Question

use additive inverse to find -24 4/5 - 6 7/10

Answer 1

To find \( -24 \frac{4}{5} - 6 \frac{7}{10} \) using the additive inverse, we first rewrite the problem in a more manageable form.

1. **Convert the mixed numbers to improper fractions:**
- For \( -24 \frac{4}{5} \):
\[
-24 \frac{4}{5} = -\left(24 \times 5 + 4\right) / 5 = -\left(120 + 4\right) / 5 = -\frac{124}{5}
\]

- For \( -6 \frac{7}{10} \):
\[
-6 \frac{7}{10} = -\left(6 \times 10 + 7\right) / 10 = -\left(60 + 7\right) / 10 = -\frac{67}{10}
\]

2. **Now we have the expression:**
\[
-\frac{124}{5} - \frac{67}{10}
\]

3. **Find a common denominator to combine the fractions.** The least common multiple of 5 and 10 is 10. We need to convert \(-\frac{124}{5}\) to a fraction with a denominator of 10:
\[
-\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10}
\]

4. **Now we can combine the fractions:**
\[
-\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10}
\]

5. **Simplify the fraction (if needed):**
\[
-\frac{315}{10} = -31 \frac{5}{10} = -31 \frac{1}{2} \quad (\text{simplifying } \frac{5}{10} \text{ to } \frac{1}{2})
\]

Finally, the result of \( -24 \frac{4}{5} - 6 \frac{7}{10} \) is:
\[
\boxed{-31 \frac{1}{2}}
\]