first you want to simplify all of the stuff that is being added because it is in parenthesis. to do this you need to get a common denominator. looking at the prime factorization of the denominators we see that 27 has a prime factorization of 2*2*2, 192 has a prime factorization of 2*2*2*2*2*2*3, and 512 has a prime factorization of 2*2*2*2*2*2*2*2*2. therefore the common denominator should be 2*2*2*2*2*2*2*2*2*3*3*3 (13824). now we have to get the three numbers to have the same denominator so: we multiply 1/27 by 512/512 to get 512/13824we multiply 11/192 by 72/72 to get 792/13824we multiply 343/512 by 27/27 to get 9261/13824now we add the tops so 512+792+9261=10565.now we have reduced the problem to (6/5)/(10565/13824).when you divide fractions you are really just multiplying by the reciprocal. so we can say (6/5) times (13824/10565). you multiply across to get 82944/52825which in decimal form is roughly 1.570
