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nincompoop
 one year ago
what is not correct about cross multiplication?
nincompoop
 one year ago
what is not correct about cross multiplication?

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Empty
 one year ago
Best ResponseYou've already chosen the best response.1as opposed to dot multiplication? :P

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.2okay, we teach or use the phrase crossmultiply without really showing why it works and even tho it appears to violate one of the key rules in maintaining an equation.

Empty
 one year ago
Best ResponseYou've already chosen the best response.1honestly I don't even know what cross multiplication is anymore, could you explain it

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.2same here... HAHA but here's the gist that I have so far gathered.

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440547770891:dw

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.2we have this fundamental rule about keeping an equation by performing the same operation we did on one side to the other side

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440547862839:dw

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.2it seems trivial at first, but I think this minor thing compounds many problems.

Empty
 one year ago
Best ResponseYou've already chosen the best response.1yeah 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
 one year ago
Best ResponseYou've already chosen the best response.1yeah, probably why I forgot what cross multiplying is because it's literally a waste of a concept haha

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.2I 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
 one year ago
Best ResponseYou've already chosen the best response.0The main issue I would foresee with it is in some cases like for the equation \(\dfrac{1}{x}=\cdots\), crossmultiplying can mislead you into thinking that that \(x=0\) might be a valid solution, which isn't good for obvious reasons.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.0cross multiplication is literally how you define rational numbers usually

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a rational number is an element of the quotient of \(\mathbb{Z}^2\) by the equivalence relation \((a,b)\sim(c,d)\Leftrightarrow adbc=0\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so \(\mathbb Q=\mathbb Z/\sim\) and we denote the equivalence class \([(a,b)]\in\mathbb Q\) as \(\frac{a}b\)
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