Question

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

−31 1/10
negative 31 Start Fraction 1 over 10 End Fraction

31 1/2
31 Start Fraction 1 over 2 End Fraction

−18 1/10
negative 18 Start Fraction 1 over 10 End Fraction

−31 1/2

Answer 1

-31 1/2 is the CORRECT answer ???????????????????????

Answer 2

To find \(-24 \frac{4}{5} - 6 \frac{7}{10}\) using the additive inverse, you can rewrite the subtraction as adding the opposite (additive inverse) of the second number. So:

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

Now, 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 need to add \(-\frac{124}{5}\) and \(-\frac{67}{10}\). First, we need a common denominator. The least common denominator (LCD) of 5 and 10 is 10.

Convert \(-\frac{124}{5}\) to have a denominator of 10:
\[
-\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10}
\]

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

Now simplify \(-\frac{315}{10}\):
\[
-\frac{315 \div 5}{10 \div 5} = -\frac{63}{2}
\]

Convert \(-\frac{63}{2}\) to a mixed number:
\[
-31 \frac{1}{2}
\]

Thus, the answer is:

\(-31 \frac{1}{2}\)

Answer 3

Yes, \(-31 \frac{1}{2}\) is the correct answer to the expression \(-24 \frac{4}{5} - 6 \frac{7}{10}\). Let's summarize how we arrived at this solution:

1. Convert the mixed numbers to improper fractions:
- \(-24 \frac{4}{5} = -\frac{124}{5}\)
- \(-6 \frac{7}{10} = -\frac{67}{10}\)

2. Find a common denominator for the fractions, which is 10:
- Convert \(-\frac{124}{5}\) to a fraction with a denominator of 10:
\[
-\frac{124}{5} = -\frac{248}{10}
\]

3. Add the two fractions:
\[
-\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10}
\]

4. Simplify \(-\frac{315}{10}\):
\[
-\frac{315 \div 5}{10 \div 5} = -\frac{63}{2}
\]

5. Convert \(-\frac{63}{2}\) to a mixed number:
\[
-\frac{63}{2} = -31 \frac{1}{2}
\]

So, \(-31 \frac{1}{2}\) is indeed the correct answer. Thank you for your patience!