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Note.-The parts, or fractions of a cent, used instead of mills, are expressed by two numbers, placed one above the other, with a line drawn between them. The under number denotes the part; and the upper one informs how many of that part are designed to be expressed: as,
one fourth; three fourths; one third ; two thirds ;
ADDITION OF FEDERAL MONEY.
Place the sums one under another, with dollars under dollars, and cents under cents, as in the following exam-ples: then, if there are no fractions, proceed in the same manner as in simple addition, observing to separate the cents of the amount from the dollars thereof, by placing a point between them. When fractions occur, find their amount in fourths;* consider how many cents these fourths will make : add them with the cents in the right hand column, and proceed as before directed.
Proof: as in Simple Addition. Note 1.-When sums are added, which consist of dollars only, their amount is dollars. When the sums consist of dollars and cents both, the two first right hand figures of their amount are cents, and all on the left of these are dollars. When the sums consist of cents only, their amount, if expressed by two figures, is cents; but if expressed by three or more figures, the two first figures on the right hand, are cents; and all on the left of these are dollars.
Note 2.-To find how many cents there are in any number of fourths of a cent, divide them by 4, and the quotient will be cents.
* In Addition, Subtraction, and Division of Federal Money, all fractions less than a fourth are omitted: and every fraction greater than a fourth is reckoned a half, three fourths, or a whole cent, according to its value: so that in these three operations no fractions are used excepting fourths—a half being counted two fourths. But in multiplication it is often material that no fraction be omitted, and that all fractions should be estimated at their real value.
8. Add the following sums; viz. 45 dollars; 156 dollars; 1000 dollars, and 750 dollars.
9. Add 48 dollars 20 cents; 14 dollars 58 cents; 100 dollars, and 500 dollars.
10. Add 4 cents; 10 cents; 55 cents; 15 cents; and 11 cents.
11. Add 12 cents; 18 cents; 561 cents ; 20 cents; 95 cents, and 42 cents.
APPLICATION. 1. Bought a hat for 4 dollars; a pair of shoes for 2 dollars 25 cents; a pair of stockings for 1 dollar 50 cents; and a pair of gloves for 75 cents. What is the cost of the whole ?
Ans. 8 dollars 50 cents. 2. Bought a Bible for 1 dollar; an English Reader for 75 cents; an Introduction for 50 cents; a slate for 314 cents; a slate pencil for ! cent; and a copy book for 123 cents. How much do they all amount to?
Ans. 2 dollars 69 cents. 3. Suppose I buy a barrel of sugar for 30 dollars 87} cents; a bag of coffee for 22 dollars 18 cents; and a bushel of salt for 1 dollax 12 cents : what sum must I pay for the whole ?
Ans. 54 dollars 183 cents. SUBTRACTION OF FEDERAL MONEY.
Place the less sum under the greater, with dollars under dollars, cents under cents, &c. as in the following examples: then if there are no fractions, proceed as in Simple Subtraction; observing to separate the dollars from the cents, in the remainder. If there is a fraction in the upper sum, and none in the lower, set it down as part of the remainder, and proceed as before directed. Y If there is a fraction in each of the sums, and the lower less than the upper, subtract the lower from the upper, and set down the difference. If there is a fraction in the lower sum, and none in the upper, subtract it from 4, and set down the difference: in this case there must be 1 added to the right hand figure of the cents, in the lower sum, before it is subtracted from the one above it. If there is a fraction in each of the sums, and the lower greater than the upper, subtract the lower from 4, add the difference to the upper, and set down the amount. In this case, as in the last, there must be 1 added to the right hand figure of the lower cents.
Proof: as in Simple Subtraction. Note.If both sums consist of dollars only, the remainder will be dollars. If both consist of cents only, the remainder will be cents. If either sum consist of dollars and cents both, the two first right hand figures of the remainder will be cents, and all on the left of these will be dollars.
13. Subtract 456 dollars from 1000 dollars.
APPLICATION. 1. Bought goods to the amount of 545 dollars 95 cents, and paid at the time of purchase, 350 dollars. How much remains to be paid ?
Ans. 195 dollars 95 cents. 2. A merchant bought a quantity of coffee, for which he paid 560 dollars. He afterwards sold it for 610 dollars 87 cents. How much did he gain by the transaction.
Ans. 50 dollars 87} cents. 3. If a storekeeper sell goods for 102 dollars, which cost-125 doilars 75 cents : how much will he lose by the sale ?
Ans. 23 dollars 75 cents. MULTIPLICATION OF FEDERAL MONEY.
Set the multiplier under the sum to be multiplied, as in the following examples: then, if there is no fraction, proceed as in Simple Multiplication ; observing to distinguish the cents from the dollars in the product. If there is a fraction in the sum, multiply it, and find how many cents are contained in its product: then multiply the cents of the sum, and add to their product the cents contained in the product of the fraction, and proceed as before directed. Or, if the multiplier exceed 12, multiply the sum omitting the fraction: then multiply the fraction, and add the number of cents contained in its product ta the product of the rest of the sum.
Proof: as in Simple Multiplication. Note.-To multiply a fraction of a cent, and find how many cents are contained in its product-multiply the upper number of the fraction, and divide its product by the under one, and the result will be the number of cents.
Note 2. When a sum is multiplied which consists of dollars only, its product is dollars. When the sum consists of dollars and cents
both, the two first right hand figures of its product are cents, and all on the left of these are dollars. When the sum consists of cents pnly, its amount, if expressed by two figures, is cents; but if expressed by three or more figures, the two first figures on the right hand are cents, and all on the left of these are dollars.
D. 8. Multiply 500 dols. by 4. Product 2000,00 9. 42 dols. 561 cts. by 3
127 , 683 10. 25 cts, by 3
75 11. 37 cts. by 5
1,871 12. 4 dols. 183 cts. by 12
50, 25 13. 10 dols. 33 cts. by 10
103, 33} 14. 5 dols. 661 cts. by 20
113, 333 29 dols. 38 cts. by 96
2820, 48 16.
102 dols. 19 cts. by 120 -12262 , 80 17. 31 dols. 171 cts. by208
6484 , 40 18. 25 dols. 183 cts. by 25
1. How much will 11 oranges come to, at 12 cents each.
Ans. I dol. 37 cts. 2. What will 10 loaves of bread come to, at 61 cents a loaf.
Ans. 624 cts. 3; What will 8 cords of wood amount to, at 4 dollars 50 cents a cord,
Ans. 36 dollars. 4. Sold 213 barrels of flour, for 6 dollars 25 cents per þarrel. What is the amount? Ans. 1331 dols. 25 cțs.
5. Bought 308 pounds of coffee at 21 cents a pound, What is the amount?
Ans. 64 dols. 68 cts. 6. How much will 132 pieces of linen come to, at 17 dollars 37_cents each?'
Ans, 2293 dols. 50 cts: