Comparing fractions: LCM, prime factorization or decimal conversion?

[mathnerd]

I am wondering which is the "most official" way to compare unlike fractions: using LCM or prime factorization or doing a straightforward conversion to decimals. My DS knows all the three methods but prefers to convert to decimals because it is speedy for him. I am not sure if this is the most accepted way or if I should ask him to use the other methods.

[justasque]

Different problems need different solutions.  Math students should be able to compare fractions a variety of formal ways, including simplifying the fractions, plus shorthand mental methods (is the numerator more or less than half the denominator, as a quick gauge of whether the fraction is more or less than a half).  The more tools in the toolbox, the better.  Most people end up preferring one method over another for routine work, and that's ok.

 

ETA:  If a textbook is asking a student to use a specific method, they should use that method, as the textbook author is presumably asking for a reason.   Often more complex methods are first taught on "easy" problems that can be solved in a simpler way, because that way the student can "see" how the method works, before moving on to more complex problems for which the "new" method is often a better approach (or the "old" method just plain can't handle).  If the student uses the older, simpler method on these problems, they miss the opportunity to practice the new method on an easy problem and see how it compares to the old.  Students who are frustrated at being asked to do this ("But why do I have to do it this harder, new way when the old way is so much easier/better?") will often lose their frustration when this reasoning is explained to them.

[regentrude]

Depends entirely on the problem and whether you have a calculator available.

Converting to decimals is very slow if you have weird denominators and no calculator; you'd often be much better off just finding the common denominator.

For example, compare 7/12 and 5/9. The quickest would be to break the denominators into prime factors and express each as 36th.

[Arcadia]

The schools here use LCM which is prime factorization.  LCM/prime factorization comes in useful down the road for prealgebra and up.

 

Is he calculating decimals mentally or using a calculator?  Mine calculates decimals mentally for the fun of it but not in the context of math problems on comparing fractions.

[kateingr]

I was taught the cross-multiply method, which is terrible--it becomes just an arbitrary procedure for comparing fractions, with no meaning attached. 

 

What I like about both the common denominator and convert to decimal methods is that they both preserve the meaning of the fractions and are reasonably intelligible to kids. Either is good, but as others said, the common denominator method comes up over and over again in algebra. Decimals are often more useful for real-life applications. 

[MrSmith]

Isn't the 'cross multiply method' equivalent to the common denominator method?  To me 'cross multiply' seems a simplified version of 'common denominator'.

 

 

I was taught the cross-multiply method, which is terrible--it becomes just an arbitrary procedure for comparing fractions, with no meaning attached. 

 

What I like about both the common denominator and convert to decimal methods is that they both preserve the meaning of the fractions and are reasonably intelligible to kids. Either is good, but as others said, the common denominator method comes up over and over again in algebra. Decimals are often more useful for real-life applications. 

 

[kateingr]

Isn't the 'cross multiply method' equivalent to the common denominator method? To me 'cross multiply' seems a simplified version of 'common denominator'.

Yes, they're essentially the same procedure...but I cross multiplied for years without realizing what I was doing or why. Introducing it as "finding a common denominator" makes the procedure make a lot more sense...and if a child then realizes that she can dispense with the actual denominator, there's no harm done at that point.

[mathnerd]

Thank you. DS was doing all the division without a calculator (he is very good at mental math). I discussed this thread with him and now he realizes that when the denominators become more complicated (for e.g. comparing 8/91 and 7/86 etc. ) he is better off not converting them to decimals. He is willing to stick with the LCM method for now and use the decimal conversion for double checking his answers :)