The sum of two rational number is -3. If one of them is `(-15)/(7)` find the other

Answer

To solve the problem step by step, we need to find the other rational number when the sum of two rational numbers is -3, and one of them is \(-\frac{15}{7}\).

### Step 1: Set up the equation
Let the other rational number be \(x\). According to the problem, we can write the equation:

\[ -\frac{15}{7} + x = -3 \]

### Step 2: Isolate \(x\)
To find \(x\), we need to isolate it on one side of the equation. We can do this by adding \(\frac{15}{7}\) to both sides:

\[ x = -3 + \frac{15}{7} \]

### Step 3: Convert -3 to a fraction
To perform the addition, we need to express -3 as a fraction with a denominator of 7. We can write -3 as:

\[ -3 = -\frac{21}{7} \]

### Step 4: Substitute and simplify
Now we substitute this back into our equation:

\[ x = -\frac{21}{7} + \frac{15}{7} \]

### Step 5: Combine the fractions
Since both fractions have the same denominator, we can combine them:

\[ x = \frac{-21 + 15}{7} \]

### Step 6: Perform the addition in the numerator
Now, we calculate the numerator:

\[ -21 + 15 = -6 \]

So, we have:

\[ x = \frac{-6}{7} \]

### Step 7: Conclusion
Thus, the other rational number is:

\[ \boxed{-\frac{6}{7}} \]

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