Use the additive inverse to find −24 4/5−6 7/10

Answer 1

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

1. Convert \(-24 \frac{4}{5}\): \[ -24 \frac{4}{5} = -\left(24 \times 5 + 4\right)/5 = -\left(120 + 4\right)/5 = -\frac{124}{5} \]

2. Convert \(-6 \frac{7}{10}\): \[ -6 \frac{7}{10} = -\left(6 \times 10 + 7\right)/10 = -\left(60 + 7\right)/10 = -\frac{67}{10} \]

Now we have: \[ -24 \frac{4}{5} - 6 \frac{7}{10} = -\frac{124}{5} - \frac{67}{10} \]

3. Find a common denominator: The least common denominator of 5 and 10 is 10. To convert \(-\frac{124}{5}\) into tenths: \[ -\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10} \]

Now we can add: \[ -\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10} \]

4. Simplify the result: \[ -\frac{315}{10} = -31 \frac{5}{10} = -31 \frac{1}{2} \]

Thus, the result of \(-24 \frac{4}{5} - 6 \frac{7}{10}\) is: \[ \boxed{-31 \frac{1}{2}} \]