rational & irrational numbers unit test part 1

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:

1. **Statement #1:** Only Column A has a rational sum. **(True)**
2. **Statement #2:** Only Column B has a rational sum. **(False)**
3. **Statement #3:** Column A and Column B both have rational sums. **(False)**

Thus, the correct response is **Statement #1**.