Let's evaluate the sums in both columns.
Column A: \[ 0.5 + \frac{3}{4} \]
First, convert \(0.5\) to a fraction: \[ 0.5 = \frac{1}{2} \]
Now, find a common denominator to add \( \frac{1}{2} \) and \( \frac{3}{4} \). The common denominator of \(2\) and \(4\) is \(4\).
Convert \( \frac{1}{2} \) to have a denominator of \(4\): \[ \frac{1}{2} = \frac{2}{4} \]
Now add: \[ \frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4} \]
So, the sum in Column A is: \[ \frac{5}{4} \] This is a rational number.
Column B: \[ \sqrt{3} + \frac{2}{5} \]
The term \( \sqrt{3} \) is an irrational number, while \( \frac{2}{5} \) is a rational number.
Since the sum of a rational number and an irrational number is always irrational, we conclude: \[ \sqrt{3} + \frac{2}{5} \] is irrational.
Now we evaluate the statements:
- Statement # 1: Only column A has a rational sum. (True, since Column A = \( \frac{5}{4} \) and Column B is irrational)
- Statement # 2: Only Column B has a rational sum. (False, since Column B is irrational)
- Statement # 3: Column A and B both have rational sums. (False)
Therefore, the correct statement is statement # 1.
So, the answer is: 1
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