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

Question

O 31 1/2
O -18 1/10
O -31 1/10
O -31 1/2

Answer 1

To find \(-24 \frac{4}{5} - 6 \frac{7}{10}\) using the additive inverse method, we can rewrite the problem as:

\[ -24 \frac{4}{5} + (-6 \frac{7}{10}) \]

Step 1: Convert mixed numbers to improper fractions

1. For \(-24 \frac{4}{5}\):

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

2. For \(-6 \frac{7}{10}\):

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

Step 2: Find a common denominator

The least common multiple of 5 and 10 is 10. We rewrite \(-\frac{124}{5}\) with a denominator of 10:

\[ -\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10} \]

Step 3: Add the fractions

Now we can add the fractions:

\[ -\frac{248}{10} + \left(-\frac{67}{10}\right) = -\frac{248 + 67}{10} = -\frac{315}{10} \]

Step 4: Simplify the fraction

Now we simplify \(-\frac{315}{10}\):

\[ -\frac{315}{10} = -31 \frac{5}{10} = -31 \frac{1}{2} \]

Conclusion

Thus, the value of \(-24 \frac{4}{5} - 6 \frac{7}{10}\) is \(-31 \frac{1}{2}\).

The correct option is: O -31 1/2.