To solve \(-24 \frac{4}{5} - 6 \frac{7}{10}\) using the additive inverse, we can first convert the mixed numbers into improper fractions.
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Convert \(-24 \frac{4}{5}\) into an improper fraction: \[ -24 \frac{4}{5} = -\left(24 \times 5 + 4\right)/5 = -\left(120 + 4\right)/5 = -\frac{124}{5} \]
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Convert \(-6 \frac{7}{10}\) into an improper fraction: \[ -6 \frac{7}{10} = -\left(6 \times 10 + 7\right)/10 = -\left(60 + 7\right)/10 = -\frac{67}{10} \]
Now we can rewrite the subtraction as follows: \[ -24 \frac{4}{5} - 6 \frac{7}{10} = -\frac{124}{5} - \frac{67}{10} \]
- To subtract these fractions, we need a common denominator. The least common multiple of \(5\) and \(10\) is \(10\).
Convert \(-\frac{124}{5}\) to have a denominator of \(10\): \[ -\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10} \]
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Now we can subtract: \[ -\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10} \]
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Now simplify \(-\frac{315}{10}\): \[ -\frac{315}{10} = -31 \frac{5}{10} = -31 \frac{1}{2} \]
Thus, the result of \(-24 \frac{4}{5} - 6 \frac{7}{10}\) is \(-31 \frac{1}{2}\).
The answer is:
\(-31 \frac{1}{2}\)