Question

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

Answer 1

To find the sum of \( -24 \frac{4}{5} - 6 \frac{7}{10} \) using the concept of additive inverse, we first need to change it into addition by using the additive inverse.

Start by rewriting the expression:

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

Next, convert the mixed numbers to improper fractions:

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

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

Now we can add the two improper fractions:

\[
-\frac{124}{5} + (-\frac{67}{10})
\]

To add these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10. Now we convert \(-\frac{124}{5}\) to have a denominator of 10:

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

Now we can add the two fractions:

\[
-\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10}
\]

To simplify \(-\frac{315}{10}\):

\[
-\frac{315 \div 5}{10 \div 5} = -\frac{63}{2}
\]

Now convert \(-\frac{63}{2}\) back to a mixed number:

\(-\frac{63}{2} = -31 \frac{1}{2}\) (since \(63 \div 2\) gives a quotient of 31 and a remainder of 1).

Thus, the final result is:

\[
-31 \frac{1}{2}
\]