rational & irrational numbers unit test part 1

Question

Evaluate the two sums and determine which statement is true enter the correct number associated with your response column A 0.5 plus 3 / 4 and column b sqrt 3+2 over 5. Statement number one only column A has a rational sum. Statement #2 only column B has a rational sum. Statement three column A and column B both have rational sums

Answer 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.