To solve \( -24 \frac{4}{5} - 6 \frac{7}{10} \) using the additive inverse, we first convert the mixed numbers to improper fractions and then add their additive inverses.
Step 1: Convert the mixed numbers to improper fractions.
-
Convert \( -24 \frac{4}{5} \): \[ -24 \frac{4}{5} = -\left(24 \times 5 + 4\right)/5 = -\left(120 + 4\right)/5 = -\frac{124}{5} \]
-
Convert \( -6 \frac{7}{10} \): \[ -6 \frac{7}{10} = -\left(6 \times 10 + 7\right)/10 = -\left(60 + 7\right)/10 = -\frac{67}{10} \]
Step 2: Add the two fractions.
To add the fractions, we need a common denominator. The least common multiple (LCM) of 5 and 10 is 10.
-
Convert \( -\frac{124}{5} \) to a denominator of 10: \[ -\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10} \]
-
Now, add the two fractions: \[ -\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10} \]
Step 3: Simplify \( -\frac{315}{10} \) into a mixed number.
- Divide 315 by 10:
- The division \( 315 \div 10 \) gives us a whole number of 31 with a remainder of 5.
So, \[ -\frac{315}{10} = -31 \frac{5}{10} \] 2. Simplify \( \frac{5}{10} \):
- \( \frac{5}{10} = \frac{1}{2} \)
Thus, \[ -\frac{315}{10} = -31 \frac{1}{2} \]
Final Answer
The result of \( -24 \frac{4}{5} - 6 \frac{7}{10} \) is: \[ -31 \frac{1}{2} \]
Therefore, the answer is \( \boxed{-31 \frac{1}{2}} \).