A New Introduction to the Science of Algebra

A New Introduction to the Science of Algebra

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1836 edition. Excerpt: ...a2--62 a3--a62 a2--62 ST X a = ST" ' r-2a-' a"d ax2 ab--6s" Jto reduce fractions of different denominators to equivalent fractions having a common denominator. Rule. (25.) Multiply all the denominators together for a common denominator, and each numerator into all the denominators, except its own, for new numerators; or, Find the least common multiple of all the denominators; this will be the common denominator. For the numerators, divide the common denominator, thus found, by each particular denominator, and multiply the quotient by the numerator. Examples. 1. Reduce-and-to a common denominator. z x x X z = xz, the common denominator; ax and bz the numerators. The fractions reduced, are, therefore, ax, bz--and--. xz xz 2. Reduce-, -. and-to a common denominator. co e ade bee. c2d cd? cde cde' 3. Reduce rr Tt and 4o to a common denominator. ax Ac. Oac 9bx, 2icdx Ans.----, ---and---. OCX OCX OCX 4. Reduce?, -r-and 2b +---to a common denominator. 6 4 b 206 18a6 4862 + 72a Ans-MB' wand "247;. 1 2a2 2a2 + 62 5. Reduce s.-r--and--=--to a common denominator. 3 4 a + 6 4a+ 46 6a2 + 6-26 24a2 + 126' Ans' 12a + 126' 12a + 16 12a +126' 6. Reduce-r-- Tt--o and--to a common denominator. 4a2 Sa' 'In In this example, the denominators have a common multi Sle, less than their continued product; and if we would reuce the fractions to their least common denominator, it is necessary to find this least common multiple. In algebraic fractions, this can generally be done by inspection, as in this example it is easy to see that 12a2 is the least common multiple of the denominators. But it may also be found by a process, analogous to that given in arithmetic (Aiith. 38), for finding the least common multiple of several numbers. Thus, 2a...show more

Product details

  • Paperback | 60 pages
  • 189 x 246 x 3mm | 127g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236574532
  • 9781236574534