Let's evaluate the sums for both Column A and Column B and determine the rationality of each.
### Column A:
First, let's calculate the sum:
[tex]\[ 0.5 + \frac{3}{4} \][/tex]
1. Convert 0.5 to a fraction:
[tex]\[ 0.5 = \frac{1}{2} \][/tex]
2. Add the two fractions:
[tex]\[ \frac{1}{2} + \frac{3}{4} \][/tex]
To add these fractions, we need a common denominator:
[tex]\[ \frac{1}{2} = \frac{2}{4} \][/tex]
So:
[tex]\[ \frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1.25 \][/tex]
### Column B:
Now, let's calculate the sum:
[tex]\[ \sqrt{3} + \frac{2}{5} \][/tex]
1. The square root of 3 is an irrational number. Let's denote it as [tex]\(\sqrt{3}\)[/tex].
2. [tex]\(\frac{2}{5}\)[/tex] is a rational number.
When adding an irrational number ([tex]\(\sqrt{3}\)[/tex]) and a rational number ([tex]\(\frac{2}{5}\)[/tex]), the sum remains irrational:
[tex]\[ \sqrt{3} + \frac{2}{5} \][/tex]
### Determine the Rationality:
- Column A: [tex]\(\frac{5}{4}\)[/tex] or 1.25 is a rational number because it can be expressed as a fraction.
- Column B: [tex]\(\sqrt{3} + \frac{2}{5}\)[/tex] is irrational because the sum of an irrational number and a rational number is always irrational.
### Conclusion:
- Column A has a rational sum.
- Column B has an irrational sum.
Based on these evaluations, none of the provided statements is true:
- 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)
Therefore, the correct statement would be:
```
0
```
