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

1. Empty

as opposed to dot multiplication? :P

2. nincompoop

lollll

3. 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.

4. Empty

honestly I don't even know what cross multiplication is anymore, could you explain it

5. nincompoop

same here... HAHA but here's the gist that I have so far gathered.

6. nincompoop

|dw:1440547770891:dw|

7. nincompoop

we have this fundamental rule about keeping an equation by performing the same operation we did on one side to the other side

8. nincompoop

|dw:1440547862839:dw|

9. nincompoop

it seems trivial at first, but I think this minor thing compounds many problems.

10. 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.

11. Empty

yeah, probably why I forgot what cross multiplying is because it's literally a waste of a concept haha

12. 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

13. 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.

14. nincompoop

correct

15. 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).

16. anonymous

cross multiplication is literally how you define rational numbers usually

17. anonymous

a rational number is an element of the quotient of $$\mathbb{Z}^2$$ by the equivalence relation $$(a,b)\sim(c,d)\Leftrightarrow ad-bc=0$$

18. anonymous

so $$\mathbb Q=\mathbb Z/\sim$$ and we denote the equivalence class $$[(a,b)]\in\mathbb Q$$ as $$\frac{a}b$$