Use the additive to find - 24 4/5 - 6 7/10.

Question

A. -31 1/2
B. 31 1/2
C. -18 1/10
D. -31 1/10

Answer 1

To solve the problem \(-24 \frac{4}{5} - 6 \frac{7}{10}\), let's follow these steps:

1. **Convert the mixed numbers to improper fractions:**
- \(-24 \frac{4}{5}\):
\[
-24 \frac{4}{5} = -\left(24 + \frac{4}{5}\right) = -\left(\frac{24 \times 5 + 4}{5}\right) = -\left(\frac{120 + 4}{5}\right) = -\left(\frac{124}{5}\right) = -\frac{124}{5}
\]
- \(6 \frac{7}{10}\):
\[
6 \frac{7}{10} = 6 + \frac{7}{10} = \frac{6 \times 10 + 7}{10} = \frac{60 + 7}{10} = \frac{67}{10}
\]

2. **Find a common denominator and convert both fractions:**
The common denominator for 5 and 10 is 10.
- Convert \(-\frac{124}{5}\) to have a denominator of 10:
\[
-\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10}
\]

3. **Subtract the fractions:**
\[
-\frac{248}{10} - \frac{67}{10} = -\left(\frac{248 + 67}{10}\right) = -\frac{315}{10}
\]

4. **Convert the improper fraction back to a mixed number:**
- First, perform the division \(315 \div 10\):
\[
315 \div 10 = 31 \text{ R } 5 \quad \Rightarrow \quad \frac{315}{10} = 31 \frac{5}{10}
\]
- Simplify \(\frac{5}{10}\) to \(\frac{1}{2}\):
\[
31 \frac{5}{10} = 31 \frac{1}{2}
\]
- Don't forget the negative sign:
\[
-31 \frac{1}{2}
\]

Therefore, \(-24 \frac{4}{5} - 6 \frac{7}{10} = -31 \frac{1}{2}\).

The correct answer is:
A. \(-31 \frac{1}{2}\)