To solve the expression \( \frac{1}{2} \times \frac{4}{3} + \frac{5}{6} \div \frac{7}{8} \), we will follow the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)):
-
Start with the multiplication: \[ \frac{1}{2} \times \frac{4}{3} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \]
-
Now, address the division: \[ \frac{5}{6} \div \frac{7}{8} = \frac{5}{6} \times \frac{8}{7} = \frac{5 \times 8}{6 \times 7} = \frac{40}{42} = \frac{20}{21} \]
-
Now combine the results: \[ \frac{2}{3} + \frac{20}{21} \]
We need a common denominator to add these fractions. The least common denominator (LCD) 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 add \( \frac{14}{21} \) and \( \frac{20}{21} \): \[ \frac{14}{21} + \frac{20}{21} = \frac{14 + 20}{21} = \frac{34}{21} \]
-
Convert \( \frac{34}{21} \) to a mixed number: \[ 34 \div 21 = 1 \text{ with a remainder of } 13 \] Thus, \( \frac{34}{21} = 1 \frac{13}{21} \).
So the final answer is:
1 13/21
The correct answer is: 1 13/21.