14. If 4 cwt. of iron cost £7 19s. 4d. what is that per pound? Ans. 4d.

QUESTIONS.

a What is Compound Division?

b When the given quantity does not exceed 12 what is the rule?

c How are you to proceed when the quantity is a composite number?

d How when it is not a composite number?

e Having the price of a hundred given, how may the "price of 1 lb. be found?

DECIMAL FRACTIONS.

DECIMAL FRACTIONS are of such a nature, as to be managed by the same method of operation as whole numbers. a] They are expressions of parts of an integer; or are, in value, less than one of the thing which they are used to signib] fy. The integer is always divided, either into 10, 100, 1000, &c. equal parts, called the denominator, which is alc] ways a unit, with as many cyphers annexed as there are figures in the numerator. Thus, ,5, ,25, ,254, with the sepdj aratrix before it, expresses the same as To 100, 1000, 254 &c. If the numerator have not so many places as the denominator has cyphers, place as many cyphers at the left hand as will make up the deficiency, as, thus, ,05; and 1000,005.

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e Cyphers placed at the right hand of decimals, are of no f] value; but when placed at the left hand, they diminish the fraction in value in a ten fold proportion; thus,,5 is five tenths of an integer, or one; but,05 is five hundredths of the same. Suppose for example, a dollar to be divided into ten parts:,5 expresses five of those parts, or one half of it; but ,05 supposes the dollar to be divided into one hundred parts, and five of them are expressed, or one twentieth.

g When integers and decimals are expressed together in the same sum, they are called mixed numbers; thus, 45,73 is a mixed number; the figures at the left hand of the separatrix being integers, and those at the right of the same point being decimals, as in the following

h Place the numbers, whether mixed or pure decimals, under each other, according to their local value.

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

EXAMPLES.

1. What is the amount of 25,342, 7,21, 143,7365, 4265,5 6,15 264,463, when added together?

25,342 7,24 143,7365

4265,5

6,15 264,463

4712,4315

The decimal points are placed directly under each other, and the whole numbers arranged to the left, and the decimals to the right of them.

Four being the greatest number of decimal places in any of the numbers, four figures are pointed off in the sum

or amount.

2. Required the sum of 325,15, 65,463, 7,0464, 4375,46, 35,005?

Ans. 4808,4244.

3. What is the sum of $144,17, $650,253, $96,75, $10,09, $695,832! Ans. $1597,095. 4. What is the sum of 643, 16,005, ,0651,75, 420, 1,46? Ans. 1081,2304. 5. Add four hundred and twenty-five, and seventy-five hundredth; six hundred and forty, and three hundred and twenty-five thousandth; ninety-five, and seven tenth; one hundred and thirty-five, and forty-six hundredth together. Ans. 1297,235

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6. What is the sum of twenty-five, and six tenth; fifteen, and nine hundredth; eight, and sixty-two thousandth; and five, and four hundredth, when added together?

Ans. 53,792.

SUBTRACTION OF DECIMALS.

RULE.

j Place the numbers according to their value; then subk] tract as in whole numbers, and point off the decimals as

3. What is the difference between 643,436 and 275,268?

Ans. 368,168.

4. What is the difference between 7635,062 and 294,46?

5. From 456,5 take 67,25. 6. From 1,9463 take,9764. 7. From 2465, take 76,435.

Ans. 7340,602. Ans. 389,25. ,9699.

Ans. 2388,565.

MULTIPLICATION OF DECIMALS.

RULE

1. Whether they are mixed numbers or pure decimals, place the factors, and multiply them as in whole numbers. m 2. Point off so many figures from the product, as there are decimal places in both factors; and if there be not so many decimal places in the product, supply the deficiency by prefixing cyphers.

DIVISION OF DECIMALS.

RULE.

1. The places of decimal parts in the divisor and quotient, counted together, must always be equal to those of the n] dividend; therefore divide as in whole numbers, and from the right hand of the quotient, point off so many places for decimals, as the decimal places in the dividend exceed those in the divisor.

o 2. If there be not so many places of decimals in the quotient as the rule requires, supply the deficit by prefixing cyphers to the left hand.

3. If, at any time, there be a remainder, or the decimal places in the divisor be more than those in the dividend, cyphers may be annexed to the remainder, and the quotient carried to any degree of exactness.

Note. In the two last examples, the separatrix is omit ted in the answer to exercise the scholar in placing it; to this the Instructor should pay particular attention.

REDUCTION OF DECIMALS.

CASE 1.

To Reduce Vulgar Fractions to Decimals.

RULE.

p Annex cyphers to the numerator and divide by the de nominator: the quotient will be the decimal required.

q The cyphers annexed are to be considered as decimals, the quotient to be pointed off according to the rule in division.

To reduce numbers of different denominations, as of Money, Weight and Measure, to their decimal value.

RULE.

r Write the given numbers, from the least to the greatest, in a perpendicular column under each other, for dividends, and divide each of them by such a number as will reduce it to the next denomination, annexing the quotient to the suc ceeding number: the last quotient will be the decimal required.

EXAMPLES.

1. Reduce 10s. 63d. to the decimal of a pound.

4 3, 12 6,75 20 10,5625

Ans. ,528125

In this example, I suppose 2 cyphers annexed to the 3, (300); which divided by 4, the number of farthings in a penny, the quotient is ,75, which I write against the 6 in the next line, and the sum thus produced, (6,75,) I divide by