... cross multiplying should NOT be used. Have students find the LCM when comparing and ordering fractions so that they will have that practice when they use it to add and subtract fractions. Another reason for the LCM is the types of problems that involve buying the bag of hot dogs and hot dog buns so that there are none left over.
As far as reducing using the GCF, I always tell them that if the fraction can be reduced, its usually with 2, 3, 5, 7 or 11. I have them try those first. GCF is also used for the types of problems such as: Amy has 12 lollipops, 6 pieces of gum, and 9 jawbreakers. If she wants to place the same number of pieces of each kind of candy, what is the greatest number of baggies she can use?
Shortcuts are quick fixes. If the students doesn't understand why it works, they will suffer when it comes to learning new material in the later grades. Don't make it harder for them than it already is (with standardized testing and all).
As for those of you that say, when are we ever gonna have to use this? Math builds muscle in the brain. The more you think, the more you learn. Its all about critical thinking skills and processes.
Why do you think so many students HATE math. It makes them THINK!