Find a rational number between `(1)/(10)and(1)/(30)`.

Explanation

To find a rational number between \( \frac{1}{10} \) and \( \frac{1}{30} \), we can follow these steps:

### Step 1: Write down the fractions
We start with the two fractions:
\[ \frac{1}{10} \quad \text{and} \quad \frac{1}{30} \]

### Step 2: Find a common denominator
The denominators of the fractions are different, so we need to convert them to a common denominator. The least common multiple (LCM) of 10 and 30 is 30.

### Step 3: Convert \( \frac{1}{10} \) to have a denominator of 30
To convert \( \frac{1}{10} \) to a fraction with a denominator of 30, we multiply both the numerator and the denominator by 3:
\[ \frac{1}{10} = \frac{1 \times 3}{10 \times 3} = \frac{3}{30} \]

### Step 4: Write the fractions with the same denominator
Now we can write both fractions with the same denominator:
\[ \frac{3}{30} \quad \text{and} \quad \frac{1}{30} \]

### Step 5: Identify the rational numbers between the two fractions
Now that we have both fractions with the same denominator, we can find a rational number between them. The rational number that lies between \( \frac{1}{30} \) and \( \frac{3}{30} \) is:
\[ \frac{2}{30} \]

### Step 6: Simplify the fraction
We can simplify \( \frac{2}{30} \) by dividing both the numerator and the denominator by 2:
\[ \frac{2}{30} = \frac{2 \div 2}{30 \div 2} = \frac{1}{15} \]

### Final Answer
Thus, a rational number between \( \frac{1}{10} \) and \( \frac{1}{30} \) is:
\[ \frac{1}{15} \]

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