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

Question

Responses

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

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

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

−18 110

Answer 1

To find $-24\frac{4}{5}-6\frac{7}{10}$ using the additive inverse, we first convert the mixed numbers into improper fractions.

1. Convert mixed numbers into improper fractions:

   For $-24\frac{4}{5}$: $$-24\frac{4}{5}=-(24\times 5+4)/5=-(120+4)/5=-\frac{124}{5}$$

   For $-6\frac{7}{10}$: $$-6\frac{7}{10}=-(6\times 10+7)/10=-(60+7)/10=-\frac{67}{10}$$

2. Now we need to find a common denominator to combine these fractions. The least common multiple of 5 and 10 is 10.

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

4. Now, we can add the fractions: $$-\frac{248}{10}-\frac{67}{10}=-\frac{248+67}{10}=-\frac{315}{10}$$

5. Convert $-\frac{315}{10}$ back to a mixed number: $$-\frac{315}{10}=-31\frac{5}{10}=-31\frac{1}{2}$$

Thus, the final answer is: $$\boxed{{\displaystyle -31\frac{1}{2}}}$$