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Ans. 1%.

1. What is the vulgar frac- 5. Reduce 0.769230 to the tion of 0.is ?

form of a vulgar fraction. Ang. H= 2. Reduce 0.72 to a vulgar

6. What vulgar fraction is fraction. Ans.y=it

equal to 0.138 ?

9X 13+8=125=numerator. 3. Reduce 0.83 to the form 900=denominator. of a vulgar fraction.

.0.138=333=6, Ans.

7. What vulgar fraction is Here 0.8 is 8 tenths, and 3

equal to 0.53 ? is 3 9ths=$ of 1 10th, or 1 8. What is the least vulgar 30th; then tit=36+36 fraction equal to 0.5925 ?

Ans. is

=ă, Ans.

Ans. 19.

4. Reduce 275463 to the form of a vulgar fraction.

Ans. 33335

9. What finite number is equal to 31.62? Ans. 3137.

REVIEW.

1. What is an Arithmetical Pro- 4. What is the common division gression ? When is the series as- of a foot ? What are these called ? cending? When descending? What What kind of series do these frac. is meant by the extremes? The tions form? What is the ratio ? means? When the first and last What is the rule for the multiplicaterins are given, how do you find tion of duodecimals? How are all the common difference? How the denominations less than a foot to be number of terras ? How the sum

regarded ? of the series?

5. What is Position ? What does 2. What is a Geometrical Pro

it suppose when single ? When gression? What is an ascending double ?

What kind of questions series ? What a descending may be solved by the former ? by What is the ratio ? When the first the latter ? term and the ratio are given, how

6. What is meant by the permudo

any

other term? When tation of quantities? How do you the first and last term and the ratio find the number of permutations? are given, how do you tind the sum Explain the reason. of the series?

7. What is meant by a periodical 3. What is annuity? When is decimal ? By a single repetend ! it in arrears? What does an annu- By a compound repetend ? How is ity at compound interest form ? a repetend denoted ? How is a poHow do you find the amount of an riodical decimal changed to an aduity at compound interest ? equivalent vulgar fraction ?

you find

PART III.

PRACTICAL EXERCISES

SECTION I.

Exchange of Currencies.

299. In £13, how many dollars, cents and mills ?

Now, as the pound has different values in different places, the annount in Federal Money will vary according to those values. In England, $1=4s. 6d=4.5s=£*=£0.225, and there £13–13:0.225—$57.777. In Canada, $1=58.= =£0.25, and there £13=13; 0.25=$52. In New England, $1=6s.=££0.30, and there, £13–13:0.3=$43.333. In New York, $1=89==£0.4, and there, £13=13:0.45 32.50. In Pennsylvania, $1=7s. 6d=7.53.=£75=£0.375, and there, £13–13;0.375=$34.666. And in Georgia, $1=

4.6+ 4s.8d.=4.6s=£

€20.0 £0.2333t, and there, £13–13:0.2333 =$55.722.

300. In £16 7s. 8d. 2qr., how many dollars, cents and mills ?

Before dividing the pounds, as above, 7s. 8d. 2qr., must be reduced to a decimal of a pound, and annexed to £16. This may be done by Art. 143, or by inspection, thus, shillings being 20ths of a pound, every 23. will be 1 tenth of a pound: therefore write half the even number of shillings for the tenths £0.3. One shilling being 1 20th=£0.05; hence, for the odd shilling we write £0.05. Farthings are 960ths of a pound, and if 960ths be increased by their 24th part, they are 1000ths. Hence 8d. 2qr.(=34qr.+1)= £0.035; and 164-0.30.05 0.035 =£16.385, which, divided as in the preceding example, give for English currency, $72.822, Can. $65.54, N. Y. $40.962, &c. Hence,

301. To change pounds, shillings, pence and farthings to Federal Money, and the reverse.

RULE.-Reduce the shillings, &c. to the decimal of a pound; then, if it is English currency, divide by 0.225; if Canada, by 0.25; if N. E., by 0.3; if N. Y., by 0.4; if Penn., by 0.375, and if Georgia, by 0.23;-the quotient will be their value in dollars, cents and mills. And to change Federal Money into the above currencies, multiply it by the preceding decimals, and the product will be the answer in pounds and decimal parts,

3. In £91, how many dol- 9. Reduce £25 15s. N. E., lars ? £91 E.=$404.444. to Federal Money. Can. $364. N. E., $303.333.

Ans. $85.833. N. Y. $227.50, &c. Ans. 4. Reduce £125, N. E. to

10. In £227 178. 5 d. N. E., Federal Money.

how many dollars, cents and

mills ? Ans. $416.666.

