Ch. VII. caufe together with the four Figures of the Divifor, they will not make up the Number of Decimals given in the Dividend, viz. feven, therefore the Quotient is to be made 034, and all the three Fi gures are to be efteem'd Decimals.

II.

Of turning

common

How common Fractions may be reduc'd or turn'd into decimal Fractions, is Fractions fhewn, Chap. 10. §. 13. Proceed we mal. now to speak of common Fractions.

into Deci

CHAP.

CHAP. VIII.

Of the Addition, Substraction, Multiplication, and Divifion, of vulgar or common Fractions: As alfo of Sexagefimal Fractions.

VU Vulgar

Ch. VIII.

Fractions,

Jlgar or common Fractions are fo I. call'd, because they were vulgarly Common or commonly made Ufe of, before that why focal decimal Fractions were invented and led. made known.

2

that The great

Difference

mon Fra

The great Difference between common and decimal Fractions lies in this, the denominative Values, or in one between Word, the Denominators of decimal Fra- Decimal &tions (like as of Integers) are known by and comthe Places of the decimal Figures, and etions, proceed regularly in a like Proportion; wherein whereas the Denominators of common Fractions are not to be known by the Places of their Figures, forafmuch as they proceed not in any regular uniform Proportion.

it lies.

Hence, in the Notation of common The De3. Fractions it is requifite, to write down nominanot only their numerative Values or Nu- tors of merators, but alfo their denominative Fractions F

common

Values are to be

writ
down.

Ch. VIII Values or Denominators.

For Inftance, 2 tenth Parts are by a common Fraction denoted ufually thus, ; whereas the fame is express'd by a decimal Fraction thus, .2, namely, (as has been above obferv'd,) the Place of the Decimal 2 being known to be the first Place of Decimals, thereby it is known alfo, that the faid 2 denotes 2 Tenths. In like manner, 2 hundredth Parts are express'd_by a common Fraction thus,, and 2 thousandth Parts thus,, whereas the former is exprefs'd as a decimal Fraction thus, .02, and the latter thus, .002: Namely, the decimal Figure 2 standing in the former Fraction in the second Place, is known thereby to denote 2 hundredth Parts; and in the latter Fraction standing in the third Place, is known thereby to denote 2 thoufandth Parts. Hence, what is exprefs'd by the common Fractions, and, and, is exprefs'd much fhorter by the Decimal ,222. And this fhorter Way of Notation by Decimals, than by common Fractions, is one Reason which has made the Ufe of decimal Fractions be fo generally preferr'd, to the Ufe of common Fracti

ons.

But

But that, wherein decimal Fractions Ch. VIII.

The Excel

Fractions

wherein it

chiefly excell common Fractions, is this, 4. that decimal Fractions (by Reason of their Denominators proceeding regularly lency of in the like Proportion, and fo being de- decimal noted by their Places, as are the Deno- above minators of Integers) are work'd after the Common, fame Manner as Integers; whereas com- chiefly mon Fractions can't be fo work'd in ma- lies. ny Cafes, (namely, as often as they have different Denominators, which proceed not regularly in a like Proportion); but must be first reduc'd to one and the fame common Denominator.

5.

Fractions

nominati

gers; ef

As often as common Fractions have the fame Denominators, they may be Common work'd as whole Numbers, and fo con of the tain no Manner of Difficulty, as fhall be fame Deshewn in the following Examples. Only on, may it may be of Use first to observe here, he work d that, (whereas the common Way of wri- as Inteting common Fractions, is to place the pecially, if Denominator under the Numerator with writ after the Method a Line between, which occafions fome herefhewn. seeming Difference between the Operations of Integers, and common Fractions of the fame Denomination; in order to take away even this feeming Difference,) it is very advisable to write common Fractions, as we write Numbers of feveral external Denominations, that is, to F 2 place

Ch. VIII. place the Denominators at the Head or Top of the Numerators of their refpeEtive common Fractions. Namely, as we denote two Shillings and fix Pence

S.

d.

thus, 2 and 6, so it seems better to denote the fame by common Fractions thus, 220. viz. of a Pound, and 6, viz. of a Shilling, than thus (as ufually)

, and. For the former Way being the fame, whereby Integers of feve ral external Denominations are denoted, hence common Fractions being exprefs'd after the fame Way, the Working of these will more appear to be agreeable to the Working of those, than if the common Fractions were exprefs'd the common Way. However, to comply with Cuftom, the common Way of Expreffing and Working common Fractions fhall not be altogether here omitted, but plac'd by the Side of the other Way.

Addition