nincompoop
  • nincompoop
what is not correct about cross multiplication?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Empty
  • Empty
as opposed to dot multiplication? :P
nincompoop
  • nincompoop
lollll
nincompoop
  • nincompoop
okay, we teach or use the phrase cross-multiply without really showing why it works and even tho it appears to violate one of the key rules in maintaining an equation.

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Empty
  • Empty
honestly I don't even know what cross multiplication is anymore, could you explain it
nincompoop
  • nincompoop
same here... HAHA but here's the gist that I have so far gathered.
nincompoop
  • nincompoop
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nincompoop
  • nincompoop
we have this fundamental rule about keeping an equation by performing the same operation we did on one side to the other side
nincompoop
  • nincompoop
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nincompoop
  • nincompoop
it seems trivial at first, but I think this minor thing compounds many problems.
Empty
  • Empty
yeah I agree, it's teaching pattern matching for no reason, just like FOIL sucks. It's just distributing. Anyone who can see 2*3=6 should be able to see (1+1)*(1+2)=6 will have to be true too.
Empty
  • Empty
yeah, probably why I forgot what cross multiplying is because it's literally a waste of a concept haha
nincompoop
  • nincompoop
I was thinking about this a while back and then I stumbled on a problem that just reminded me that this needs to be addressed. http://openstudy.com/study#/updates/55dcf68ee4b03aeb8dc1a352
anonymous
  • anonymous
The main issue I would foresee with it is in some cases like for the equation \(\dfrac{1}{x}=\cdots\), cross-multiplying can mislead you into thinking that that \(x=0\) might be a valid solution, which isn't good for obvious reasons.
nincompoop
  • nincompoop
correct
anonymous
  • anonymous
I suppose there's no issue if you're dealing with concrete rational numbers, and perhaps it's useful as a sort of mnemonic device. You just have to be careful (as anyone doing math should be).
anonymous
  • anonymous
cross multiplication is literally how you define rational numbers usually
anonymous
  • anonymous
a rational number is an element of the quotient of \(\mathbb{Z}^2\) by the equivalence relation \((a,b)\sim(c,d)\Leftrightarrow ad-bc=0\)
anonymous
  • anonymous
so \(\mathbb Q=\mathbb Z/\sim\) and we denote the equivalence class \([(a,b)]\in\mathbb Q\) as \(\frac{a}b\)

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