Using a factor tree to reduce a fraction? Good Idea?I am trying to figure out how one reduces 180/100 to 9/5My factor tree for 180 is 90 *2 - 30*3 -5*6 - 2*3Thus my ' numbers are 2*3*5 = 30Maybe I have totally forgotten how to reduce a fraction like this, however, what method should I use if I can not see it automatically?

Question

Using a factor tree to reduce a fraction? Good Idea?I am trying to figure out how one reduces 180/100 to 9/5My factor tree for 180 is 90 *2 - 30*3 -5*6 - 2*3Thus my &#039; numbers are 2*3*5 = 30Maybe I have totally forgotten how to reduce a fraction like this, however, what method should I use if I can not see it automatically?

Trey Ross · Accepted Answer

You should use method such that a number is divisible by 2 if it&#039;s last digit is even,it&#039;s divisible by 3 and 9 if their sum of digits is divisible by 3 or 9(in that order)  180  =  2  ⋅  90  =      2    2    ⋅  45  =      2    2    ⋅  3  ⋅  15  =      2    2    ⋅      3    2    ⋅  5    100  =  2  ⋅  50  =      2    2    ⋅  25  =      2    2    ⋅      5    2                        2        2            ⋅              3        2            ⋅      5                      2        2            ⋅              5        2              =            3      2        5    =      9    5

Fletcher Hays · Accepted Answer

By the Euclidean algorithm    (  180  ,  100  )  =  (  80  ,  100  )  =  (  80  ,  20  )  =  (  0  ,  20  )  =  20.  .  Cancel this gcd.Euclid&#039;s algorithm is very efficient, so generally this method will be quickest.

Using a factor tree to reduce a fraction? Good Idea? I am trying to figure out how one reduces 180/

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