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Note. To multiply by 10, 100, &c., is simply annexing as many ciphers to the multiplicand, as there are ciphers in the multiplier. (Art. 59.) Hence,

208. To reduce dollars to cents, annex two ciphers. To reduce dollars to mills, annex three ciphers.

To reduce cents to mills, annex one cipher.

OBS. To reduce dollars and cents to cents, erase the sign of dollars and the separatrix. Thus, $25.36 reduced to cents, becomes 2536

cents.

4. In $5, how many cents?
5. How many mills in $364?
6. How many mills in $621 ?
7. How many cents in $6245 ?
8. Reduce $75.26 to cents.
9. Reduce $625.48 to cents.

CASE II.

10. In 4500 cents, how many dollars?

Suggestion. Since 100 cents make 1 dollar, 4500 cents will make as many dollars as 100 is contained times in 4500. And 4500÷100=45. Ans. $45.

11. In 150 mills, how many cents? Ans. 15 cents. 12. In 25000 mills, how many dollars? Ans. $25.

Note.—To divide by 10, 100, &c., is simply cutting off as many figures from the right of the dividend as there are ciphers in the divisor. (Art. 80.) Hence,

209. To reduce cents to dollars, cut off two figures on the right.

To reduce mills to dollars, cut off three figures on the right.

To reduce mills to cents, cut off one figure on the right.

OBS. The figures cut off are cents and mills.

QUEST.-208. How are dollars reduced to cents? Dollars to mills? Cents to mills? Obs. Dollars and cents to cents? 209. How are cents reduced to dollars? Mills to dollars? Mills to cents? Obs. What are the figures cut off?

13. In 325 cents, how many dollars? Ans. $3.25. 14. In 423 mills, how many cents? Ans. 42c. 3m. 15. In 4320 mills, how many dollars?

16. How many dollars in 63500 cents? 17. How many cents in 4890 mills?

210. Since Federal Money is expressed according to the decimal system of notation, it is evident that it may be subjected to the same operations and treated in the same manner as decimal fractions.

ADDITION OF FEDERAL MONEY.

Ex. 1. A man bought a cow for $15.75, a calf for $2.375, a sheep for $3.875, and a load of hay for $8.68: how much did he pay for all?

Operation.

15.75

2.375

3.875 8.68

$30.680 Ans.

We write the dollars under dollars, cents under cents, &c. Then add each column separately, and point off as many figures for cents and mills, in the amount, as there are places of cents and mills in either of the given numbers.

211. Hence, we derive the following

GENERAL RULE.

Write dollars under dollars, cents under cents, &c., so that the same orders or denominations may stand under each other. Add each column separately, and point off the amount as in addition of decimal fractions. (Art. 187.)

OBS. If either of the given numbers have no cents expressed, it is customary to supply their place by ciphers.

2. A farmer sold a firkin of butter for $9.28, a cheese for $1.17, a quarter of veal for 56 cents, and a bushel of wheat for $1.12: how much did he receive for the whole ?

QUEST.-211. How is Federal Money added? How point off the amount? Obs. When any of the given numbers have no cents expressed, how is their place supplied?

3. A man bought a hat for $5.375, a cloak for $35.68, and a pair of boots for $4.75: how much did he pay for all? 4. What is the sum of $37.565, $85.20, $90.03, and $150.638 ?

5. What is the sum of $10.385, $46.238, $190.62, and $23.036 ?

6. What is the sum of $23.005, $16.03, $110.738, and $131.26?

7. What is the sum of 63 dolls. and 4 cts., 86 dolls. and 10 cts., and 47 dolls. and 37 cts.?

8. What is the sum of $608.05, $365.205, $2.268, and $47.006 ?

9. What is the amount of 11 dolls. 3 cts. and 5 mills, 16 dolls. and 8 mills, 49 dolls. 7 cts. and 8 mills?

10. What is the amount of 100 dolls. and 61 cts., 51 dolls. and 3 cts., 65 dolls. 8 cts. and 3 mills?

11. What is the amount of 95 dolls. 67 cts. and 8 mills, 120 dolls. 45 cts., 101 dolls. 7 cts. and 9 mills ?

12. A lady bought a bonnet for $6.67, a pair of gloves for $0.625, a pair of shell combs for $0.75, and a cap for $2.50 what was the amount of her bill?

