to a fimple Examples. 1. Let it be required to reduce of of Fraction of the fame Value. First 3 x I xa= 34 the new Numerator. Secondly bx cxdbed the new Denominator. bxcx за Confequently-bed is the new Fraction required. a+b 2. Let it be required to reduce f d of of of 1 to a fingle Fraction of the fame Value. :ab:xIxIxq=ag + b g the Numerator. fxic+d: x pxr = fcpr+fdpr the Denominator. Confequently ag+bg fcpr+fdpr is the fimple Fraction required. CHA P. III, and IV. Addition and Subtraction of Fractional Quantities. W Hat hath been done by the Rules in the foregoing Chapter, is chiefly to fit and prepare Fractions of different Denominations for Addition, or Subtraction as Occafion requires; wiz. 1. If the Fractions to be Added, or Subtracted, be Compound ones, they must be reduc'd to fimple or pure Fractions (by Sect. 4. of the foregoing Chap.) 2. If they have not a common Denominator, they must be reduc'd to Fractions of the farne Value that will have a common Denominator (by Sect. 1. Chap. 2.) That being done, Addition and Subtraction are thus perform'd. Kule. Add or Subtract their Numerators, as Occafion requires; and under their Sum or Remainder fubfcribe the common Denominator, with a Line between them. Examples 4. Suppose it was required to add b,f- and Firft, the Fractional Parts are 웅, - 옴 and + 1; Secondly, dxpxp=dpp is the common Denominator, Thirdly, expx p = c pp; - q xd xp = qd p, and cxdxpcdp are the Numerators; Wherefore CPP gdp + cdp dpp gd + cd dp (by Sect. 3. Chap. 2.) is the Sum of the Fractional Parts; confequently the Sum required, is b+f+8+ cp. qd + cd dp d 5. Again, Let it be required to add of to dpb d : Confequently bp 2d-4 is qis bp First Ixd=d; Secondly bxp=bp; therefore is (by Sect. 4. Chap. 2.) = the Sum required. 4. d Let it be required to take 4 + 2/ Secondly, ap + d a+c qual to ly. and b+d are (by Sec. 1. Chap 2.) e bap+bd+dap -- dd and pa+pc Confequently pa+pe-bap-bd-dap- dd pb+pd mainder required, 5. Again, Let it be required to take of 8a Note, The Univerfal Method of Adding and Subtracting either whole or fracted Quantities is by + and respectively. F CHAP. V. Multiplication of Fractional Duantities. Irft prepare mix'd Quantities (if there be any to be Multiplyed) by reducing them to Fractions of the fame Denomination (by Sect. 1. Chap. 2.), and whole Quantities by Subfcribing an Unit under 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. Examples. 응-25 3. Suppose it was required to Multiply 24+25 by 36+4c. These prepar'd for the Work, as above directed, will stand thus, N.B. Any Fraction is Multiplyed by its Denominator by caft ing off, or taking away the Denominator. Firft, bx:ab: xf=baf+bbf, the Numerator, Sec. cxb+c: x1 = cb + cc, the Denomin. the Product required. of, or CHAP. CHAP. VI. Division of Fractional Quantities. HE Fractional Quantities being prepar'd, as directed in the laft Chapter; then, Kule. 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 required. thus, Or thus ab) abd (abcd = (by Seff. 3. Chap. 2.) abd cf I |
