State in each case whether true or false:
`(5)/(11)` is a rational number.

Answer

To determine whether the statement "(5)/(11) is a rational number" is true or false, we can follow these steps:

### Step 1: Understand the Definition of Rational Numbers
A rational number is defined as any number that can be expressed in the form of \( \frac{p}{q} \), where:
- \( p \) and \( q \) are integers
- \( q \neq 0 \)

### Step 2: Identify the Values of \( p \) and \( q \)
In the expression \( \frac{5}{11} \):
- The numerator \( p = 5 \)
- The denominator \( q = 11 \)

### Step 3: Check if \( p \) and \( q \) are Integers
Both 5 and 11 are integers. Therefore:
- \( p = 5 \) is an integer
- \( q = 11 \) is an integer

### Step 4: Check if \( q \) is Not Equal to Zero
Since \( q = 11 \), we check:
- \( q \neq 0 \) is true because 11 is not equal to zero.

### Step 5: Conclusion
Since both conditions for a rational number are satisfied (i.e., \( p \) and \( q \) are integers, and \( q \) is not zero), we conclude that \( \frac{5}{11} \) is a rational number.

Thus, the statement "(5)/(11) is a rational number" is **True**.

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