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To add fractions, the first thing we need to ensure is that the fractions share the same denominator. The denominator is the number below the fraction line. It tells us into how many parts the whole is divided. For example, in the fraction \(\frac{9}{19}\), 19 is the denominator. When fractions share the same denominator, like in our exercise with \(\frac{-9}{19}\) and \(\frac{17}{19}\), it means that the pieces are of the same size. Thus, it simplifies the addition process, because we can just add the numerators directly.

The numerators are the numbers above the fraction line in a fraction. They tell us how many parts of the whole we have. In the fraction \(\frac{9}{19}\), 9 is the numerator. When adding fractions with the same denominator, you can directly sum up the numerators. For instance, in our exercise, we have the numerators \(−9\) and \(17\). Adding these together gives us the numerator of the final fraction: \(-9 + 17 = 8\). The denominator remains the same.

Adding fractions involves getting common denominators and then summing the numerators. In our example, we had \(\frac{-9}{19}\) and \(\frac{17}{19}\) which already had a common denominator. This made it straightforward. We only needed to add the numerators. Therefore, \(\frac{-9 + 17}{19} = \frac{8}{19}\). Here's a brief step-by-step of how you can approach such problems:
1. Check if the fractions have the same denominator.
2. If they do, add the numerators and keep the denominator unchanged.
3. Place the resulting sum of the numerators over the common denominator.
For fractions with different denominators, you'd first need to find a common denominator before adding the numerators.