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What identity is this? (Division to multiplication )

  1. Nov 30, 2012 #1
    This isn't a homework help issue, I just want to know what identity(?) this is.

    a/b to ab

    or A^2/B^2 to (A^2)(B^2)
     
  2. jcsd
  3. Nov 30, 2012 #2

    Mark44

    Staff: Mentor

    There is no identity that converts a/b to ab, nor is there one to convert A2/B2 to A2B2.

    What you might be thinking of is this one:

    $$ \frac{a}{b} = a \cdot \frac{1}{b}$$

    In other words, dividing by a number b is the same as multiplying by the reciprocal of b (1/b).
     
  4. Nov 30, 2012 #3

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    Or maybe this one:$$
    \frac a {\frac 1 b} = ab$$
     
  5. Nov 30, 2012 #4

    rcgldr

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    Homework Helper

    Although this probably isn't what you're looking for, there is a way to implement division or more specifically 1/b by iterating multiplications and additions via Newton Raphson method, but this seems unlikely to be what you're looking for.

    For 1/b the iternation is:

    xi+1 = xi (2 - b xi)

    This converges quadratically. For integers, usually a table of bytes is used to get the initial approximation.
     
  6. Nov 30, 2012 #5
    Yea, thanks everyone. I thought that was possible, but obviously it's not lol.
     
  7. Dec 1, 2012 #6

    HallsofIvy

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    Yet another possibility: A/B= AB-1
     
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