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5. Reduce 0.769230 to the form of a vulgar fraction. Ans. 19

6. What vulgar fraction is equal to 0.138 ? 9×13+8=125-numerator. 900 denominator.

.0.138 38, Ans. 7. What vulgar fraction is equal to 0.53? Ans.

8. What is the least vulgar fraction equal to 0.5925? Ans. 19.

9. What finite number is equal to 31.62? Ans. 3133.


1. What is an Arithmetical Progression? When is the series ascending? When descending? What is meant by the extremes? The means? When the first and last terms are given, how do you find the common difference? How the number of terms? How the sum of the series?

2. What is a Geometrical Pro

gression? What is an ascending series? What a descending? What is the ratio? When the first term and the ratio are given, how do you find other term? any When the first and last term and the ratio are given, how do you find the sum of the series?

3. What is annuity? When is it in arrears? What does an annuity at compound interest form ? How do you find the amount of an annuity at compound interest?

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Exchange of Currencies.

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

Now, as the pound has different values in different places, the amount in Federal Money will vary according to those values. In England, $1=4s. 6d. 4.5s.—£45 £0.225, and there £13 13÷0.225-$57.777. In Canada, $1=5s=


£0.25, and there £13-13 0.25-$52. In New England, $1=6s.=£5-£0.30, and there, £13—13÷÷0.3=$43.333. In New York, $1-888-£0.4, and there, £13—13÷÷÷0.4— 32.50. In Pennsylvania, $1-7s. 6d. 7.58.£75=£0.375, and there, £13—13÷0.375 $34.666. And in Georgia, $1= 4.6+ 4s. 8d.-4.6s.£200 £0.2333+, 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 2s. 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 16+0.3+0.05+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,

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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, N. E. to Penn. add †, Penn. to N. E. subtract, N. Y. to Penn. subtract, Penn. to N. Y. add, N. E. to Can. subtract, Can. to N. E. add д, &c.

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

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



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.

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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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