Find the sum:
`(-9)/(10) + (22)/(15)`

Answer

To find the sum of the rational numbers \(-\frac{9}{10}\) and \(\frac{22}{15}\), we will follow these steps:

### Step 1: Identify the denominators
The denominators of the two fractions are 10 and 15.

### Step 2: Find the Least Common Multiple (LCM)
To add the fractions, we need a common denominator. The LCM of 10 and 15 is 30.

### Step 3: Convert the fractions to have the same denominator
Now, we will convert each fraction to have the denominator of 30.

- For \(-\frac{9}{10}\):
\[ -\frac{9}{10} = -\frac{9 \times 3}{10 \times 3} = -\frac{27}{30} \]

- For \(\frac{22}{15}\):
\[ \frac{22}{15} = \frac{22 \times 2}{15 \times 2} = \frac{44}{30} \]

### Step 4: Add the fractions
Now that both fractions have the same denominator, we can add them:
\[ -\frac{27}{30} + \frac{44}{30} = \frac{-27 + 44}{30} \]

### Step 5: Perform the addition in the numerator
Calculating the numerator:
\[ -27 + 44 = 17 \]

### Step 6: Write the final result
Thus, the sum of the two fractions is:
\[ \frac{17}{30} \]

### Final Answer
The final answer is \(\frac{17}{30}\).

---