Hi, Monica.

When you "add" a positive and negative number, you actually find the difference of the two numbers, then keep the sign of the larger value.

In this case, we will subtract the two numbers and the answer will be negative because 17 5/9 is larger than 14 4/5.

To subtract the fractions, you have to find a common denominator, a number that is a multiple of both 9 and 5. The smallest number you can use is 45.

-17 5/9 = -17 25/45

14 4/5  =  14 36/45

You can't subtract 36/45 from 25/45, so you have to regroup or borrow from the whole number. One whole is 45/45, so:

-17 25/45 = -16 25/45 + 45/45   which is     -16 70/45

Now your problem is:

-16 70/45

 14 36/45            

You can subtract that and get  -2 34/45 and this cannot be simplified further, so your answer is  -2 34/45.

Hope this helps!

Kathye