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

Question

Responses

3112
31 Start Fraction 1 over 2 End Fraction

−31110
negative 31 Start Fraction 1 over 10 End Fraction

−18110
negative 18 Start Fraction 1 over 10 End Fraction

−3112

Answer 1

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

1. Convert \(-24 \frac{4}{5}\) to an improper fraction: \[ -24 \frac{4}{5} = -\left(24 \times 5 + 4\right) = -\left(120 + 4\right) = -124 \text{ (as an improper fraction)} = -\frac{124}{5} \]

2. Convert \(-6 \frac{7}{10}\) to an improper fraction: \[ -6 \frac{7}{10} = -\left(6 \times 10 + 7\right) = -\left(60 + 7\right) = -67 \text{ (as an improper fraction)} = -\frac{67}{10} \]

Next, unite the two fractions \(-\frac{124}{5}\) and \(-\frac{67}{10}\). To add these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10.

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

Now we can add the two fractions: \[ -\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10} \]

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

So, the final answer is: \[ \boxed{-31 \frac{1}{2}} \]