Let's evaluate both sums in Column A and Column B.
Column A: \[ 0.5 + \frac{3}{4} \]
First, let's convert \(0.5\) to a fraction: \[ 0.5 = \frac{1}{2} \]
Now we have: \[ \frac{1}{2} + \frac{3}{4} \]
To add these fractions, we need a common denominator. The least common denominator (LCD) of \(2\) and \(4\) is \(4\): \[ \frac{1}{2} = \frac{2}{4} \]
Now, we can add the fractions: \[ \frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4} \]
So, the sum for Column A is: \[ \frac{5}{4}, \text{ which is rational}. \]
Column B: \[ \sqrt{3} + \frac{2}{5} \]
The term \(\sqrt{3}\) is an irrational number. \( \frac{2}{5} \) is a rational number. The sum of a rational and an irrational number is always irrational. Therefore: \[ \sqrt{3} + \frac{2}{5} \text{ is irrational}. \]
Now we can summarize the results:
- Column A has the sum \( \frac{5}{4} \) (rational).
- Column B has the sum \( \sqrt{3} + \frac{2}{5} \) (irrational).
Reviewing 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)
Thus, the correct statement is: Statement #1 is true.
The final answer is: Statement # (1) is true.
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