Question

Use the rules of adding rational numbers to solve. Calculators are not allowed.

−2 1/2+6 2/3 (1 point)
Responses

9 1/6

4 1/3

−4 1/6

4 1/6

Answer 1

To solve \( -2 \frac{1}{2} + 6 \frac{2}{3} \), we can follow these steps:

1. Convert the mixed numbers into improper fractions.
- For \( -2 \frac{1}{2} \):
\[
-2 \frac{1}{2} = -\left(2 \times 2 + 1\right) / 2 = -\frac{5}{2}
\]
- For \( 6 \frac{2}{3} \):
\[
6 \frac{2}{3} = 6 \times 3 + 2 / 3 = \frac{20}{3}
\]

2. Now, we need to find a common denominator to add these two fractions. The denominators are 2 and 3.
- The least common denominator (LCD) is 6.

3. Convert both fractions to have a denominator of 6:
- For \( -\frac{5}{2} \):
\[
-\frac{5}{2} = -\frac{5 \times 3}{2 \times 3} = -\frac{15}{6}
\]
- For \( \frac{20}{3} \):
\[
\frac{20}{3} = \frac{20 \times 2}{3 \times 2} = \frac{40}{6}
\]

4. Now, we can add the two fractions:
\[
-\frac{15}{6} + \frac{40}{6} = \frac{-15 + 40}{6} = \frac{25}{6}
\]

5. Convert the improper fraction back to a mixed number:
\[
\frac{25}{6} = 4 \frac{1}{6}
\]

Therefore, the answer is \( 4 \frac{1}{6} \).

Hence, the correct response is:
**4 1/6**.