Question

Which of the following expressions results in a positive number?
Responses

0 .25 + - (0 .75)



- 5/2 + (- 5/2)



8 1/3 + (-7 1/5)

-8/3 + 8/4

Answer 1

Let's evaluate each expression to determine which one results in a positive number.

1. **\( 0.25 + - (0.75) \)**:
\[
0.25 - 0.75 = 0.25 - 0.75 = -0.50 \quad (\text{Negative})
\]

2. **\( -\frac{5}{2} + (-\frac{5}{2}) \)**:
\[
-\frac{5}{2} - \frac{5}{2} = -\frac{10}{2} = -5 \quad (\text{Negative})
\]

3. **\( 8 \frac{1}{3} + (-7 \frac{1}{5}) \)**:
First, convert mixed numbers to improper fractions:
\[
8 \frac{1}{3} = \frac{25}{3}, \quad -7 \frac{1}{5} = -\frac{36}{5}
\]
To add these, we need a common denominator, which is 15:
\[
\frac{25}{3} = \frac{125}{15}, \quad -\frac{36}{5} = -\frac{108}{15}
\]
Now add:
\[
\frac{125}{15} - \frac{108}{15} = \frac{17}{15} \quad (\text{Positive})
\]

4. **\( -\frac{8}{3} + \frac{8}{4} \)**:
First, get \(\frac{8}{4} = 2\):
\[
-\frac{8}{3} + 2 = -\frac{8}{3} + \frac{6}{3} = -\frac{2}{3} \quad (\text{Negative})
\]

From the evaluations:

- The first expression results in -0.50 (Negative).
- The second expression results in -5 (Negative).
- The third expression results in \(\frac{17}{15}\) (Positive).
- The fourth expression results in -\(\frac{2}{3}\) (Negative).

**Conclusion**: The expression that results in a positive number is:
**\( 8 \frac{1}{3} + (-7 \frac{1}{5}) \)**.