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Q. Now tell mee what use fractions are of in Arithmetick?
A. They are of like use with whole numbers.
Q. And are there the same kinds or species in fractions, as in whole numbers?
A. Yea, only some put a dif∣ference in the order of teaching them, that the easiest may bee first taught.
Q. But what mean you by species?
A. I mean several kindes of working, or several Rules, as some call them.
Q. Then rehearse the order of Rules as they are taught.
A. Numeration, Reduction, Multiplication, Division, Ad∣dition, Substraction.
Q. What sheweth Numeration in fractions?
A. It sheweth how to set down, or express any fraction, part or parts of an unite.
Q. how is that done?
A. It is done by setting down two numbers one over another, with a line drawn betwixt them, whereof the lower number sig∣nifieth how many parts the whole unite is divided (or sup∣posed to bee divided) into; and
the uppermost number sheweth how many of those parts the fraction contains.
Q. How are those two numbers called?
A. The uppermost, (or num∣ber above the line) is called the numerator, and the other below the line is called the denomina∣tor.
Q. Shew an Example or two to explain this.
A. Three quarters is set down, with a 4 under the line, signifying the number of parts the unite is divided into; and 3 above the line, shewing how many of those parts the fraction expresseth or signifieth.
Q. Give another Example.
A. Five seventh parts is ex∣prest by 5 above the line, and 7 below it, thus 5/7.
Q. Is the greatest number al∣waies set lowest?
A. Yea, in such as are proper fractions.
Q. Are there then any im∣proper fractions?
A. There are sometimes whole numbers or mixt num∣bers exprest in form of fra∣ctions, which are not properly fractions, because a fraction is alwaies lesser than an unite, but these are either equal to, or grea∣ter than an unite.
Q. Explain this by an Example or two.
A. Two halfs 2/2, three thirds 3/3, five fifths, 5/5, &c. are whole unites, onely exprest like fra∣ctions; also nine quarters is a mixt number exprest thus, 9/4, and signifies two unites and a quar∣ter more.
Q. Why are such exprest like fractions?
A. For aptness, or for ease in working.
Q. What else is considerable in Numeration?
A. This, that as numbers in∣crease infinitely above an unite, so fractions decrease or grow less infinitely under an unite.
Q. I remember you mentioned decimal fractions before, how are such exprest?
A. They are exprest by an u∣nite, and 1, 2, 3, 4. or more ci∣phers below the line, according to the number of places, or parts the fraction is exprest in, and with figures and ciphers a∣bove the line, expressing the number of such parts that the fraction contains.
Q. Make this plain by an
Example, two or three.
A. One half or 5 tenths is ex∣prest by 5 above the line, and an unite with one cipher, signi∣fying ten or tenths under the line thus 5/10.
Secondly, 1/4, or 25 hundreds, is writ with 25 above the line, and 100 under the line thus 35/100.
Q. How set you down 75 thou∣sand parts?
A. Thus with a cipher, a 7, and a 5 above the line, and an unite and three ciphers below the line, 075/1000.
Q. Are decimals alwaies ex∣prest thus?
A. They are often exprest by their numerator, onely se∣parated from the unite place by a prick, and the denominator is understood to consist of so ma∣ny
ciphers, as there are places in the numerator, and an unite before them to the left hand.
Q. Shew mee one Example or two.
A. First, Five hundreths is writ with a cipher, and a 5 thus 05, where 100 is understood for denominator.
Secondly, 34 ten thousand parts is exprest thus 0034, where 10000 is understood for denominator.
Q. Is there any thing more herein to bee noted, before wee leave numeration?
A. Yea, that not an unite only may bee divided infinitely into fractions or parts, but also any of those parts or fractions may bee divided also infinitely into other parts, called fractions of fractions, and those also a∣gain
subdivided infinitely, &c.