Question

Use the additive inverse to find −24 4/5−6 7/10 .(1 point)
Responses

−18110
negative 18 Start Fraction 1 over 10 End Fraction

−3112
negative 31 Start Fraction 1 over 2 End Fraction

−31110
negative 31 Start Fraction 1 over 10 End Fraction

3112

Answer 1

To find the sum of \(-24 \frac{4}{5}\) and \(-6 \frac{7}{10}\) using the additive inverse, we will first convert mixed numbers into improper fractions and then find their sum.

1. **Convert the mixed numbers to improper fractions:**
- For \(-24 \frac{4}{5}\):
\[
-24 \frac{4}{5} = -\left(24 \times 5 + 4\right) / 5 = -\frac{120 + 4}{5} = -\frac{124}{5}
\]
- For \(-6 \frac{7}{10}\):
\[
-6 \frac{7}{10} = -\left(6 \times 10 + 7\right) / 10 = -\frac{60 + 7}{10} = -\frac{67}{10}
\]

2. **Find a common denominator to add the fractions:**
- The least common denominator (LCD) of 5 and 10 is 10. Convert \(-\frac{124}{5}\) to have a denominator of 10:
\[
-\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10}
\]

3. **Add the two fractions:**
\[
-\frac{248}{10} + -\frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10}
\]

4. **Simplify \(-\frac{315}{10}\) to a mixed number:**
\[
-\frac{315}{10} = -31 \frac{5}{10} = -31 \frac{1}{2}
\]

Thus, the final answer is:

\[
\boxed{-31 \frac{1}{2}}
\]

Among your options, the correct response is: **\(-31 \frac{1}{2}\)**.