What is the rule of thumb when converting an improper fraction to mixed number when the improper fraction can also be reduced?

Question

Supposed you have the improper fraction 60/8.  This can be converted to the mixed number by dividing first (resulting in 7 4/8) and then reducing to 7 1/2,  OR you can reduce first to 15/2 and then divide to get 7 1/2.  Is there a rule of thumb as to whether it is better to divide or reduce as your first step?  My sense is that dividing first is better so you don't have to reduce very large numbers, especially if presented with large fractions like 1750/32, but I was interested in what the accepted practice is?  Thanks!

Answer 1

Suppose (not supposed)!.

 

The best way, I believe, is to factor 60 and 8 so that you can cancel matching factors. You could go down all the way to primes, but in practice, with good understanding of the multiplication table, you would say 4(15) ÷ 4(2) and the fours would cancel, leaving you with 15/2, which I hope you would quickly turn into 7½.

 

I believe that's why so much emphasis is placed on factoring--THIS is one of the places where it pays off.