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I LIX. TO REDUCE DECIMALS OF HIGHER DENOMINA

TIONS TO WHOLE NUMBERS OF LOWER DENOMINA-
TIONS.

This rule is the reverse of the last.
Let us take the answer to the first example. Reduce ,775£.
to whole numbers of lower denominations.

OPERATION,
£ ,775

In this example, ,775£. reduced 20 to shillings, that is, multiplied by

20, gives 15,5, (for ciphers on the 8. 15,500 right of a decimal are of no value ;) 12

then the decimal part ,5 x 12=

6,00=6d. Ans. 15 s. 6 d.
d. 6,000
Hence we derive the following

RULE.
Q. How do

you proceed?
A. Multiply the given decimal as in Reduc-
tion; that is, pounds by what makes a pound,
ounces by what makes an ounce, &c.

Q. How many places do you point off in each product for decimals ?

A. As many as there are decimal places in the given decimal.

Q. Where will you find the answer ?

A. The several denominations on the left hand of the decimal points will be the answer.

More Exercises for the Slate. The following examples are formed by taking the answers in the last rule; of course, the answers in this may be found in the examples of that. The examples in each are numbered so as to correspond.

2. Reduce ,378125£. to whole numbers of lower denomina tions. (For Ans, see ex. No. 2, 1 LVIII.)

3. What is the value of ,25 of a pound?
4. What is the value of ,003125 of a pound ?
5. What is the value of ,6875 of a yard ?
6. What is the value of ,375 of a dollar ?
7. What is the value of ,9375 of a yard ?
8. What is the value of 7375 of a pound Troy?

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Application of the two foregoing Rules. 1. What will 4 yards of cloth cost, in pounds, at 7 s. 6 d. a yard? 7 s. 6 d., reduced to a decimal,=,375£. X 4 yds. = £1,500

20 10,000 Ans., 1£. 10 s. 2. At $6 a cwt., what will 2 cwt. 2 qrs. of rice cost? A. $15. 3. At $20 a ton, what will 15 cwt. 2 qrs. of hay cost ?

A. $15,50. 4. What cost 6 cwt. Oqr. 7 lbs. of sugar, at $11,25 a cwt.?.

A. $68,203 + 5. What cost 60 gals. 1 pt. of rum, at $ ,78 a gallon?

4. $46,8977 6. At $1,25 a bushel, what will 36 bu. O pk. 4 qts. cost?

1. $45,156736 7. At $4,75 a yard, what will 20 yds. 2 qrs. of broadcloth cost?

A. $125,874. 8. At 2£. 10 s. a cwt., what will 6 cwt. 3 qrs. of rice cost? 2£. 10 s.=2,5£., and 6 cwt. 3 qrs. 6,75 cwt.; then, 6,75 X 2,5=16,875£. X 20=17,5 s. X 12=6d. A. 16£. 17 s. 6 d.

9. What will 6 gallons 2 qts. of brandy cost, in pounds, at 15 shillings a gallon? A. 4£. 11 s. 6 d.

REDUCTION OF CURRENCIES.

I LX. An apology may by some be deemed necessary for the omission, in this work, of much that is contained in other treatises, respecting what is called “ the currencies of the different United States. The author, however, deems it rather necessary to apologize for introducing the subject at all. Those merely nominal currencies, originally derived from Great Britain, have long been obsolete in law, and ought to become so in practice. So long, however, as that practice continues, it may be necessary to retain a brief notice of it in elementary works.

Note. It was not intended that the following Table should be exact in every particular to a mill, but enough so to correspond with the pecuniary calculations current among men of business; and, as such, it will be committed to memory more easily.

The design of the Table is not ihat it should be learned by rote, but by actual calculations from a few data: thus, as 1 farthing is į of a cent, thea 2 farthings are g. Again, as 3 d. is 4 cents, and 3 s. are 50 cents, then 3 s. 3d

aro 54 cents, It would be well for the teacher to direct the attention of the pupil to this object by explanations.

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TABLE. 1 farthing

of a penny,

1 of a cent. 2 farthings.

of a penny,

of a cent. 3 farthings.

of a penny,

1 cent.
4 farthings.

