To solve the expression \( \frac{1}{2} \times \frac{4}{3} + \frac{5}{6} \div \frac{7}{8} \), we will start with the multiplication and division separately before combining the results.
Step 1: Perform the multiplication \( \frac{1}{2} \times \frac{4}{3} \)
\[ \frac{1}{2} \times \frac{4}{3} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \]
Step 2: Perform the division \( \frac{5}{6} \div \frac{7}{8} \)
Dividing by a fraction is the same as multiplying by its reciprocal, so: \[ \frac{5}{6} \div \frac{7}{8} = \frac{5}{6} \times \frac{8}{7} = \frac{5 \times 8}{6 \times 7} = \frac{40}{42} = \frac{20}{21} \]
Step 3: Combine the results from Step 1 and Step 2
Now we need to add \( \frac{2}{3} + \frac{20}{21} \). To do this, we need a common denominator. The least common multiple of 3 and 21 is 21.
Convert \( \frac{2}{3} \) to have a denominator of 21: \[ \frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21} \]
Now we can add: \[ \frac{14}{21} + \frac{20}{21} = \frac{14 + 20}{21} = \frac{34}{21} \]
Step 4: Convert to a mixed number
The improper fraction \( \frac{34}{21} \) can be converted to a mixed number: \[ 34 \div 21 = 1 \quad \text{(remainder } 13\text{)} \] This gives us the mixed number: \[ 1 \frac{13}{21} \]
Thus, the calculated result is: \[ 1 \frac{13}{21} \]
Conclusion
The correct answer is B. 1 13/21.