To find \(-24 \frac{4}{5} - 6 \frac{7}{10}\) using the additive inverse, we can rewrite the problem as:
\[ -24 \frac{4}{5} + (-6 \frac{7}{10}) \]
First, let's convert the mixed numbers to 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 \(-6 \frac{7}{10}\): \[ -6 \frac{7}{10} = -\left(6 \times 10 + 7\right) / 10 = -\left(60 + 7\right) / 10 = -\frac{67}{10} \]
Next, we need a common denominator to add these two fractions. The least common denominator of 5 and 10 is 10.
Convert \(-\frac{124}{5}\) to a fraction with a denominator of 10: \[ -\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10} \]
Now, we can add the two fractions: \[ -\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10} \]
Now, simplify \(-\frac{315}{10}\): \[ -\frac{315}{10} = -31 \frac{5}{10} = -31 \frac{1}{2} \]
Thus, the final answer is: \[ \boxed{-31 \frac{1}{2}} \]
So, the correct response is a. −31 1/2.
1 answer