Question

Use the additive inverse to find −24 4/5 −6 7/10 .(1 point)
Responses

A. 31 1/2

B. −31 1/2

C. −18 1/10

D. −31 1/10

Answer 1

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

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

First, convert the mixed numbers to improper fractions.

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

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

Next, we need to add these two improper fractions. To do this, we need a common denominator. The least common multiple of 5 and 10 is 10.

Now 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 \(-\frac{248}{10}\) and \(-\frac{67}{10}\):
\[
-\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10}
\]

Now, simplify \(-\frac{315}{10}\):
\[
-\frac{315}{10} = -31 \frac{5}{10} = -31 \frac{1}{2}
\]

Thus, the final answer is:

**B. \(-31 \frac{1}{2}\)**