SUBTRACTION OF FEDERAL MONEY.

Ex. 1. A man bought a horse for $56.50, and a cow for $23.38: how much more did he pay for his horse than his cow?

Operation.

$56.50

23.38

$33.12 Ans.

We write the less number under the greater, placing dollars under dollars, &c., then subtract, and point off the answer as in subtraction of decimals.

212. Hence, we derive the following

GENERAL RULE.

Write the less number under the greater, with dollars under dollars, cents under cents, &c., then subtract, and point off the remainder as in subtraction of decimal fractions. (Art. 189.)

OBS. If either of the given numbers have no cents expressed, it is customary to supply their places by ciphers.

2. A man owing $57.35, paid $17.93: how much does he still owe? Ans. $39.42. 3. A grocer bought two hogsheads of molasses for $68.90, and sold it for $79.26: how much did he gain by the bargain?

4. A man owed a debt of $105, and paid all but $23. 67: how many dollars did he pay ?

5. A merchant bought a quantity of silks for $237.63, and sold it for $196.03: how much did he lose?

6. A drover bought a flock of sheep for $357, and sold them for $17.33 less than he paid for them: how much did he sell them for?

7. What is the difference between 365 dolls. 7 cts. and 208 dolls. 20 cts. ?

8. From 1 cent subtract 6 mills.

9. From 1 dollar, 6 cts. and 7 mills, take 89 cts. and 3 mills.

10. From 96 dollars, 6 cents, take 41 dolls., 63 cents, and 8 mills.

11. From 100 dollars, 10 cents, and 3 mills, take 1 cent and 5 mills.

12. From 1000 dollars, 6 cents, take 100 dolls. and 5 mills.

MULTIPLICATION OF FEDERAL MONEY.

213. In Multiplication of Federal Money, as well as in simple numbers, one of the given factors must always be considered as an abstract number. (Art. 45. Obs. 2.)

Ex. 1. How much will 5 yards of cloth cost, at $1.75 per yard?

QUEST.-212. How is Federal Money subtracted? How point off the remainder? Obs. When either of the given numbers have no cents expressed, how is their place supplied? 213. In Multiplication of Federal Money, what must one of the given factors be considered?

Operation.
$1.75
5

$8.75 Ans.

If 1 yard costs $1.75, 5 yards will obviously cost 5 times as much. Hence, we multiply the price of 1 yard by the number of yards, and point off two figures for decimals in the product. (Art. 191.)

2. How much will 15.8 yards of fringe cost, at 12 cents per yard?

Operation.

15.8
.12

Reasoning as before, 15.8 yards will cost 15.8 times 12 cents. But in performing the multiplication, it is more convenient to make the 12 cents the multiplier, and the result will be the same as if it was placed for the multiplicand. (Art. 47.) Point off the product as before.

$1.89 6

214. Hence, when the price of one article, one pound, one yard, &c., is given, to find the cost of any number of articles, pounds, yards, &c.

Multiply the price of one article and the number of articles together, and point off the product as in multiplication of decimals. (Art. 191.)

3. Multiply $45.035 by 6.2. Ans. $279.217.

215. From the preceding illustrations we derive the following

GENERAL RULE.

Multiply as in simple numbers, and point off the product as in multiplication of decimal fractions. (Art. 191.)

OBS. 1. When the price or the quantity contains a common fraction, the fraction should be changed to a common decimal. (Art. 197.) 2. In business operations, when the mills in the answer are 5, or over, it is customary to call them a cent; when under 5, they are disregarded.

QUEST.-214. When the price of 1 article, 1 pound, &c., is given, how is the cost of any number of articles found? 215. What is the rule for Multiplication of Federal Money? Obs. When the price or quantity contains a common fraction, what should be done with it?

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