To find \(-24 \frac{4}{5} - 6 \frac{7}{10}\) using the additive inverse, we can rewrite the expression by changing the second term into its additive inverse.
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First, convert the mixed numbers into improper fractions: \[ -24 \frac{4}{5} = -\left(24 \times 5 + 4\right)/5 = -\frac{124}{5} \] \[ -6 \frac{7}{10} = -\left(6 \times 10 + 7\right)/10 = -\frac{67}{10} \]
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Next, find the additive inverse of the second term: \[ -(-6 \frac{7}{10}) = 6 \frac{7}{10} \] So, we will add instead: \[ -24 \frac{4}{5} + 6 \frac{7}{10} \]
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Now we need a common denominator to add the fractions. The least common multiple of 5 and 10 is 10.
Convert \(-\frac{124}{5}\) to a fraction with a denominator of 10: \[ -\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10} \]
The second fraction \(\frac{67}{10}\) stays the same.
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Now we can add: \[ -\frac{248}{10} + \frac{67}{10} = \frac{-248 + 67}{10} = \frac{-181}{10} \]
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Converting \(\frac{-181}{10}\) back to a mixed number gives us: \[ -18 \frac{1}{10} \]
Therefore, the answer is \(-18 \frac{1}{10}\).