The sum of two rational numbers is `-5/4` If one of them is -3, find the other.

Answer

To find the other rational number when the sum of two rational numbers is \(-\frac{5}{4}\) and one of them is \(-3\), we can follow these steps:

### Step 1: Set up the equation
Let the two rational numbers be \(x\) and \(y\). According to the problem, we have:
\[ x + y = -\frac{5}{4} \]
Given that one of the numbers, \(x\), is \(-3\), we can substitute this value into the equation:
\[ -3 + y = -\frac{5}{4} \]

### Step 2: Isolate \(y\)
To find \(y\), we need to isolate it on one side of the equation. We can do this by adding \(3\) to both sides:
\[ y = -\frac{5}{4} + 3 \]

### Step 3: Convert \(3\) to a fraction
To add these two numbers, we should express \(3\) as a fraction with a common denominator. The number \(3\) can be written as:
\[ 3 = \frac{3 \times 4}{4} = \frac{12}{4} \]
So now we have:
\[ y = -\frac{5}{4} + \frac{12}{4} \]

### Step 4: Perform the addition
Now that both fractions have the same denominator, we can add them:
\[ y = \frac{-5 + 12}{4} = \frac{7}{4} \]

### Step 5: Conclusion
Thus, the other rational number is:
\[ y = \frac{7}{4} \]

### Summary
The other rational number is \(\frac{7}{4}\).

---