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o RELUCTION.

2. Borrowed 10 English guineas at 28s, each, and 24 English crowns at 6s. and Sd. each; how many pistoies at 22s. each, will pay the debt? Ans. 20. 3. Four men brought each 171.10s, sterling value in gold into the mint, how many guineas at 21s, each must they receive in return? Ans. 66 guin. 14s. 4. A silversmith received three ingots of silver, each weighing 27 ounces, with directions to make them into spoons of 2 oz., cups of 5 oz., salts of 1 oz., and snuff-boxes of 2 oz., and deliver an equal number of each; what was the number 1 Ans. 8 of each, and 1 oz. over. 5. Admit a ship's cargo from Bordeaux to be 250 pipes, 130 hlids, and 150 quarter casks, [] holds.] how many gallons in all; allowing every pint to be a pound, what burden was the ship of 1 Ans. 44.415 gals. and the ship's burden was 158 tons, 12 cwt. 2 qrs. 6. In 15 pieces of cloth, each piece 20 yards, how many French Ells? - Ans. 200. 7. In 10 bales of cloth, each bale 12 pieces, and each piece 25 Flemish Ells, how many yards? Ans. 2250. 8. The forward wheels of a wagon are 14 feet in cit. crumference, and the hind wheels 15 feet and 9 inches; how many more times will the forward wheels turn round than the hind wheels, in running from Boston to New-York, it being 248 miles? Ans. 7167. 9. How many times will a ship 97 feet 6 inches long, sail her length in the distance of 12800 leagues and ten yards? Ans. 20795.08. 10. The sun is 95,000,000 of miles from the earth, and a cannon ball at its first discharge flies about a mile in 71 seconds; how long would a cannon ball be, at that rate in flying from here to the sun ? Ans. 22 yr. 216 d. 12 h. 40m. 11. The sun travels through 6 signs of the zodiac in half a year; how many degrees, minutes, and seconds? Ans. 180 deg. 10800 min. 648000 sec. 12. How many strokes does a regular clock strike in 365 days, or a year? ans. 56940. 13. How long will it take to count a million, at the rate of 50 a minute? Ans. 33.3 h. 20 m. or 13 d. 21 h. 20 m.

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PRACTIONS. co

14. The national debt of England amounts to about 279 millions of pounds sterling; how long would it take to count this debt in dollars (4s. 6d. sterling) reckoning without intermission twelve hours a day at the rate of 50 dols, a minute, and 365 days to the year? Ans, 94 years, 134 days, 5 hours, 20 min.

FRACTIONS.

FRACTIONS, or broken numbers, are expressions for any assignable part of a unit or whole number, and (in general) are of two kinds, viz.

WULGAR AND DECIMAL.

A Vulgar Fraction, is represented by two numbers placed

one above another, with a line drawn between them, thus, &c. signifies three fourths, five eighths, &c.

The figure above the line, is called the numerator, and

at below it, the denominator;
5 Numerator.
Thus, | -
s Denominator.

The denominator (which is the divisor in division) shows how many parts the integer is divided into; and the nume rator (which is the remainder after division) shows howma ny of those parts are meant by the fraction.

A fraction is said to be in its least or lowest terms, when it is expressed by the least numbers possible, as : when reduced to its lowest terms will be 1, and or is equal to 1, &c.

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To abbreviate or reduce fractions to their lowest terms.

Rule.-Divide the terms of the given fortion by any number which will divide them without a remainder, and the quotients again in the ame manner; and so on, till it appears that there is no number

greator than 1, which will divide them, and the fraction will be in its --torns.

Ex-MPLEs. 1. Reduce of to its lowest terms. (3) (2) 8); # =#-o-; the Answer.

2. Reduce 4; to its lowest terms. Ans. 1 3. Reduce is to its lowest terms. Ans. A 1. Reduce or to its lowest terms. Ans.

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-] -na-TION5. 7. tl. What is the value of to of a day? Ans. 16 h. 36 min. 55, a sec. Pro-LEM III. To reduce any given quantity to the fraction of any greater denomination of the same kind. Rule.—Reduce the given quantity to the lowest term inentioned for a numerator; then reduce the integral part to the same term, for denominator; which will be the fraction required. Exa-P-Es1. Reduce 13s.6d. 24rs. to the fraction of a pound. 20 integral part 13 62 given sum.

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The integer is always divided either into 10, 100, 1000 &c. equal parts; consequently the denominator of the frac tion will always be either 10, 100, 1000, or 10000, &c. which being understood, need not be expressed; for the true value of the fraction may be expressed by writing the numerator only with a point before it on the left hand thus, or is written ,5; or ,45; For ,725, &c.

But if the numerator has not so many places as the denominator has ciphers, put so many ciphers before it, viz. at the left hand, as will make up the defect; so write ro, thus, ,05; and room thus, ,006, &c.

Note. The point prefixed is called the separatrix.

Decimals are counted from the left towards the right hand, and each figure takes its value by its distance from the unit's place; if it be in the first place after units, (orseparating point) it signifies tenths; if in the second, hun dredths, &c. decreasing in each place in a tenfold propor tion, as in the following

NUMERATION T-a-o.

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Ciphers placed at the right hand of a decimal fraction do not alter its value, since every significant figure continues to possess the same place: so ,5,50 and 500 are all the same value, and equal to so, or .

But ciphers placed at the left hand of decimals, decrease their value in a tenfold proportion, by removing them further from the decimal point. Thus, 5 ,05 ,005, &c. are five tenth parts, five hundredth parts, five thousandth parts. &c. respectively. It is therefore evident that the magnitude

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