To solve the expression \( \frac{1}{2} \times \frac{4}{3} + \frac{5}{6} \div \frac{7}{8} \), we will break it down step by step.
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Calculate \( \frac{1}{2} \times \frac{4}{3} \): \[ \frac{1}{2} \times \frac{4}{3} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \]
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Calculate \( \frac{5}{6} \div \frac{7}{8} \): Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{5}{6} \div \frac{7}{8} = \frac{5}{6} \times \frac{8}{7} = \frac{5 \times 8}{6 \times 7} = \frac{40}{42} = \frac{20}{21} \]
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Add the two results together: Now, we have: \[ \frac{2}{3} + \frac{20}{21} \]
To add these fractions, we need a common denominator. The least common multiple of 3 and 21 is 21.
Convert \( \frac{2}{3} \) to a fraction with a denominator of 21: \[ \frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21} \]
Now we can add: \[ \frac{14}{21} + \frac{20}{21} = \frac{14 + 20}{21} = \frac{34}{21} \]
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Convert \( \frac{34}{21} \) to a mixed number: \(\frac{34}{21}\) is greater than 1. To convert it to a mixed number: \[ 34 \div 21 = 1 \quad \text{(remainder 13)} \] So, \[ \frac{34}{21} = 1 \frac{13}{21} \]
Therefore, the final result of the calculation is: \[ \boxed{1 \frac{13}{21}} \]
So the correct answer from the choices is 1 13/21.
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