Find a rational number between `-(1)/(2)and(1)/(6)`.

Explanation

To find a rational number between \(-\frac{1}{2}\) and \(\frac{1}{6}\), we can follow these steps:

### Step 1: Write down the two numbers
We start with the two rational numbers:
\[ -\frac{1}{2} \quad \text{and} \quad \frac{1}{6} \]

### Step 2: Convert to a common denominator
To find a rational number between them, we need to express both fractions with a common denominator. The denominators are 2 and 6. The least common multiple (LCM) of 2 and 6 is 6.

Now, we convert \(-\frac{1}{2}\) to a fraction with a denominator of 6:
\[ -\frac{1}{2} = -\frac{1 \times 3}{2 \times 3} = -\frac{3}{6} \]

So now we have:
\[ -\frac{3}{6} \quad \text{and} \quad \frac{1}{6} \]

### Step 3: Identify rational numbers between the two fractions
Now that both fractions have the same denominator, we can easily identify rational numbers that lie between \(-\frac{3}{6}\) and \(\frac{1}{6}\).

The rational numbers between \(-\frac{3}{6}\) and \(\frac{1}{6}\) can include:
- \(-\frac{2}{6}\)
- \(-\frac{1}{6}\)
- \(0\) (which can be written as \(\frac{0}{6}\))

### Step 4: Choose one rational number
Among the identified rational numbers, we can choose any one of them. For example, we can choose:
\[ -\frac{2}{6} \quad \text{or} \quad 0 \]

### Final Answer
Thus, one rational number between \(-\frac{1}{2}\) and \(\frac{1}{6}\) is:
\[ -\frac{2}{6} \quad \text{or} \quad 0 \]

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