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2. Borrowed 10 English guineas at 28s. cach, and 24 English crowns at 6s. and 8d. each ; how many pistoles at 22s. each will pay the debt ?

ins. 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?

Ans. 8 of each, and 1 oz. over. 5. Admit a ship’s cargo from Bordeaux to be 250 pipes, 130 hhds. and 150 quarter casks ( 1 hhds.) how many gallons in all ; allowing every pint to be a pound, what burden was the ship of? Ans. 44415 gals. and

the ship's burden was 158 tons, 12cwt. 2grs. 6. In 15 pieces of cloth, each piece 20 yds. how many French Ells?

Ans. 200, 7. In 10 bales of cloth, cach bale 12 pieces, and each piece 25 Flemish Ells, how many yards? Ans. 2250.

8. The forward wheels of a waggon are 14. feet in circumference, and the hind wheels 15 feet 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 ter yards

Ans. 2079508. 10. The sun is 95,000,000 of miles from the eart'., anal a cannon bail at its first discharge flies about a me in 7 seconds ; how long would a cannon ball be, at tat rate in flying from here to the sun ?

ins. 29yr. 21611. 12). 40ni. 11. The Sun travels through G signs of the Zodiac in half a year ; how many degrees, minutes and seconds ?

Ans. 180deg. 10Soomin. 648000sec. 12. How many strokes does a regular clock strike in 365 days, or a year.

dis. 56030. of a 13. How long will it take to run a million at the rate

Gus. S35k,

6 How much is 4 of an hundred weight :

Ans. 3qrs.725. 10.10. ht. What is the value of of a mile ?

Ins. 6fur. 26po. 11ft. 8. How much is of an cut. ?

Ans. Sgrs. Slb. 1oz. 12,dr. 9. Reduce of an Ell English to its proper quantity.

Ans. 2grs. Sina. 10. IIow much is of a hlad. of wine? Ans. 54 gal. 11. What is the value of of a day?

Shes. 16h. Somin. 53 sec.

PROBLEM 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 mention
ed for a numerator; then reduce the integral part to the
same term, for å denominator: which will be the frac.
tion required.
1. Reduce 135. 64. 2qrs. to the fraction of a pound.

20 Integral part 13 6 2 given slim.
12

12

fo

EXAMPLES.

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ins.

98

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960 Denominator. 650 Num. Ans. $56=956 2. What part of an hundred weight is Sqrs. 1415.

Sgrs. 1415,=981). 3. What part of a yard is Sqrs. Ina.?

lins. 4. What part of a pound sterling is 138. 4d.? Ans. 5. What part of a civil year is 3 weeks, 4 days ?

Ans, 25 6. Whatopart of a mile is Efur. 26po. Syas. Sit. ? fur. po. yd. ft. fert. 6 26 3 904400 Num.

a mile =5280 Denom. 7. Reduce 7oz. 4pwt. to the fraction of a pound troy.

Ins. 8. What part of an acre is 2 roods, 20 poles ? Jns.

Ans.

9. Reduce 54 gallons to the fraction of a hogshead of wine. to. What part of a hogshead is 9 gallons ?

Ans. 11. What part of a pound troy is 10oz. 10pwt. 10grs.?

Ans. Most

DECIMAL FRACTIONS. A Decimal Fraction is that whose denominator is an unit, with a cypher, or cyphers annexed to it, Thus, , røg: rogo, &c. &c.

The integer is always divided either into 10, 100, 1000, &c. equal parts ; consequently the denominator of the fraction 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, fo, is written ,5; 1,45; 16:36 ,725, &c.

But if the numerator has not so many places as the denominator has cyphers, put so many cyphers before it, viz. at the left hand, as will'make up

the defect ; so write såp thus, ,05; and 1067 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, (or separating point) it signifies tenths; if in the second, hundredths, &c. decreasing in cach place in a tenfold proportion, as in the following

NUMERATION TABI.E.

Millions.
C. Thousands
erX. Thousands
A Thousands.
«Hundreds.
Tens.
fons Units.

no Tenth parts.
so Hundredth parts.

Thousandth parts.
cx. Thousandth parts.
C. Thousandth parts.

Millionth parts.

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Whole Vumbers.

6 Decine 8

Cyphers placed at the right hand of a decimal fraction do not alter its value, since every significant figure contimes to possess the same place: so ,5 ,50 and 9500'are endrim sa mevalue, and equal to sort,

Saisers placed at the left hand of decimals, decrease teir value in a tenfold proportion, by removing them iartner from the decimal point. Thus, ,5 ,05 ,005, de. are five tenth parts, five hundredth parts, five thousandth parts, &c. respectively. It is therefore evident that the magnitude of a decimal fraction, compared with another, does not depend upon the number of its figures, but upon the value of its first left hand figure: for instance, a fraction beginning with any figure less than 9 sudli as ,899299, &c. if extended to an infinite number of figures, will not equal ,9.

ADDITION OF DECIMALS.

RULE.

1. Place the numbers, whether inixed or pure decimal under each other, according to the value of their places

2. Find their sum as in whole numbers, and point of so many places for the decimals, as are equal to the greatest number of decimal parts in any of the given numbers.

EXAMPLES.

1. Find the suni of 41,653-4-36,054-24,009-+1,6.

(41,653 Thus,

24,009
1,6

sum, 103,512 which is 103 integers, and 10 parts of an unit

. Or, it is 103 units, and 3 tenth parts, 1 hundredth part, and 2 thousandth parts of an unit, or 1.

Hence we may observe, that Decimals, and FEDERAL Money, are subject to one, and the same law of notation and consequentiy of operation.

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For since dollar is the money unit; and a dime being the tenth, a cent the hundredth, and a mill the thousands, part of a dollar, or unit, it is evident that any number of dollars, dimes, cents and mills, is simply the expression of dollars, and decimal parts of a dollar; Thus, 11 dollars, 6 dimes, 5 cents, H 11,65 or 114%, dol. &c.

2. Add the following mixed numbers together. #. (3) }

ards. Ounces. Dollars. 46,23456 12,3456 48,9103 24,90400 7,891 1,8191 17,00411 2,34 3,1030 3,01111 5,6 ,7012

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12. To 9.999999 add one millionth part of an unit. and the sum will be 10. 13. Find the sum of

Twenty-five hundredths, - - - - -
Three hundred and sixty-five thousandths,
Six tenths, and nine millionths, - - - -

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