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I homeschool and I love the fun side of this theory, but it is dangerous to use it as an exclusive means to solving fractional equations. They WILL need to know how to determine common denominators later in school. Another danger, that would apply to my son, is if he thought he knew a short cut he would apply it all the time, even for problems that would need done the traditional way. He will do anything to make his math "easier", hence he would only remember the "short cut". I'm no mathematician; I too struggle with, but the simpler way would make it more difficult later. I agree it could be used after fractions are mastered as a quicker solution.
Always good to have several strategies on hand for someone who just doesn't quite understand
I don't think you do any favors by teaching a trick without the real understanding. And, it takes repetition, again and again.
It reminds me of my school days.
Adding and Subtracting Fractions
Adding and subtracting Fractions
Butterfly method for adding subtracting fractions.
Adding and subtracting fractions with unlike denominators
Waldorf ~ 4th grade ~ Math ~ Fractions ~ art
Fraction Getting to Know You