To evaluate the two sums in Column A and Column B, we first perform the calculations.
Column A: \[ 0.5 + \frac{3}{4} \]
We can convert \(0.5\) to a fraction: \[ 0.5 = \frac{1}{2} \]
Next, we need a common denominator to add \(\frac{1}{2}\) and \(\frac{3}{4}\). The common denominator for \(2\) and \(4\) is \(4\).
Convert \(\frac{1}{2}\) to have a denominator of \(4\): \[ \frac{1}{2} = \frac{2}{4} \]
Now add the fractions: \[ \frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4} \] So, the sum in Column A is: \[ \frac{5}{4} \text{ (which is rational)} \]
Column B: \[ \sqrt{3} + \frac{2}{5} \]
Here, \(\sqrt{3}\) is an irrational number, and \(\frac{2}{5}\) is a rational number. The sum of a rational number and an irrational number is always irrational. Therefore, the sum in Column B is: \[ \sqrt{3} + \frac{2}{5} \text{ (which is irrational)} \]
Now we can compare the results:
- Column A: \(\frac{5}{4}\) (rational)
- Column B: \(\sqrt{3} + \frac{2}{5}\) (irrational)
Now, we analyze the statements provided:
- 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)
The correct statement is: Statement #1 is true.
Thus, the answer is: 1