Find a rational number between `2` and `3`.

Options

A. `(9)/(2)`
B. `(7)/(2)`
C. `(5)/(2)`
D. `(11)/(2)`

Answer

To find a rational number between 2 and 3, we can follow these steps:

### Step 1: Identify the two numbers
We start with the two numbers given in the question, which are 2 and 3.

### Step 2: Calculate the average of the two numbers
To find a rational number between 2 and 3, we can calculate the average (or midpoint) of these two numbers. The formula for the average of two numbers \(X\) and \(Y\) is:

\[ \text{Average} = \frac{X + Y}{2} \]

In our case, \(X = 2\) and \(Y = 3\).

### Step 3: Substitute the values into the formula
Now we substitute the values into the formula:

\[ \text{Average} = \frac{2 + 3}{2} \]

### Step 4: Simplify the expression
Now, we simplify the expression:

\[ \text{Average} = \frac{5}{2} \]

### Step 5: Verify that the result is between 2 and 3
Finally, we need to check if \(\frac{5}{2}\) is indeed between 2 and 3. We know that:

\[ 2 < \frac{5}{2} < 3 \]

This confirms that \(\frac{5}{2}\) is a rational number between 2 and 3.

### Conclusion
Thus, a rational number between 2 and 3 is \(\frac{5}{2}\).

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