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In an equation

$ 4 = \frac{32}{ 8}$

You can exchange the denominator on the right side with the numerator of the left side.

$ 8 = \frac{32}{4}$

Is there a name for this action / process?

Thanks a lot in advance

vidyarthi
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Wolfgang Adamec
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  • Use MathJax while writing next time-http://meta.math.stackexchange.com/questions/5020/tex-latex-mathjax-basic-tutorial-and-quick-reference – vidyarthi Nov 26 '16 at 06:29
  • Out of curiosity, why have people decided this process needs a name? – mrob Nov 26 '16 at 07:14
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    @mrob, depending on what you mean, I'd argue that people haven't decided this process needs a name. – Mark S. Nov 26 '16 at 07:22

1 Answers1

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I'm not sure what exactly you're asking for, so here are two guesses:

1: The operation done to the equation

You have:

  • "multiplied both sides of the equation by $8$ and then divided both sides by $4$"
  • or "divided through by $4$ and then multiplied through by $8$"
  • or simply "multiplied both sides of the equation by 2"

For example, $4=\dfrac{32}8\to4*8=32\to8=\dfrac{32}4$.

2: The idea behind that operation

You may be thinking about/using the "commutative property of multiplication" to change the division sentence you're writing. Since $4*8=8*4=32$, you can write either division sentence and they're both valid.

On "cross-multiplication"

I don't think "cross-multiply" should be used for this operation (as a couple have suggested in deleted answers). Since 4 ends up in a denominator, it's not getting multiplied. Additionally, this is not an example of the three different things people usually call "cross-multiplication"; for more details, see Nix the Tricks

Community
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Mark S.
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  • thanks for your comment. I thought that 4 is multiplied to 1 in the fenominator and 8 to 1 in the numerator. – vidyarthi Nov 26 '16 at 07:28
  • @vidyarthi That would certainly involve two multiplications, but would be a (new?) meaning that isn't one of the most common two/three for the phrase. – Mark S. Nov 26 '16 at 07:29