What must be added to negative nine and eight tenths to yield negative fifteen and four hundred sixty five thousandths?

This is a bit of a tricky one since we are working with thousandths as the denominator. First, we want the common denominator, so we can multiply 8/10 by 100 to get 1000 as that denominator. This gives 800/1000. Next, let's solve the whole numbers. You must add a negative number to a negative number if you want a smaller answer, so we add -5, which means we now have -14 and 800/1000. Now, we subtract absolute value of the larger negative, or our goal, -15 and 465/1000, minus 14 and 800/1000. This yields 665/1000. Now we can add this value to our previous subtraction of 5. 

So, the answer is 5 and 665/1000.

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