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Let's first explore what negative fractions are. Negative fractions have a minus sign in front of them, which indicates that they are less than zero. For instance, \(-\frac{5}{16}\) is a negative fraction. When adding or subtracting negative fractions, it's important to take care of both the negative signs and the actual addition or subtraction. In this exercise, we are adding \(-\frac{5}{16}\) and \(-\frac{9}{16}\). Each fraction is composed of a negative numerator. When we add these, the principal operation still applies: adding the numerators while keeping the common denominator. Therefore, \(-5 + (-9) = -14\). This result is then placed over the denominator, giving \(-\frac{14}{16}\), which can be simplified further.

Simplifying a fraction means reducing it to its simplest form. Simplifying helps in making the fraction easier to understand and manage. For example, in this exercise, after combining the fractions, we ended up with \(-\frac{14}{16}\). To simplify this fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD). The fraction \(-\frac{14}{16}\) simplifies by recognizing that both 14 and 16 can be divided by 2, resulting in \(-\frac{7}{8}\). Simplifying fractions helps in better understanding the proportion they represent, and it ensures the fraction is in its most reduced form.

The greatest common divisor (GCD), also known as the greatest common factor (GCF), is the largest number that can exactly divide two integers without leaving a remainder. In the context of simplifying fractions, the GCD is used to reduce the fraction to its simplest form. For instance, in our exercise, the fraction \(-\frac{14}{16}\) needs to be simplified. The GCD of 14 and 16 is 2. By dividing both the numerator (14) and the denominator (16) by their GCD, we simplify \(-\frac{14}{16}\) to \(-\frac{7}{8}\). To find the GCD, you can list out all the factors of the two numbers and identify the largest one they have in common. Simplifying fractions using the GCD ensures that the fraction is reduced to its smallest possible form.