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

Question

Responses

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

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

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

−31 1/2

Answer 1

To find \(-24 \frac{4}{5} - 6 \frac{7}{10}\) using the additive inverse, we convert the subtraction into addition using the additive inverse of the second number.

1. First, let's convert the two mixed numbers into improper fractions:

   • For \(-24 \frac{4}{5}\):

     • \(24 \times 5 + 4 = 120 + 4 = 124\), so \(-24 \frac{4}{5} = -\frac{124}{5}\).

   • For \(6 \frac{7}{10}\):

     • \(6 \times 10 + 7 = 60 + 7 = 67\), so \(6 \frac{7}{10} = \frac{67}{10}\).

2. Now, we rewrite the subtraction using the additive inverse: \[ -24 \frac{4}{5} - 6 \frac{7}{10} = -\frac{124}{5} + \left(-\frac{67}{10}\right). \]

3. To add these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10. We convert \(-\frac{124}{5}\) to a denominator of 10: \[ -\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10}. \]

4. Now, our expression looks like this: \[ -\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10}. \]

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

So the final result is \(-31 \frac{1}{2}\).

The correct response is: −31 1/2.