Question
Use the additive inverse to find −24 4/5−6 7/10.(1 point)%0D%0AResponses%0D%0A%0D%0A−18 1/10%0D%0Anegative 18 Start Fraction 1 over 10 End Fraction%0D%0A%0D%0A−31 1/2%0D%0Anegative 31 Start Fraction 1 over 2 End Fraction%0D%0A%0D%0A−31 1/10%0D%0Anegative 31 Start Fraction 1 over 10 End Fraction%0D%0A%0D%0A31 1/2
Answers
GPT-4o mini
To find \(-24 \frac{4}{5} - 6 \frac{7}{10}\) using the additive inverse, we can rewrite the expression by changing the second term into its additive inverse.
1. First, convert the mixed numbers into improper fractions:
\[ -24 \frac{4}{5} = -\left(24 \times 5 + 4\right)/5 = -\frac{124}{5} \]
\[ -6 \frac{7}{10} = -\left(6 \times 10 + 7\right)/10 = -\frac{67}{10} \]
2. Next, find the additive inverse of the second term:
\[ -(-6 \frac{7}{10}) = 6 \frac{7}{10} \]
So, we will add instead:
\[ -24 \frac{4}{5} + 6 \frac{7}{10} \]
3. Now we need a common denominator to add the fractions. The least common multiple of 5 and 10 is 10.
Convert \(-\frac{124}{5}\) to a fraction with a denominator of 10:
\[ -\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10} \]
The second fraction \(\frac{67}{10}\) stays the same.
4. Now we can add:
\[
-\frac{248}{10} + \frac{67}{10} = \frac{-248 + 67}{10} = \frac{-181}{10}
\]
5. Converting \(\frac{-181}{10}\) back to a mixed number gives us:
\[
-18 \frac{1}{10}
\]
Therefore, the answer is \(-18 \frac{1}{10}\).
1. First, convert the mixed numbers into improper fractions:
\[ -24 \frac{4}{5} = -\left(24 \times 5 + 4\right)/5 = -\frac{124}{5} \]
\[ -6 \frac{7}{10} = -\left(6 \times 10 + 7\right)/10 = -\frac{67}{10} \]
2. Next, find the additive inverse of the second term:
\[ -(-6 \frac{7}{10}) = 6 \frac{7}{10} \]
So, we will add instead:
\[ -24 \frac{4}{5} + 6 \frac{7}{10} \]
3. Now we need a common denominator to add the fractions. The least common multiple of 5 and 10 is 10.
Convert \(-\frac{124}{5}\) to a fraction with a denominator of 10:
\[ -\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10} \]
The second fraction \(\frac{67}{10}\) stays the same.
4. Now we can add:
\[
-\frac{248}{10} + \frac{67}{10} = \frac{-248 + 67}{10} = \frac{-181}{10}
\]
5. Converting \(\frac{-181}{10}\) back to a mixed number gives us:
\[
-18 \frac{1}{10}
\]
Therefore, the answer is \(-18 \frac{1}{10}\).