Question

Use the additive inverse to find −24 4/5−6 7/10 .(1 point) Responses −18 1/10 negative 18 Start Fraction 1 over 10 End Fraction −31110 negative 31 Start Fraction 1 over 10 End Fraction −31 1/2 negative 31 Start Fraction 1 over 2 End Fraction 31 1/2

Answer 1

answer in numbers only

Answer 2

To solve \( -24 \frac{4}{5} - 6 \frac{7}{10} \) using the additive inverse, we first convert the mixed numbers to improper fractions and then add their additive inverses.

### Step 1: Convert the mixed numbers to improper fractions.

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

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

### Step 2: Add the two fractions.

To add the fractions, we need a common denominator. The least common multiple (LCM) of 5 and 10 is 10.

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

2. **Now, add the two fractions**:
\[
-\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10}
\]

### Step 3: Simplify \( -\frac{315}{10} \) into a mixed number.

1. **Divide 315 by 10**:
- The division \( 315 \div 10 \) gives us a whole number of 31 with a remainder of 5.

So,
\[
-\frac{315}{10} = -31 \frac{5}{10}
\]
2. **Simplify \( \frac{5}{10} \)**:
- \( \frac{5}{10} = \frac{1}{2} \)

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

### Final Answer
The result of \( -24 \frac{4}{5} - 6 \frac{7}{10} \) is:
\[
-31 \frac{1}{2}
\]

Therefore, the answer is \( \boxed{-31 \frac{1}{2}} \).

Answer 3

-31 1/2