Evaluate the two sums and determine which statement is true. Enter the correct number associated with your response.

Column A Column B
0.5+3/4


√3+2/5


Statement #1: Only Column A has a rational sum.

Statement #2: Only Column B has a rational sum.

Statement #3: Column A and Column B both have rational sums.

1 answer

To evaluate Column A and Column B, we will calculate each sum step-by-step.

Column A: \[ 0.5 + \frac{3}{4} \]

Convert \(0.5\) to a fraction: \[ 0.5 = \frac{1}{2} \]

Now add \(\frac{1}{2}\) and \(\frac{3}{4}\): To add these fractions, we need a common denominator. The least common denominator of \(2\) and \(4\) is \(4\): \[ \frac{1}{2} = \frac{2}{4} \]

Now add: \[ \frac{2}{4} + \frac{3}{4} = \frac{2+3}{4} = \frac{5}{4} \]

Column A Sum: \[ \frac{5}{4} \quad \text{(This is a rational number.)} \]


Column B: \[ \sqrt{3} + \frac{2}{5} \]

Here, \(\sqrt{3}\) is an irrational number, while \(\frac{2}{5}\) is a rational number.

The sum of an irrational number and a rational number is always irrational. Thus: \[ \sqrt{3} + \frac{2}{5} \quad \text{(This is an irrational number.)} \]


Conclusion:

  • Column A has a sum of \(\frac{5}{4}\) which is rational.
  • Column B has a sum of \(\sqrt{3} + \frac{2}{5}\) which is irrational.

So, the true statement is:

Statement #1: Only Column A has a rational sum.

Therefore, the answer is Statement #1.