Question

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

−2 1/2+6 2/3

Answer 1

To solve the problem \(-2 \frac{1}{2} + 6 \frac{2}{3}\), we 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 \(6 \frac{2}{3}\):
\[
6 \frac{2}{3} = 6 \times 3 + 2 / 3 = \frac{18 + 2}{3} = \frac{20}{3}
\]

2. Now we have:
\[
-\frac{5}{2} + \frac{20}{3}
\]

3. Before we can add these fractions, we need a common denominator. The denominators are 2 and 3. The least common denominator (LCD) of 2 and 3 is 6.

4. Convert both fractions to have the common denominator of 6.

For \(-\frac{5}{2}\):
\[
-\frac{5}{2} = -\frac{5 \times 3}{2 \times 3} = -\frac{15}{6}
\]

For \(\frac{20}{3}\):
\[
\frac{20}{3} = \frac{20 \times 2}{3 \times 2} = \frac{40}{6}
\]

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

6. The result can be expressed as a mixed number:
\[
\frac{25}{6} = 4 \frac{1}{6}
\]

Thus, the final answer is:
\[
\boxed{4 \frac{1}{6}}
\]