Ans. $759 57cts. 3m. 5. Change $100 to each of the foregoing currencies.

11. In $1.612, now many $100%£22 10s. Eng=£25 shillings, pence and farthings? Can.-£30 N. E=£40 N. Y. =£37 10s. Penn.

12s. 10 Y. 6. In $1111.111, how

many pounds, shillings, pence and

12. Reduce £33 13s. N. Y., farthings ?

to Federal Money. £333 6s. 8d. N. E.

Ans. $84.125. Ans.

13. In £1 ls. 104d. Penn., 7. In £1 ls. 103d. N. E.,

how
many

dollars ? how many dollars ?

Ans. $2.917. Ans. $3.646. 8. In £1 ls. 103d. N. Y., 14. In £1 ls. 104d. Can., how many dollars ?

how
many

dollars ?
Ans. $2.735.

Ans. $4.376.

Ans. { 12:80.N.E.

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302. The following rules, founded on the relative value of the several currencies, may sometimes be of use :

To change Eng. currency to N. E. add , N. E. to N. Y. add }, N. Y. to N. E. subtract 4, N. E. to Penn. add 4, Penn. to N. E. subtract }, N. Y. to Penn. subtract 16, Penn. to N. Y. add I's, N. E. to Can. subtract , Can. to N. E. add }, &c.

15. In $255.406, how many 16. Change £240 15s. N. pounds, shillings, pence and E. to the several other curfarthings?

rencies. (£76 12s. 5d. N. E.

(£321 Os. Od. N. Y. Ans. £102 3s. 3d. N. Y.

£300 18s. 9d. Penn. £95 15s. 6 d. Penn.

Ans.

£200 12s. 6d. Can. £63 17s. Ofa. Can.

$802.50 Fed. Mon.

TABLE

303. Of the most common gold and silver coins, containing their weight fineness, and intrinsic value in Federal Money.

Country. | Names of coins. | Weight. | Fineness. 1 Value.

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SILVER COINS.
Dollar.
Half Dollar.
Quarter Dollar.
Dime.
Crown.
Half Crown.
Shilling.
Crown.
5 franc piece.
Dollar (old).
Dollar (new).
Rix Dollar (con.).
Florin (do.).
Rix Dol. (conv.).
Florin (do.).
New Crusade.
Ducatoon.
Gilder, or flor.
Rix dollar.
Goldgilder.

416.
208.
104.

41.6
464.50
232.25

92.90 451.62 386.18 418.47 418.47 450.90 225.45 432.93 216.46 265.68 504.20 162.70 443.80 301.90

oz. pwt.
10 14
10 14
10 14
10 14
11 2
11 2
11 2
10 171
10 16
11 0
10 15
10 133
10 13
10
10
10 16
11 5
10 183
10 113
8 5

1.000 0.500 0.250 0.100 1.111 0.556 0.222 1.06 0.898 0.991; 0.972 1.037 0.519 0.926 0.463 0.615 1.222 0.375 1.009 0.602

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Nota. The current values of several of the above coins differ somewhat from their intrinsic value, as expressed in the table.

SECTION II.

MENSURATION.

1. Mensuration of Superficies.

304. The area of a figure is the space contained within the bounds of its surface, without any regard to thickness, and is estimated by the number of squares contained in the same; the side of those squares being either an inch, a foot, a yard, a rod, &c. Hence the area is said to be so many square inches, square feet, square yards, or square rods, &c.

305. To find the area of a parallelogram (65), whether it be a square, a rectangle, a rhombus, or a rhomboid.

RULE.-Multiply the length by the breadth, or perpendicular height, and the product will be the area.

1. What is the area of a square whose side is 5 feet?

3. What is the area of a rhombus, whose length is 12 rods, and perpendicular height 4 ?

Ans. 48 rods.

erer

4. What is the area of a Ans. 25 ft.

rhomboid 24 inches long, and 8 wide ?

Ans. 192 inches. 5

5. How many acres in a 2. What is the area of a rectangular piece of ground, rectangle, whose length is 9, 56 rods long, and 26 wide ? and breadth 4ft. ? Ans. 36ft. 56X26_160–910. Ans.

306. To find the area of a triangle. (64) RULE 1.-Multiply the base by half the perpendicular height, and the product will be the area.

RULE 2.-If the three sides only are given, add these together, and take half the sum ; from the half sum subtract each side separately ; multiply the half sum and the three remainders continually together, and the square root of the last product will be the area of the triangle.

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