Emerald Heart

Ok, you start with prime factorization again. Then look at the primes that are in common, and not in common. You want both fractions to share the same primes in their denominators. So if the first fraction has a prime (in the denom) that the second does not, then multiply the second fraction by (a/a), where a is that prime that the second fraction doesnt have. Remember it is legal to multiply anything by (a/a)= 1 because you multiolication by 1 doesn't change the number. Do this for all the primes that the second fraction doesnt have. Then switch roles, and do it for the first fraction

11/10 = 11/(2*5) first fraction call it A

10/15 = 10/(3*5) second fraction call it B

We see that A and B share 5 in their denoms, so thats good. But A has 2 that B does not. We want to put a 2 in Bs denom. Multiply B by (2/2)

B*1=B*(2/2) = (10/(3*5) ) * (2/2) = (2*10)/(2*3*5)

Anything else in A that B is missing? No, so now swith roles. B has 3 that A does not have. So multiply A by 1=3/3

A=A*1= A*(3/3) = ( 11/(2*5)) * (3/3) = (3*11)/(2*3*5)

Now A and B have the same denoms

Note that if A = 11/(2*5*5)

and B= 10/(3*5)

A has an extra 5 that B does not have, so you have to give B that extra 5 using the same process. The powers of the prime must match. Basically, the denoms must be exactly the same, same number of each type of prime.