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When you are adding fractions, it is crucial that the fractions have the same denominator. If they do not, you will need to find a common denominator before adding. In our exercise, both fractions, \(-\frac{1}{2}\) and \(-\frac{1}{2}\), already have the same denominator, which makes the addition process straightforward. You only need to add the numerators together. When the denominators are the same, you combine the fractions by adding the numerators and keeping the common denominator unchanged. This transforms our addition into \(-1 + (-1)\) over 2, leading to a new fraction of \(-\frac{2}{2}\). Make sure to always check if the fractions you're working with share a common denominator before starting the addition process.

After combining fractions, the next step is to simplify or reduce the resulting fraction. Simplifying a fraction means expressing it in the simplest form where the numerator and denominator share no common factors other than 1. In our exercise, we ended up with the fraction \(-\frac{2}{2}\). To simplify this, you divide both the numerator and the denominator by their greatest common divisor (GCD). For \(-\frac{2}{2}\), the numerator and the denominator are both 2, so the GCD is 2. By dividing both by this GCD, we get \-1\. Simplifying fractions makes them easier to understand and more useful in further calculations.

Handling negative numbers correctly is essential in mathematics, especially when combining and simplifying fractions. In our exercise, both fractions were negative: \-\frac{1}{2}\ and \-\frac{1}{2}\. When adding negative numbers, you sum their absolute values and then place a negative sign before the result. In simpler terms, adding \-1\ and \-1\ is the same as adding 1 and 1, but with a negative sign: \(-1 + (-1) = -2\). Negative numbers affect both the numerators and the way you interpret the final simplified fraction. As a rule of thumb, always keep track of the negative signs throughout your calculations to avoid mistakes. If both the numerator and denominator end up being negative, the fraction itself is positive because two negative signs cancel each other out. But in our case, we have \-\frac{2}{2}\, which simplifies directly to \-1\.