Let's evaluate both sums in Columns A and B.
Column A: \[ 0.5 + \frac{3}{4} \] Convert \(0.5\) to a fraction: \[ 0.5 = \frac{1}{2} \] Now add: \[ \frac{1}{2} + \frac{3}{4} \] To add these fractions, we need a common denominator. The least common multiple of \(2\) and \(4\) is \(4\). Convert \(\frac{1}{2}\) to have a denominator of \(4\): \[ \frac{1}{2} = \frac{2}{4} \] Now we can add: \[ \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \] Thus, the sum in Column A is: \[ \frac{5}{4} \quad \text{(which is rational)} \]
Column B: \[ \sqrt{3} + \frac{2}{3} \] Here \(\sqrt{3}\) is an irrational number, and \(\frac{2}{3}\) is a rational number. The sum of a rational number and an irrational number is always irrational. Thus: \[ \sqrt{3} + \frac{2}{3} \quad \text{(which is irrational)} \]
Conclusion:
- Column A has a rational sum: \(\frac{5}{4}\)
- Column B has an irrational sum: \(\sqrt{3} + \frac{2}{3}\)
Now, looking at the statements:
- Statement #1: Only Column A has a rational sum. (True)
- Statement #2: Only Column B has a rational sum. (False)
- Statement #3: Columns A and Column B both have rational sums. (False)
The correct answer is: 1 (for Statement #1)