Question

Perform the indicated operation. \(-7 \frac{5}{8}+2 \frac{1}{6}\)

Short answer

Answer: The sum is -5 11/24.

Step-by-step solution

Convert Mixed Numbers to Improper Fractions

First, let's convert \(-7 \frac{5}{8}\) and \(2 \frac{1}{6}\) to improper fractions. For \(-7 \frac{5}{8}\), the improper fraction will be: \(-\frac{7\times 8 + 5}{8} = -\frac{61}{8}\) For \(2 \frac{1}{6}\), the improper fraction will be: \(\frac{2\times 6 + 1}{6} = \frac{13}{6}\) So the problem becomes: \(-\frac{61}{8} + \frac{13}{6}\)

Find the Common Denominator and Add the Fractions

Now, we must find the common denominator for both fractions. The least common multiple of 8 and 6 is 24. Let's convert both fractions to have a denominator of 24. \(-\frac{61}{8} \times \frac{3}{3} = -\frac{183}{24}\) \(\frac{13}{6} \times \frac{4}{4} = \frac{52}{24}\) Now, add the two fractions: \(-\frac{183}{24} + \frac{52}{24} = -\frac{131}{24}\)

Convert Improper Fraction to Mixed Number

Now, let's convert the improper fraction \(-\frac{131}{24}\) back to a mixed number. Divide 131 by 24: \(131 \div 24 = 5\) with a remainder of 11. So, \(-\frac{131}{24} = -5 \frac{11}{24}\) The final answer is \(\boxed{-5 \frac{11}{24}}\).