Fraction Comparison Reflection

      Today in math class we learned a variety of ways to compare fractions. Their are three ways, one is to reason, another is to lower common denominator, and finally cross product/cross multiplication. 

      The first one is to reason. Well, when is it a good time to use reasoning? It is good to use reasoning when the fractions are easy, simple, and obvious.  

 An example is: 13/24     and    30/50
  Well, we know 24 divided      50 divided by 2=25. 30-25=5. 
by 2= 12. 13-12=1. So 13/24 so which one is greatest is obvious.
is very close to one half. 
          So, the greatest factor is 30/50.
Another method is, the LCD ( lower common denominator). When is it a good idea to use LCD? It is good when the lower common denominator has the higher denominator is one of their multiple. Basically saying when you have common denominators.

 An example is: 2/5     and           4/20    
   This is the lower common        Since this is higher, we don't have to do           denominator so we will put         anything.  When we get the other fraction 
attention to this on.                    then we see the difference. I am doing the 
Let's think, what * 5=                greatest. 
20. Well how much does
5 go into 20. 4 times,
so 5*4=20. We always have
to do the same to the top as
we did to the bottom. So, the
top is 8. The new fraction is 
8/20.                                   
                                             
 Now that we have the two fractions 
2/5 (8/20) and 4/20 we can figure 
which is greatest. Well, 8 is greater then 4 so,
2/5 is > then 4/20.
Finally, cross product/cross multiplication. How do we use cross products at the right time? It is good when you are having a hard time, there is no common denominator, and you can't solve it in your head. 

 An example is: 2/8     and    3/9
                        We have to cross and multiply.

2         3
8   and 9   Then we do 9*2 because cross product, and that's how you do it. 9*2=18. Then we do it opposite, so 8*3=24.  So 3/9 has 18 and 2/8 have 24. 24 is greater (>) then 18.

                             So, 2/8 is > the 3/9.

 I learned a lot from these methods and I hope you did too. Now, I can use these and make my life a lot easier to compare fractions. 

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