Evaluate the sums and determine which statement is true.

Column A
Column B
0.7 + 1.8
1 + 0.25

Statements:
1. Only Column A has a rational sum.
2. Only Column B has a rational sum.
3. Both Column A and Column B have rational sums.

1 answer

First, let's calculate the sums for both Column A and Column B.

Column A: \( 0.7 + 1.8 \)

Converting to fractions if necessary:

  • \( 0.7 = \frac{7}{10} \)
  • \( 1.8 = \frac{18}{10} \)

Now we can add them: \[ 0.7 + 1.8 = \frac{7}{10} + \frac{18}{10} = \frac{25}{10} = 2.5 \]

Column B: \( 1 + 0.25 \)

Converting \( 0.25 \) to a fraction:

  • \( 0.25 = \frac{1}{4} \)

Now we can add: \[ 1 + 0.25 = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \]

Now, we can summarize the results:

  • The sum of Column A is \( 2.5 \).
  • The sum of Column B is \( \frac{5}{4} \).

Both \( 2.5 \) and \( \frac{5}{4} \) are rational numbers.

Now, let's analyze the statements:

  1. Only Column A has a rational sum. (False)
  2. Only Column B has a rational sum. (False)
  3. Both Column A and Column B have rational sums. (True)

The correct choice is: Statement 3 is true. Both Column A and Column B have rational sums.