Let's add the fractions:

$\frac{2}{9} + \left( -\frac{3}{10} \right) + \left( -\frac{7}{10} \right)$

Step 1: Combine the fractions with the same denominator first. We have $-\frac{3}{10}$ and $-\frac{7}{10}$, so:

$-\frac{3}{10} - \frac{7}{10} = -\frac{10}{10} = -1$

Step 2: Now add $\frac{2}{9}$ to $-1$. To do this, we need a common denominator. The least common denominator (LCD) of 9 and 1 is 9, so we rewrite $-1$ as $-\frac{9}{9}$.

$\frac{2}{9} + \left( -\frac{9}{9} \right) = \frac{2}{9} - \frac{9}{9} = \frac{-7}{9}$

Thus, the final answer is:

$\boxed{-\frac{7}{9}}$

Would you like a detailed breakdown of any steps or have further questions on this?

Here are some related questions:

1. How do you add or subtract fractions with different denominators?
2. What is the process for finding the least common denominator?
3. How do you convert a mixed number to an improper fraction?
4. What happens when you add fractions with negative values?
5. How do you simplify a fraction after adding or subtracting?

Tip: Always convert to a common denominator when adding or subtracting fractions!