To solve $(10 \frac{7}{9}) + (-9 \frac{2}{3})$, let's first convert the mixed numbers into improper fractions.

1. Convert $10 \frac{7}{9}$ to an improper fraction: $10 \frac{7}{9} = \frac{10 \times 9 + 7}{9} = \frac{90 + 7}{9} = \frac{97}{9}$

2. Convert $-9 \frac{2}{3}$ to an improper fraction: $-9 \frac{2}{3} = -\frac{9 \times 3 + 2}{3} = -\frac{27 + 2}{3} = -\frac{29}{3}$

3. Find a common denominator: The least common multiple of 9 and 3 is 9. Convert $-\frac{29}{3}$ to a fraction with a denominator of 9: $-\frac{29}{3} = -\frac{29 \times 3}{3 \times 3} = -\frac{87}{9}$

4. Add the fractions: $\frac{97}{9} + \left(-\frac{87}{9}\right) = \frac{97 - 87}{9} = \frac{10}{9}$

The result is $\frac{10}{9}$, which can also be expressed as a mixed number: $\frac{10}{9} = 1 \frac{1}{9}$

Final Answer:

$(10 \frac{7}{9}) + (-9 \frac{2}{3}) = 1 \frac{1}{9}$

Would you like more details or have any questions?

Related Questions:

1. How do you subtract mixed numbers with different denominators?
2. How can improper fractions be converted back to mixed numbers?
3. What is the method for finding the least common multiple of two numbers?
4. How does adding negative fractions work?
5. What is the process for converting a negative mixed number to an improper fraction?

Tip:

When adding or subtracting mixed numbers, converting them to improper fractions first simplifies the process.