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Divifion of Vulgar Fractions.

ULE. Prepare the given fractions as directed in multiplication, and multiply the denominator of the divifor into the numerator of the dividend, for the numerator of the quotient, and the product of the other two parts is its denominator and both conftitute the quotient.

Thus divided by. Here 5 × 9 45 the numerator, and 3 X 20 60 the denominator, hence the quotient is +5 = 3 which was required. 45

The Single Rule of Three Direct in Vulgar Fractions.

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ULE. Reduce the fractions as before directed, and ftate or range the quantities fo that the first and third terms may be of one name, then multiply the denominator of the ft. term, into the numerators of the 2d. and 3d. terms for the numerator of the 4th. term, and the continued product of the other three parts, will be its denominator. Thus,

If 3 yards of broad cloth coft 21. what will yards coft ?

1027

Then as yd:

1 X 14 X 72

144 1. = 91.33 =9l. 12s. anfwer.

The Rule of Three Inverfe in Vulgar Fractions.

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ULE. When stated as before directed, multiply the denominator of the 3d term, into the product of the numerators of the other two terms, for the nume

rator

rator of the anfwer, and the continued product of the other three parts for its denoininator, and that fraction conflitutes the anfwer; when reduced to its proper quantity, as need may require.

Thus if it be required to find what quantity of fhalloon that is of a yard wide, will line 71 yards of

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UESTIONS in this rule are most naturally and elegantly performed by rwo operations of the fingle rule, as before directed.

Thus if 501. in 5 months gain 31., what time will 251. require to gain 11. at the rate?

10X 103 × 4

I O

And as 1.3m. :: 51.:

8251.

206

m. the answer which was required.

The fame by the univerfal rule of proportion.

If 7 men in 3 weeks working 14 hours

per day, do a piece of work; in how many weeks will 9 men and a boy that works a man's day work, working 16 hours per day, finish 3 fuch pieces and ?

f.

Decimal Fractions.

DECIMALS, of I

part of an integer or whole thing, as I pound, I yard, i gallon, hundred weight &c. in tenth parts, hundred parts, thoufand parts, tens of thousand parts,

hundreds of thousand parts, milion parts, ten milion parts &c.t

Decimal fractions are wrote down with a dot before them thus, .584 and are expreffed thus, 5 tenths, 8 hundred parts, 4 thousand parts.

Any decimal fraction may be expressed as a vulgar fraction, by making the decimal the numerator without its dot, and puting as many cyphers, for the denominator, as there are decimal places in the numerator, with a 1 on the left hand fide.

Thus, .584-584 and .7483

7453

10000

Whole numbers by annexing cyphers to them are increased in a tenfold proportion. Thus, 1 with a cypher becomes 10, with two cyphers 100, with 3 cyphers 1000, but decimals by prefixing cyphers decrease in a tenfold proportion.

As I tenth with a cypher prefixed. Thus, .01 is one hundredth part, and with two cyphers, thus, .001 becomes one thousandth part &c.

N. B. As a cypher or cyphers before whole numbers, have no effect to alter their value, fo cyphers after decimals do not effect their value.

There

There are three forts of decimal fractions, (viz.) finite or terminate as .25, infinite or repetend as .665 for ever, and circulating or recurring."

As .7483483483 i 1&c. hence in writing down a repetend the repeating figure is cancelled with a dash thus, .276, and in writing a circulate the first and last are cancelled thus, .476845 to fhew what figures circulate, 0925,2 TAM

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ULE. Place fimiliar or component parts under one another, as tenth parts, under tenth parts, hundreds, under hundreds &c. and add as in whole numbers minding to place your dot or seperatris under itself in the fum.

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To fubtract Decimal Fractions.

ULE. Place as directed in addition, and borrow 10 if need be, and fubtract as in whole numbers. Thus, .847.298.549 the difference,

Multiplication of Decimal Fractions.

ULE. Multiply as in whole numbers, and fepe

there are decimal places in both factors.

Multiply

Divifion of Decimal Fractions.

ULE. Divide as in division of whole numbers

the divider, (which may be done by annexing cyphers to the dividend when needful) and prick of that excess in the quotient, for the decimal places in the divifor andgotient nuft always be equal to the decimal places in the dividend..

Divide 16.8509592. by 68.472 68.472)16.8509592-2461 the quotient.

Reduction of Decimal Fractions.

Cofe ft. To reduce a vulgar fraction to a decimal.

RULE. Divide the numerator with cyphers annexed by the denominator, and the quotient is the decimal required.

If the fraction be a compound, or a mixed one, it must be reduced to a fimple one, and then put into decimals.

.3 and 5+ = 5.66&c.

= .642857 &c.