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EXAMPLES.

Divide £788 19s. 2d. equal- What is the commission on £448 1s. 11 d. at 4 per cent? 448 1 112.

ly between 100 men.

100)7,88 19 2

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Having the price of a cut. to know how much it is per lb.

2. RULE. Find the price of 1 or 2 quarters, and then

divide by the component parts.

If 5 cwt. of iron cost £8 15s. Od. how much is it

5)8 15 0

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If of a farm is worth $450, what is the whole valued

Ans. $1200.

DECIMAL FRACTIONS.

A DECIMAL FRACTION is that, whose denominator is an unit, with as many ciphers annexed to it as the numerator has places, and is usually expressed by writing the numerator only, with a point before it, called the separatrix; thus,, 1,1%, are decimal fractions, and are expressed by ,5,25 ,125 respectively.

125

The figures to the left hand of the separatrix are whole numbers; thus 4,5 yards is 4 yards and 5 tenths, or one half of another yard.

Ciphers, placed to the right hand of decimals, make no alteration in their value; for,5,50,500, &c. are decimals of the same value, being each equal to ; but when placed to the left hand, the value of the fraction is decreased in a ten-fold proportion; thus,5,05,005, &c. are 5 tenth parts, 5 hundredth parts, 5 thousandth parts, respectively.

The different value of figures will appear plainer by the following

TABLE.

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From this table it appears, that as whole numbers increase in a ten-fold proportion from units to the left hand, so decimals decrease in the same proportion to the right: and that in decimals, as in whole numbers, the place of a figure determines its relative value.

Examples for writing Decimals.

Five tenths

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Four hundred and forty-one millionths
Four hundreds, and forty-one millionths

ADDITION OF DECIMALS.

,5

,05

,005

,00005

,053

5,15

,000015

,809

800,009

,00018

1,01

,000441

400,000041

RULE. Place the given numbers so that the decimal points may stand directly under each other, then add as in whole numbers, and point off so many places for decimals to the right as are equal to the greatest number of the decimal places in any of the given numbers.

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Required the sum of twenty-nine and three-tenths, three hundred and seventy-four and nine millionths, ninety-seven and two hundred and fifty-three thousandths, three hundred and fifteen and four hundredths, twenty-seven, one hundred and four tenths. Ans. 942,993009.

Required the sum of ten dollars and twenty-nine cents, ninety-three cents and three mills, nine cents and six mills, and two dollars and eight mills.

Ans. 13 dols. 32 cts. 7 mills.

SUBTRACTION OF DECIMALS.

RULE. Place the given numbers so that the decimal points may stand directly under each other, and then point off the decimal places as in addition.

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From two thousand and sixteen hundredths take one thousand and four, and four millionths. Ans. 996,159996.

From twenty-four thousand nine hundred and nine and one tenth take fourteen thousand and twenty-nine thousandths. Ans. 10909,071.

Take eighty-five and seven hundred and thirty-seven thousandths from one hundred. Ans. 14,263. From five hundred and thirty-one dollars two cents take one hundred and seventeen dollars three cents and four mills. Ans. 413 dols. 98 cts. 6 mills.

MULTIPLICATION OF DECIMALS.

Multiply exactly as in whole numbers, and from the product cut off as many figures for decimals to the right hand as there are decimals in both factors; but if the product should not have so many, supply the defect by prefixing ciphers.

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NOTE. To multiply decimal fractions by 10, 100, 1000, &c. is only to remove the separatrix so many places towards the right as there are ciphers.

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Multiply twenty-nine and three tenths by seventeen.

Ans. 498,1.

Multiply twenty-seven thousandths by four hundredths.

Ans. ,00108.

Multiply two thousand and four and two tenths by twentyAns. 54113,4.

seven.

DIVISION OF DECIMALS.

RULE. Divide as in whole numbers, and from the right hand of the quotient point off as many places for decimals as the decimal places in the dividend exceed those of the divisor. If the places of the quotient are not so many as the rule requires, supply the defect by prefixing ciphers. If at any time there be a remainder, or the decimal places in the divisor are more than those in the dividend, ciphers may be annexed to the dividend, and the quotient carried to any degree of exactness.

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The various kinds that ever occur in division are included

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