Find two rational numbers between -3 and -2.

Answer

To find two rational numbers between -3 and -2, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given numbers**: We have two numbers, \( x = -3 \) and \( y = -2 \). We know that \( x < y \) because -3 is less than -2.

2. **Calculate the mean of -3 and -2**:
\[ \text{Mean} = \frac{x + y}{2} = \frac{-3 + (-2)}{2} = \frac{-5}{2} \]
This gives us the first rational number, which is \( -\frac{5}{2} \).

3. **Find another rational number**: Now we can find another rational number between -3 and -\(\frac{5}{2}\). We can take the mean of -3 and -\(\frac{5}{2}\):
\[ \text{Mean} = \frac{-3 + \left(-\frac{5}{2}\right)}{2} \]
To compute this, we first convert -3 into a fraction with a denominator of 2:
\[ -3 = -\frac{6}{2} \]
Now substituting:
\[ \text{Mean} = \frac{-\frac{6}{2} + \left(-\frac{5}{2}\right)}{2} = \frac{-\frac{11}{2}}{2} = -\frac{11}{4} \]
This gives us the second rational number, which is \( -\frac{11}{4} \).

4. **Final Result**: The two rational numbers between -3 and -2 are:
- \( -\frac{5}{2} \)
- \( -\frac{11}{4} \)

### Summary:
Thus, the two rational numbers between -3 and -2 are \( -\frac{5}{2} \) and \( -\frac{11}{4} \).

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