Doing fractions we were trying out NOT flipping the second fraction - and just divide the numerator of the first fraction by the numerator of the second and then similarly to divide one denominator by the other - and it worked! Even with simplifying the fractions, until...
*UNTIL both denominators were "the same" and "prime numbers".*
It seems that if both denominators are prime numbers AND the same prime numbers - then you CAN NOT simplify them - (when the same prime number is one of the numerators).
*Is there a rule somewhere in math regarding this?*
NOTE: We came across this when dividing
1 \ (1\3)
= (3/3) / (1/3)
If you cancel the first fraction numerator (3) with the second fraction denominator (3) the answer is 1/3 which is wrong as it should be 3.
If you flip the second fraction and cancel down the 3's and do it as multiplication its works!
*What's the connection between flipping the second fraction and simplifying it working?*
Granted, we are possible getting a little caught up in details. But we find this an interesting thing and can't quite get our heads around what's going on. Any help would be appreciated :)