ; the residue is to be divided between 7 sons; what will each one receive?
5. How much coffee, at 25 cents a pound, may be had for 100 bushels of rye, at 87 cents a bushel ?
Ans. 348 pounds. 6. At 12 cents a pound, what must be paid for 3 boxes of sugar, each containing 126 pounds ?
7. If 650 men receive $86675 each, what will they all receive ?
8. A merchant sold 275 pounds of iron, at 64 cents a pound, and took his pay in oats, at $0$50 a bushel; how many bushels díd he receive?
9. How many yards of cloth, at $4'66 a yard, must be given for 18 barrels of flour, at $9'32 a barrel ?
10. What is the price of three pieces of cloth, the first containing 16 yards, at $3$75 a yard; the second, 21 yards, at $450 a yard: and the third, 35 yards, at $5ʻ125 a yard ?
1 32. It is usual, when goods are sold, for the seller to deliver to the buyer, with the goods, a bill of the articles and their prices with the amount cast up. Such bills are sometimes called bills of parcels.
Boston, January 6, 1827. Mr. Abel Atlas
Bouglu of Benj. Burdett 125 yards figured Satin, at $250 a yard,
$31'25 8. sprigged Tabby,. 1-25
Salem, June 4, 1827. Mr. James Paywell
Bought of Simeon Thrifty 3 hogsheads New Rum, 118 gal. each, at $0‘31a gal. 2 pipes French Brandy, 126 and 132 gal. . 1'12}. i hogshead brown Sugar, 94 cwt.
10'34 cwt. 3 casks of Rice, 2 cwt. I qr. 17 lb. each, '05 5 hags Coffee, 15 lb. each,
(23 I chest hyson Tea, 86 lb.
"92 Received payment,
$706'521 For Simeon Thrifty,