Does cross multiplication work on any fraction?

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maxmac97

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Does cross multiplications work on any fraction that has different denominators? I have tryed it on some fractions and it works and I tryed it on others and it didn't work. if the number on the end is even you divide by 2 to reduce it and if it is odd you divide by 3 or 5 right ?
 
"Cross multiplication" doesn't work on any one fraction! You need two fractions: if \(\displaystyle \frac{a}{b}= \frac{c}{d}\) then, multiplying on both sides by b, \(\displaystyle a= \frac{bc}{d}\) and then, multiplying on both sides by d, \(\displaystyle ad= bc\).
 
maxmac97 said:
Does cross multiplications work on any fraction that has different denominators? I have tryed it on some fractions and it works and I tryed it on others and it didn't work. if the number on the end is even you divide by 2 to reduce it and if it is odd you divide by 3 or 5 right ?
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Since one fraction can't have "different denominators", I assume you are talking about using it on pairs of fractions. But I've seen the term "cross multiplication" used in at least two valid ways (and other wrong ways!); so we really need to see your examples in order to be sure what you are asking about, and what it is that went wrong.

The rest of what you say, also, doesn't make much sense by any interpretation I can think of. Please be as complete as you can in explaining your question.
 
I would NEVER cross multiply unless I was trying to decide which of two fractions is larger--and even then I would more often then not use other tricks I know.

In solving x/3 = 4/5 do not cross multiply! It is the most inefficient thing in mathematics I have ever seen! You move (in this case) the 5 to the numerator and then move it back to the denominator!! HallsofIvy was right on the mark when stated to do cross multiplication in two steps. In fact after Halls 1st step you have the solution as x = (3*4)/5 = 12/5.

Just use half cross multiplication by just moving the 3 and not the 5!
 
5*4 = 20
20*3 = 60
60*2 = 120
120*1 = 120

Above laborious process replaced by symbol !

Please google "introduction to factorials"
 
Denis said:
5*4 = 20
20*3 = 60
60*2 = 120
120*1 = 120

Above laborious process replaced by symbol !

Please google "introduction to factorials"
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I thought it would be
1*2=2
2*3=6
6*4=24
25*5=120
Hmm we got the same answer. What a coincidence.
 
Jomo, what would you do if you had to solve, say, \(\displaystyle \frac{x+2}{x-3} = \frac{x-4}{x+1}\) ?
 
Harry_the_cat said:
Jomo, what would you do if you had to solve, say, \(\displaystyle \frac{x+2}{x-3} = \frac{x-4}{x+1}\) ?
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Wait n' see: his answer will be: cross-multiplication, of course :)
It sure is mine!

Anyhow, he'll be in the corner for "25*5=120" minutes....
 
I'd observe that the denominators have no common factor, so that the LCD is their product, and then cross-multiply knowing that the result will be the same as the slightly more time-consuming process of explicitly multiplying by the LCD and canceling. In other words, I'd cross-multiply, but not blindly, knowing that if there were a common factor, that would lead to considerably more work.

Of course, I'm still waiting for maxmac97 to explain the last sentence of the question, which makes me very curious.
 
Dr.Peterson said:
I'd observe that the denominators have no common factor, so that the LCD is their product, and then cross-multiply knowing that the result will be the same as the slightly more time-consuming process of explicitly multiplying by the LCD and canceling. In other words, I'd cross-multiply, but not blindly, knowing that if there were a common factor, that would lead to considerably more work.

Of course, I'm still waiting for maxmac97 to explain the last sentence of the question, which makes me very curious.
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You are experienced with this type of math so you can cross multiply. However a student who isn't all that strong should not (ever)cross multiply. It seems that when a student does not know what to do they cross multiply. When they have an expression, they cross multiply. I think that it is best if students never hear/learn the term cross multiply. Just like you, I have seen students make mistakes all the time by cross multiplying, so why teach it to them if they do not need it?
 
I wasn't saying anything about how to teach the subject; I was responding to what you said you yourself would do, by demonstrating how a good thinker thinks.

As it happens, though I more or less agree with what you say, I do teach about cross-multiplication (not as a primary method), because my students have already learned it (too well, as you say) elsewhere. I don't think I can excise it from their minds and prevent them from ever doing it, so I might as well teach them the right way to think about it, so they'll use it only when appropriate (I hope).

One could argue, also, that we shouldn't deprive good students of a good shortcut just because others will use it incorrectly. Why not teach them all how to think well? Maybe then they can all become good at it.

But I have no desire to argue over teaching methods. That's not what I'm here for.
 
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