In a jewelry store, rings makeup 5/9 of the inventory. earrings make up 4/15 of the inventory. how many times greater is the ring inventory than the earring inventory?

First let's make the denominators equal, so that we can compare the two fractions more easily.
To do this, we have to find a number that both 15 and 9 divide into. The smallest number that this can happen to is 45.

15 x 3 = 45
9 x 5 = 45

So we have to multiply 15 by 3 in order to make it into 45. If we're changing the denominator, the numerator must change too, by the same multiplier.

4 ---> 4 x 3 = 12
--
15 ---> 15 x 3 = 45

4/15 = 12/45

5 ---> 5 x 5 = 25
--
9 ---> 9 x 5 = 45

5/9 = 25/45

To find how many times more rings there are, we divide 25 by 12. As the result of this isn't an integer, we leave the answer as a fraction:

There rings inventory is 25/12 times bigger than the earrings inventory.