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6. Add the following sums, $ 18.165, $ 701.63, $ 151.161, $375.089, and $ 471.017.

Ans. $ 1717.062. 7. Bought a horse for eighty-seven dollars nine cents, a pair of oxen for sixty-five dollars twenty cents, and six gallons of molasses for two dollars six cents five mills; what was the amount of

my
bill ?

Ans. $ 154.355. 8. Sold a calf for three dollars eight cents, a bushel of corn for ninety-seven cents five mills, and three bushels of

rye

for three dollars five cents; what was the amount received ?

Ans. $ 7.105.

SUBTRACTION OF UNITED STATES MONEY.

OPERATION.

cts. m.

109. Ex. 1. · From 106 dollars 7 cents 7 mills, take 92 dollars 83 cents 8 mills.

Ans. $ 13.239. We write the less number under the

greater, place mills under mills, cents under 1 0 6.0 77

cents, and dollars under dollars, and subtract 9 2.8 38 as in subtraction of simple numbers (Art. Ans. 1 3.2 3 9

50), and separate the dollars from the cents

in the answer by the decimal point. RULE. Write the several denominations of the subtrahend under the corresponding ones of the minuend.

Subtract as in subtraction of simple numbers, and place the decimal point directly under that above.

Proof. — The proof is the same as in subtraction of simple numbers.

EXAMPLES.
2.
3.
4.

5. $ cts. m.

cts. m. 8 7 1.1 61 47 8.4 77 1 6 7.1 6 3 1 6 3.1 67 8 9.9 18 1 9 9.9 91

9 8.0 9 7

9.0 9 8 78 1.2 4 3

cts. m.

cts. m.

6. Bought a farm for $ 1728.90, and sold it for $ 3786.98; what did I gain by my bargain?

7. Gave $ 79.25 for a horse, and $106.875 for a chaise, and sold them both for $ 200; what did I gain ?

8. Bought a farm for $ 8967, and sold it for nine thousand eight hundred seventy-six dollars seventy-five cents; what did I gain?

Ans. $ 909.75.

9. Bought a barrel of flour for $ 7.50, three bushels of rye for $ 2.75, and three cords of wood at $ 5.25 a cord; I sold the flour for $ 6.18, the rye for $ 3.00, and the wood for $ 6.75 a cord; what was gained by the bargain? Ans. $ 3.43.

10. A young lady went a “ shopping." Her father gave her a twenty-dollar bill. She purchased a dress for $8.16, a muff for $ 3.19, a pair of gloves for $ 1.12, a pair of shoes for $ 1.90, a fan for $0.19, and a bonnet for $ 3.08 ; how much money did she return to her father?

Ans. $ 2.36.

MULTIPLICATION OF UNITED STATES MONEY.

110. Ex. 1. What will 365 barrels of flour cost at $ 5.75 a barrel ?

Ans. $ 2098.75.

OPERATION.

$ 5.7 5

3 6 5 28 7 5 3 450 17 2 5 $ 2 0 9 8.7 5 Ans.

We multiply as in multiplication of simple numbers, and, obtaining the product in cents, the lowest denomination of the multiplicand, we reduce them to dollars by pointing off two places at the right for cents (Art. 107).

RULE. - Multiply as in multiplication of simple numbers.

The product will be in the lowest denomination in the multiplicand, which must be pointed off as in reduction of United States money.

Proof. — The proof is the same as in multiplication of simple numbers.

EXAMPLES. 2. What will 126 pounds of butter cost at 13 cents a pound ? 3. What will 63 pounds of tea cost at 93 cents a pound ?

4. What will 43 tons of hay cost at 13 dollars 75 cents a ton ?

Ans. $ 591.25. 5. If 1 pound of pork is worth 7 cents 3 mills, what are 46 pounds worth?

Ans. $ 3.358. 6. If i hundred of beef cost 3 dollars 28 cents, what are 76 hundred worth ?

7. What will 96 thousand feet of boards cost at 11 dollars 67 cents a thousand ?

Ans. $ 1120.32. 8. If a barrel of cider be sold for 2 dollars 12 cents, what will be the value of 169 barrels ?

Ans. $ 358.28.

9. What will be the value of a hogshead of wine, containing 63 gallons, at 1 dollar 63 cents a gallon ? Ans. $ 102.69.

10. Sold a sack of hops, weighing 396 pounds, at 11 cents 3 mills a pound; to what did it amount? Ans. $ 44.748.

11. Sold 19 cords of wood, at $ 5.75 a cord; to what did it amount ?

12. Sold 169 tons of timber, at $ 4.68 a ton; what did I receive?

13. Sold a hogshead of sugar, weighing 465 pounds; to what did it amount, at 14 cents a pound ?

Ans. $ 65.10. 14. What will be the amount of 789 pounds of leather at 18 cents a pound ?

Ans. $ 142.02. 15. What will be the expense of 846 pounds of sheet-lead at 5 cents 7 mills a pound ?

