How do you get the answer to 7 3/5 / (2 1/5 - 14/15)?

Question

The answer to the problem is 6 but I can't figure out how to arrive at the answer.  Please help.

comeon Level F 98a

Answer 1

The first thing I would recommend would be to change all the mixed fractions into improper fractions.

So 7 3/5 = (7*5)+3 = 38/5

2 1/5 = (2*5)+1 = 11/5

and 14/15 is fine as is.

So the denominator becomes 11/5 - 14/15. You need a common denominator. If you multiply the first fraction by 3/3, you get 33/15. So 33/15 - 14/15 = 19/15.

When you divide fractions, you actually multiply the top by the reciprocal of the bottom so you end up with 38/5 / 19/15 = 38/5 * 15/19.

Now you can reduce. 38 and 19 both have 19 as a factor so 38 becomes 2 and 19 becomes 1. Also, 5 and 15 have 5 as a factor so 5 becomes 1 and 15 becomes 3.

38  x   15    =  2  x  3    =   6   =     6
5         19        1      1         1