It's always a useful thing to know how to compare fractions using different methods. That way, you can get the answer in seconds (most likely).
Everyone knows how to cross multiply. That times that, and this times this, but it may not be the most efficient way. For instance, if the question asks for the greater fraction, and the choices are 9/16 and 3/8, you know that 9/16 is more that 1/2 (which is 8/16), and 3/8 is less than 1/2 (which is 4/8), so instantly, you know that 9/16 is greater, without having to do the tedious multiplying. This method is actually also called reasoning. Sometimes, you don't have to go for halves; the other benchmarks like 1/5 and 1/3 would work as well.
Sometimes, when reasoning doesn't work, and cross multiplying is just too complicated, determining the LCD might work. If the question was: Which is greater: 369/900 or 87/300, you can easily find out is greater by simply determining the LCD (sometimes it doesn't have to be the least common denominator). I know that 900 has 3 300s in it, so 300x3=900. However, you have to do the same thing to the numerator, and 87x3=261. So now, it's 261/300 and 369/900. All you've got to do is state the obvious: 369/900 is greater. (Ta-da!)
Sadly, there are times when there's no way of "cheating", and you'll have to do the traditional cross multiply. Fortunately, if you knew the easier "cheating" ways, that wouldn't be often.
you explained well how to use different methods
ReplyDeleteThis is awesome! I really liked how you included a bunch of examples to explain your point. I also really liked how you explained each method thoroughly, so the reader really understands how to do the skill/method.
ReplyDeleteI like the way you made your explanation sound interesting.
ReplyDeleteIt was easy to understand, and it was fun to read!