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

Question

Responses

31 1/2
31 Start Fraction 1 over 2 End Fraction

−31 1/2
negative 31 Start Fraction 1 over 2 End Fraction

−31 1/10
negative 31 Start Fraction 1 over 10 End Fraction

−18 110

Answer 1

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

1. Convert mixed numbers into 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 need to find a common denominator to combine these fractions. The least common multiple of 5 and 10 is 10.

3. Convert \( -\frac{124}{5} \) to a denominator of 10: \[ -\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10} \]

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

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

Thus, the final answer is: \[ \boxed{-31 \frac{1}{2}} \]