To evaluate the sums in Column A and Column B, we start with each column separately.
Column A: \[ 0.5 + \frac{3}{4} \] First, we convert \(0.5\) to a fraction: \[ 0.5 = \frac{1}{2} \] Now we can add the two fractions: \[ \frac{1}{2} + \frac{3}{4} \] To add these, we need a common denominator. The common denominator between \(2\) and \(4\) is \(4\): \[ \frac{1}{2} = \frac{2}{4} \] 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: \[ \sqrt{3} + \frac{2}{5} \] Here, \( \sqrt{3} \) is an irrational number. Since the sum of a rational number and an irrational number is always irrational, we know that: \[ \sqrt{3} + \frac{2}{5} \quad (\text{which is irrational}) \]
Now we compare the sums from both columns:
- Column A: \( \frac{5}{4} \) (rational)
- Column B: \( \sqrt{3} + \frac{2}{5} \) (irrational)
Now we evaluate the statements:
- Statement #1: Only Column A has a rational sum. (True)
- Statement #2: Only Column B has a rational sum. (False)
- Statement #3: Column A and Column B both have rational sums. (False)
Based on the evaluations, the true statement is: Statement #1.
So the final answer is: 1
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