And the Quotient is x1, by which I Divide the afore faid Divilor thus, Wherefore x-I is the greatest common Divifor fought, by which the given Fraction will be reduc'd to Se&t. by this If by proceeding in the foregoing Manner, you find the great eft common Divifor to be; then the Fraction is in its leaft Terms already. Note, Some Fractional Quantities are reduc'd to their leaft Terms by Dividing the Numerator and Denominator feverally, by the greateft common Measure of their feveral Members; thus 49ed42cd+ 294bd 35qbd +28dc is reduc'd to 7e 6c +42b 596 + 40 by Dividing the given Numerator and Denominator feverally by 7d, the greatest common Divifor of their feveral Members. Sect. 4. To reduce a Compound Fration, to a Simple one of the fame Value. Kule. Multiply the Numerators by each other continually for a new Numerator, and the Denominators continually for a new Denominator; fo this new Fraction is that required. Examples. 1. Let it be required to reduce 2 of of to a Simple d 34, the new Numerator. is the new Fraction required. 2. Let it be required to reduce to a Single Fraction of the fame Value. I P a + b x 1 x I x qaq + bq, the new Numerator. fx c + d x pxr=fcpr + fdpr, the new Denominator. Confequently ag bg aqbq is the Simple Fraction required. fcpr fdpr CHA P. III. and IV. Addition and Subftraxion of Frational Quantities. W Hat bath been done by the Rules in the next foregoing Chapter, is chiefly to fit and prepare Fractions of different Denominations for Addition, or Subftraction, as occafion requires; viz. 1. If the Fractions given to be added, or Substracted, be Compound ones, they must be reduc'd to Simple or Pure Fractions (by Sect. 4. of the next foregoing Chap.) 2. If they have not a Common Denominator, they must be reduc'd to Fractions of the fame Value, that will have a Common Denominator (by Sect. 1. Chap. 2.) That being done, Addition and Substraction are thus perform❜d. Hule. Add or Subftra&t their Numerators, as occafion requires; and under their Şum or Difference, fubfcribe the Common Denominator. Suppose it was required to add b + +-2, and g+ into ว 2 and +. d P p Secondly, dxpxpdp, the common Denominator. Thirdly, 9-qd+cd dp cp2 → gdp + cdp dpp (by Sea. 3. Chap. II.) is the Sum of the Fractional Parts: Confequently the Sum required is ++8+ ep-gd + cd der required. Let it be required to take a First, a + is (by Sect. a. Chap. II.) 2. a + c ap+d b + d and and P pa + pc bap + bd + dap -† d3 Confequently pat pc - bap-bd-dap-d 3 I Again, Let it be required to take of 2 of b 4 of 3 of is (by Sect. 4. Chap. II)= a 36 from P apd P are (by Sect. 1. Chap. II.) respectively. pb + pd 8a And Note, The univerfal manner of Adding and Substracting either Whole, or Fracted Quantities, is by and respectively. CHAP. V. Multiplication of Fracional Quantities. Firft prepare mix'd Quantities (if there be any to be Multiplyed) by reducing them to Fractions of the fame Denomination. (by Sect. 1. Chap. II.) And whole Quantities by subscribing an Unit under each of them: then Kule. Multiply the Numerators together for a new Numerator, and the Denominators together for a new Denominator; then this new Fraction is the Product required. b Suppose it was required to Multiply 34 +2—25 by 36+46. These prepar'd for the Work as above directed, will stand thus, C X 3 6bac + 3bb 75bc8acc+4bc C N, B. N.B. Any Fraction is Multiplyed by its Denominator, by cafting off, or taking away the Denominator. of, or the First, bx a + b x f = baf +bbf, the Numerator Product required. T CHAP. VI. Division of Fractional Quantities. He Fractional Quantities being prepar'd as directed in the last Aule. Multiply the Numerator of the Dividend, by the Denominator of the Divifor, for a new Numerator; and Multiply the Denominator of the Dividend by the Numerator of the Divifor, for a new Denominator; fo this new Fraction, is the Quotient requi red. Thus ab abd (abde (by Seff. 3. Chap. 11.) of |