Ans. $ 48.222. 16. When potash is sold for $ 132.55 a ton, what will be the price of 369 tons ?

Ans. $ 48910.95. 17. What will 365 pounds of beeswax cost at 18 cents 4 mills a pound?

Ans. $ 67.16. 18. If 1 pound of tallow cost 7 cents 3 mills, what are 968 pounds worth?

Ans. $ 70.664.

DIVISION OF UNITED STATES MONEY.

111. Ex. 1. If 78 barrels of fish cost $ 303.42, what will 1 barrel cost ?

Ans. $ 3.89.

OPERATION.

78 ) $ 3 0 3.4 2 ( $ 3.8 9

2 3 4

694 6 2 4

We divide as in division of simple numbers, and point off as many places for cents in the quotient as there are for cents in the dividend.

702
7 02

RULE. Divide as in division of simple numbers.

The quotient will be in the lowest denomination of the dividend, which must be pointed off as in reduction of United States money.

Note. – When the dividend consists of dollars only, and is either smaller than the divisor or not divisible by it without a remainder, reduce it to a lower denomination by annexing two or three ciphers, as the case may require, and the quotient will be cents or mills accordingly.

When it is required to find the number of times one sum of money is contained in another, both sums, if of different denominations, must be reduced to the same, before dividing.

Proof. - The proof is the same as in division of simple numbers.

EXAMPLES. 2. Bought 11 chests of tea 3. How many yards of for $234.30. What did I give cloth at 9 cents a yard can a chest? Ans. $ 21.30. be bought for $28.89 ?

Ans. 321 yards.

OPERATION.

OPERATION.

11) $2 3 4.3 0

9 ) 2 8 8 9 Ans. $ 2 1.3 0

Ans.

321 yards. 4. When 19 bushels of fine salt can be bought for $30.87}, what costs one bushel ?

5. At 12 cents a pound, how many pounds of sugar can be bought for $51 ?

6. If 78 barrels of fish cost $303.42, what will one barrel cost?

7. Bought 42 bushels of pears for $73.50 ; what cost one bushel ?

Ans. $ 1.75. 8. How many yards of broadcloth at $ 2.75 a yard can be bought for $904.75 ?

Ans. 329 yards. 9. When rye is sold at the rate of 628 bushels for $ 471.00, what is that a bushel ?

Ans. $ 0.75. 10. If it should cost $ 1460 to support a family 365 days, what would be the expense a day?

Ans. $ 4. 11. How many gallons of oil at $ 1.621 a gallon can be bought for $ 234 ?

12. If 1624 pounds of pork cost $ 97.44, what cost one pound?

Ans. $ 0.06. 13. If 47 thousand shingles cost $ 176.25, what is the cost per thousand ?

Ans. $ 3.75. 14. Bought 148 tons of plaster of Paris for $ 337.44; what was it per ton ?

Ans. $ 2.28. 15. At $ 37.75 an acre, how many acres of land may be bought for $1774.25 ?

Ans. 47 acres. 16. At 67 cents a pound, how many chests of tea, each weighing 59 pounds, can be bought for $ 672.01 ? Ans. 17 chests.

17. How many bushels of wheat at $ 1.25 a bushel can be bought for $ 863.75 ?

Ans. 691 bushels.

18. Sold 169 tons of timber for $790.92 ; what cost one ton?

19. What cost one pound of leather, if 789 pounds cost $ 142.02 ?

20. If 369 tons of potash cost $ 48910.95, what will be the price of one ton ?

Ans. $ 132.55. 21. Bought 47 hogsheads of salt, each hogshead containing 7 bushels, for $ 368.48; what cost one bushel ? Ans. $ 1.12.

GENERAL PRINCIPLES AND APPLICATIONS.

112. ANALYSIS is an examination of a question by resolving it into its parts, in order to consider them separately, and thus, by reasoning from the nature of the question, to render each step in the solution plain and intelligible.

113. An aliquot part of any number or quantity is such a part as will exactly divide that number or quantity. Thus, 3 is an aliquot part of 6; and 4, an aliquot part of 16.

114. The method of performing operations by means of aliquot parts is called PRACTICE, or ANALYSIS by ALIQUOT PARTS.

115. In business calculations frequent use is made of the following

ALIQUOT PARTS OF A DOLLAR. 50 cents 1 of $1. 121 cents j of $ 1. 33} cents { of $ 1.

10 cents

To of $1. 25 cents of $1.

64 cents It of $ 1. 20 cents of $1.

5 cents

zb of $1.

PRACTICAL QUESTIONS BY ANALYSIS. 116. The price of a unit of any quantity being given, to find the cost of that quantity.

Ex. 1. If 1 barrel of flour cost $7, what will 125 barrels cost?

ANALYSIS. Since 1 barrel costs $ 7, 125 barrels will cost 125 times as much : $ 7 X 125 = $ 875.

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