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2. Received from my correspondent in Liverpool, a cargo of goods, amounting, as per invoice, to 10001. sterling; how much of this country's money am I indebted to my correspondent for said goods?

As 11. : 444 cts. : : 10001. $ 4440 Ans. 3. B. H. Everard, of Sligo, (Ireland,) shipped a cargo of Irish linen to John Agnew, of New York, amounting, as per invoice, to 9801. How many dollars will John Agnew give B. H. Everard credit for in his books ?

As 11. : 410 cts. : : 9801. $4018 Ans. 4. John Agnew, of New-York, shipped a cargo of flaxseed and white-oak staves to B. H. Everard, of Sligo, amounting, as per invoice, to 3980 dolls. How much Irish money will B. H. Everard give John Agnew credit for in his books ? As 410 cts. : 11. :: 398000 ets. 9701. 14s. 7d. + Ans.

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DECIMALS.

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A Decimal Fraction has always an unit for its denomi, nator, with a cipher or ciphers annexed to it, as there are figures in the numerator, which being understood need not be expressed, for the true value of the fraction may be expressed by writing the numerator only, with a dot on the left hand; thus, is ,5 and too is ,25 &c.

But if the numerator has not so many places as the denominator has ciphers, put as many ciphers before it, at the left hand, as will make up the deficiency; thus, té is ,05

is ,005 &c. The point prefixed is called the separatrix, as it serves to distinguish the fraction, and also separates it from the whole number.

Decimal fractions are always counted from the left hand, towards the right, and each is estimated by its distance from the unit's place, or the first figure of the denominator, towards the left hand; thus, ,2 is two-tenths, ,3 is threetenths, ,05 is five hundredths, 2005 is five thousandths, &c.

Ciphers, placed to the right hand of decimals, make no alteration in their value, for ,5 ,50 ,500 &c. are all equal to 4, and have the same value; but when prefixed, or put before decimal, they decrease the fraction in a tenfold proportion, as in the following table.

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ADDITION. Place the numbers exactly under each other, according to the value of their places; then add as in whole numbers, and point off as many places to the right hand, for the decimal fraction, as are equal to the greatest number of decimals in any of the given numbers.

EXAMPLES.

1,5 3,05 76,070 14,0006

27,5"
49,65
76,0106
17,3067

8,75 19,115 36,8945 20,90765

97,6206

4. Add ,7569 + ,25 + ,654 + ,199 parts of a dollar together.

Ans. 1,8599 dollars. 5. Add 72,5 + 32,071 + 2,1574 + 371,4 + 2,75 acres together.

Ans. 480,8784 acres. 6. Add 71,467 + 27,94 + 16,084 + 98,009 + 86,5 days together.

Ans. 300 days. 7. Add twenty-five hundredths, three hundred and sixtyfive thousandths, six-tenths, and nine millionths together.

Ans. 1,215009.

SUBTRACTION. RULE. Place the numbers according to their value, and then proceed as in subtraction of whole numbers, and dot off the decimals as in addition.

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MULTIPLICATION. Rule. Multiply as in whole numbers, and from the product point off as many figures for decimals to the right hand, as there are decimals in both factors; but if the product will not admit of so many, supply the defect by prefixing ciphers.

EXAMPLES.

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RULE. Divide as in whole numbers, but observe that the decimal places of the quotient and divisor be equal in num. ber with those in the dividend; and from the right hand of the quotient point off as many places for decimals, as the decimal places in the dividend exceed those in the divisor. If the places in the quotient be not so many as the rule requires, prefix as many ciphers to the left hand of the

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quotient as will supply the defect; and if the decimal places in the divisor be more than those in the dividend, annex as many ciphers to the dividend as will make it equal to the divisor. ' If there happens to be a remainder, you may annex ciphers to it, and carry on the quotient to any degree of exactness you please.

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Ans.

1,5 3

3,3333 + 2

3,5 ,9

10 ,1812

,23068+ 8,31

,154+ ,365

608,21+ ,22

3,65 2,2

36,5 365

,00821+ 24,3

52,12 1,12

,5 12

8,333+ ,1347

535,68+ ,0457

2,735+ 282

,0035461+

,125

NOTE. When decimals, or whole numbers, are to be divided by 10, 100, 1000, &c. (with ciphers annexed to unity,) it is performed by removing the separatrix in the dividend so many places towards the left hand, as there are ciphers in the divisor. 18 Divide 672 by 10

Ang. 67,2 19

672
100

6,72 20

3672

672 1000

CONTRACTIONS OF DECIMALS.

MULTIPLICATION CONTRACTED. Rule. Write the unit's place of the multiplier under that of the multiplicand, which place you intend to keep in the product; then invert the order of all the other figures, that is, write them all the contrary way. In multiplying, always begin at that figure in the multiplicand, which stands over the figure you are then multiplying withal, and set down the first figure of each particular product directly one under the other; but yet a due regard must be had to the increase arising from the figures on the right hand of that figure in the multiplicand, at which you begin to multiply. This will appear more plain by the following

EXAMPLE

1. Multiply 2,368645 by 8,2175, and let there be only four places of decimals retained in the product.

According to the directions, first write down the multiplicand, and under it write the multiplier thus: Place the 8, it being the unit's place of the multiplier, under $, the fourth place of decimals. in the multiplicand, and write the rest of the figures quite contrary to the usual way, as in the follow. ing work; then begin to multiply, first the 5 which is left out, (only with regard to the increase, which must be carried from it,) saying, 8 times 5 is 40, carrying 4 in your mind, and 8 times 4 is 32, and 4 1 carry is 36; set down 6, and carry 3, and proceed through the rest of the figures, as in common multiplication. Then begin to multiply with 2, saying, 2 times 4 is 8, for which I carry 1, (because it is above 5,) and 2 times 6 is 12, and i that I carry is 13; set down 3, and carry 1, and proceed through the rest of the figures. Then multiply with 1, saying, once 6 is 6, for which carry 1, and once 8 is 8, and 1 is 9, which set down, and proceed. Then multiply with 7, saying, 7 times 8 is 56, and carry 6, (because it is above 55,) and 7 times Ś is 21, and 6 that I carry is 27; set down 7, and carry 2, and proceed. Then multiply with 5, saying, 5 times 3 is 15, for which carry 2, and 5 times 2 is 10, and 2 I carry is 12, which set down, and add all the products together, and you will have 19,6107. See the work.

Multiply 2,38645
Ву

5712,8

19,0916
4773
239
167
12

Ans. 19,6107 In multiplying the figure left ont every time, next the right band, in the multiplicand, if the product be 5, or upwards to 10, you carry 1; and if it be 15, or upwards to 20, carry %; and if 25, or upwards to 30, carry 3.

I will work the same question the common way, by which you may see all the figures on the right hand of the black line wholly omitted.

Three figures are sufficient to express a decimal fraction."

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