Find two rational numbers laying between `(-1)/(3) and (1)/(2)`.

Answer

To find two rational numbers between \(-\frac{1}{3}\) and \(\frac{1}{2}\), we can follow these steps:

### Step 1: Identify the two rational numbers
We need to find two rational numbers that lie between \(-\frac{1}{3}\) and \(\frac{1}{2}\).

### Step 2: Calculate the average of the two numbers
To find a rational number between the two, we can calculate the average of \(-\frac{1}{3}\) and \(\frac{1}{2}\):
\[ \text{Average} = \frac{-\frac{1}{3} + \frac{1}{2}}{2} \]

### Step 3: Find a common denominator
To add the fractions, we need a common denominator. The denominators are 3 and 2. The least common multiple (LCM) of 3 and 2 is 6.

### Step 4: Convert the fractions to have the same denominator
Convert \(-\frac{1}{3}\) and \(\frac{1}{2}\) to have a denominator of 6:
\[ -\frac{1}{3} = -\frac{2}{6} \quad \text{and} \quad \frac{1}{2} = \frac{3}{6} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ -\frac{2}{6} + \frac{3}{6} = \frac{1}{6} \]

### Step 6: Calculate the average
Now, we can find the average:
\[ \text{Average} = \frac{\frac{1}{6}}{2} = \frac{1}{12} \]

### Step 7: Find another rational number
To find another rational number, we can take the average of \(\frac{1}{12}\) and \(\frac{1}{2}\):
\[ \text{Average} = \frac{\frac{1}{12} + \frac{1}{2}}{2} \]

### Step 8: Convert \(\frac{1}{2}\) to have a denominator of 12
Convert \(\frac{1}{2}\) to have a denominator of 12:
\[ \frac{1}{2} = \frac{6}{12} \]

### Step 9: Add the fractions
Now, add \(\frac{1}{12}\) and \(\frac{6}{12}\):
\[ \frac{1}{12} + \frac{6}{12} = \frac{7}{12} \]

### Step 10: Calculate the average
Now, we can find the average:
\[ \text{Average} = \frac{\frac{7}{12}}{2} = \frac{7}{24} \]

### Conclusion
The two rational numbers between \(-\frac{1}{3}\) and \(\frac{1}{2}\) are \(\frac{1}{12}\) and \(\frac{7}{24}\).