Question

According to the Closure Property, which of these sums results in a rational number?
(1 point)
36 + 221
Pi+ 4
06+ 9/10
0.643892553… + 3/4

Answer 1

To determine which of the given sums results in a rational number, we remember that rational numbers can be expressed as the quotient of two integers (i.e., in the form p/q, where p and q are integers, and q is not zero).

Let's analyze each sum:

1. **36 + 221**:
- Both 36 and 221 are rational numbers (they can be expressed as themselves over 1).
- Thus, 36 + 221 = 257, which is also a rational number.

2. **π + 4**:
- π is an irrational number.
- Adding an irrational number (π) to a rational number (4) results in an irrational number.
- Therefore, π + 4 is not a rational number.

3. **06 + 9/10**:
- 06 is equivalent to 6, which is rational.
- 9/10 is also a rational number.
- Thus, 6 + 9/10 = 6.9 (or 69/10), which is a rational number.

4. **0.643892553… + 3/4**:
- The decimal 0.643892553… is a repeating decimal and can be treated as a rational number.
- 3/4 is a rational number.
- The sum of two rational numbers is also rational, so this sum is rational as well.

From these evaluations, we find that:

1. **36 + 221** results in a rational number.
2. **06 + 9/10** results in a rational number.
3. **0.643892553… + 3/4** results in a rational number.
4. **π + 4** does not result in a rational number.

Thus, the sums that result in rational numbers are:
- 36 + 221
- 06 + 9/10
- 0.643892553… + 3/4

Any one of the first three could be an accepted answer for a sum resulting in a rational number.