Let's evaluate the sums in Column A and Column B.
Column A: \(0.5 + \frac{3}{4}\)
First, we can 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) between 2 and 4 is 4. We convert \(\frac{1}{2}\): \[ \frac{1}{2} = \frac{2}{4} \]
Now we can add: \[ \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \]
Column B: \(\frac{\sqrt{3} + 2}{5}\)
In this case, \(\sqrt{3}\) is an irrational number, and adding 2 (a rational number) to \(\sqrt{3}\) yields an irrational number: \[ \sqrt{3} + 2 \text{ is irrational.} \] Dividing an irrational number by a rational number (5) still results in an irrational number: \[ \frac{\sqrt{3} + 2}{5} \text{ is also irrational.} \]
Now we summarize the results:
- Column A: \(\frac{5}{4}\) (rational)
- Column B: \(\frac{\sqrt{3} + 2}{5}\) (irrational)
Based on this information, we can 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)
Thus, the correct response is Statement #1.
1 answer