Fill in the blanks.
The reciprocal of positive rational number is ………….. .

Answer

To solve the question "The reciprocal of a positive rational number is …………..", we can follow these steps:

### Step 1: Understand the concept of a positive rational number.
A positive rational number is any number that can be expressed as the fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers, \( b \neq 0 \), and \( a \) is greater than 0.

**Hint:** Remember that rational numbers can be positive or negative, and we are specifically looking at the positive ones.

### Step 2: Define the reciprocal.
The reciprocal of a number \( x \) is defined as \( \frac{1}{x} \). For a fraction \( \frac{a}{b} \), the reciprocal is \( \frac{b}{a} \).

**Hint:** Think about what happens when you multiply a number by its reciprocal.

### Step 3: Find the reciprocal of a positive rational number.
Let’s take a positive rational number \( x \). If \( x = \frac{a}{b} \) (where \( a > 0 \) and \( b > 0 \)), the reciprocal of \( x \) is:

\[ \text{Reciprocal of } x = \frac{1}{x} = \frac{b}{a} \]

**Hint:** When you find the reciprocal, you are essentially flipping the fraction.

### Step 4: Determine the sign of the reciprocal.
Since both \( a \) and \( b \) are positive (because \( x \) is a positive rational number), the reciprocal \( \frac{b}{a} \) is also positive.

**Hint:** Consider the properties of positive numbers: the division of two positive numbers results in a positive number.

### Final Answer:
Thus, we can conclude that the reciprocal of a positive rational number is also a positive rational number.

**Fill in the blank:** The reciprocal of a positive rational number is **positive rational number**.