To add these fractions, we need to find a common denominator. The common denominator for 14, 25, 10, and 16 is 1400.

Now, let's convert each fraction to have a denominator of 1400:

6/-14 = -300/700
4/25 = 224/1400
5/10 = 700/1400
-3/16 = -131.25/1400

Now, we can add the fractions:

-300/700 + 224/1400 + 700/1400 - 131.25/1400

To add the fractions, we add the numerators and keep the denominator the same:

(-300 + 224 + 700 - 131.25)/1400

Simplifying the numerator:

(593.75)/1400

Therefore, the sum of the fractions is 593.75/1400.