Find three rational number between -1 and 7.

Explanation

To find three rational numbers between -1 and 7, we can follow these steps:

### Step 1: Identify the two numbers
Let \( x = -1 \) and \( y = 7 \).

### Step 2: Calculate the mean of the two numbers
To find a number between \( x \) and \( y \), we can calculate the mean (average) of \( x \) and \( y \):
\[ a_1 = \frac{x + y}{2} = \frac{-1 + 7}{2} = \frac{6}{2} = 3 \]

### Step 3: Find another number between \( x \) and \( a_1 \)
Now we need to find a number between \( x \) and \( a_1 \). We will calculate the mean of \( x \) and \( a_1 \):
\[ a_2 = \frac{x + a_1}{2} = \frac{-1 + 3}{2} = \frac{2}{2} = 1 \]

### Step 4: Find a third number between \( x \) and \( a_2 \)
Next, we will find a number between \( x \) and \( a_2 \) by calculating the mean of \( x \) and \( a_2 \):
\[ a_3 = \frac{x + a_2}{2} = \frac{-1 + 1}{2} = \frac{0}{2} = 0 \]

### Step 5: List the three rational numbers
The three rational numbers we found between -1 and 7 are:
- \( a_1 = 3 \)
- \( a_2 = 1 \)
- \( a_3 = 0 \)

### Final Answer
The three rational numbers between -1 and 7 are **3, 1, and 0**.

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