1} cent.
Pence.
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6 30,

42 23 1 and 2

1912
9 33,

46
3
4 1 and
3
21 13 0

50 4 1 and 4 16, 22 3 3

54 41 611 and 5 are 17, or 2313 6 42,

584 5 7 1 and 6

25 13 9 45, 6 are 84 1 and

0

66 7 8 are 272 4 and 3

71 8 11 1 and 9 are 29 4 and 6 54, 75 9 are 1211 and 10 are 22, or 3034 and 9

79 10 are 14 | 1 and 11 are 23, or 311 5 and 0 are 60, 11 15 1 and 12 are 24, or 331 5 and 6 12 163 12 and 3 are 27, or 373 16 and 0 72,

1. At 3 farthings a yard, what will 2 yards of tape cost in cents ?

2. What will 2 sticks of twist cost, in cents, at d. a stick? At } d. a stick? At d. a stick ?

3. At 7 d. apiece, how many cents will buy 1 inkstand ? Will buy 2? Will buy 3? $ ? 5? 6?

4. How many cents must you pay for 2 rulers, at 9 d. apiece? For 4? For 6? For 8? For 16 ? For 24? For 32 ?

5. What will 2 yards of lace come to, in cents, at 1 s. 6 d. a yard? What will 3 yards ? What will 4 yards ? What will 6 yards ?

6. When oats are 3 s. 6 d. a bushel, how many cents will buy 2 bushels ?

7. When rye is 3 s. a bushel, how many cents will buy 2 bushels ? How many 3 bushels ? How many 4? How

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8. When corn is 4 s. 6 d. a bushel, what are 2 bushels worth in cents? What 4 bushels ? What 8 bushels? What 12 bushels ?

9. How many cents make a dollar ? A. 100.

10. If a Latin Grammar cost 6 shillings, how many dollars will buy 2? How many 4? How many 6? How many 8? How many 20 ?

11. What will 2 barrels of flour come to, at 30 shillings per barrel? What will 3? What will 6 ? What will 77

12. If you buy a book for 1 shilling and 6 pence, and give the bookseller a fifty-cent piece, how many cents in change must he give you?

13. If you buy a Latin Grammar for 4 shillings and 9 pence, and give the bookseller 1 dollar, how many cents must he pay you

u? 14. If you have 4) pence a week, how many weeks will come to a dollar ? How many to 2? How many to 3?

15. If I pay 1 s. 6 d. for 1 meal of victuals, how many meals can I have for a dollar ? For 2 dollars ? For } a dollar? For } of a dollar ? For 3 dollars ? For 4?

16. When broadcloth is 12 s. a yard, for how many dollars can you buy 2 yards ? How many 3? How many

5? 17. You buy a hat for 18 shillings, and give the storekeeper a five dollar bill; how many dollars must he give you in change?

18. How many cents are 2 s. 2 d.? 2 s. 5 d.? 2 s. 7 d.? 2 s. 10 d.? 3s. 1 d.? 3 s. 5 d.? 3 s. 8 d.? 4s. 2 d.? 48. 5 d.? 4 s. 7 d.? 7 8.7 d.? 9 s. O d.? 10 s. 6 d.? 12 s. ? 12 s. 6 d.? 12 s. 9 d.? 13 s.? 14 s. 6 d.? 15 s.? 158. 6 d.? 15 s. 9 d.? 16 s. 6 d. ? 17 s. 6 d.? 18 s.? 21 s.? 24 s.? 27 s.? 30 s. ? 36 s.? 42 s. ?

48 s.?

54 s.? 60 s.? 66 8. ?

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Q. What is that, which you have now been doing, called ?
A. Reduction of Currencies.

Q. Are pounds, shillings, pence and farthings the same in all countries ?

A. They are the same in name, but not in value.

Q. What was their value formerly in England and her American colonies ?

A. The same.
Q. What has occasioned the difference in value ?

A. The legislatures of these colonies emitted, or put in circulation, bills, which depreciated in value in various degrees.

Q. What is the number of shillings, which it takes in any state, to make a dollar, called ?

A. The currency of that state.

Q. How many shillings make a dollar in the New England States,
Virginia, Kentucky, and Tennessee ?

A. 6 shillings.
Q. What name does the currency of these states take?
Ă. The New England currency.

NEW ENGLAND CURRENCY.-To reduce this Currency to
Federal Money, and Federal Money again to the same Currency:

Q. What part of a pound is $1, or 6s. of this currency?
A. =1t; decimally,= ,3.
1. How many dollars in 3£. 8 s. 3 d.?

By reducing 3£. 8 s. 3 d. to decimals, by. I LVIII., we have 3,4125£. Now, since every ,3 of a pound is a dollar, it is evident, that, as many times as ,3 is contained in 3,4125£., so many dollars there will be, thus :

The pupil must recollect that, in division OPERATION.

of decimals, there must be the same num

ber of decimals in the divisor and quotient ,3 ) 3,4125

that there is in the dividend. There are 4 in

the dividend, and 1 in the divisor; consa$ 11,375, Ans. quently, there must be 3 pointed off in the

quotient. 2. How many pounds in $11,375 ?

This example being the reverse of the last, it is evident that we must multiply by ,3. OPERATION. $11,375 ,3

It will be recollected by the pupil, A.3£.8 s. 3 d. 3,41 25 in pointing off, that there must be as

20

many decimal places in the product, as there are decimal places in both

multiplier and multiplicand. 8,2500

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