To simplify the complex fraction \( \frac{1/2}{5/8} + \frac{1}{4} \), we can follow these steps:
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Simplify the complex fraction \( \frac{1/2}{5/8} \):
- When dividing fractions, we multiply by the reciprocal. Thus, \[ \frac{1/2}{5/8} = \frac{1}{2} \times \frac{8}{5} = \frac{1 \times 8}{2 \times 5} = \frac{8}{10} = \frac{4}{5} \]
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Add \( \frac{4}{5} \) and \( \frac{1}{4} \):
- To add these two fractions, we need a common denominator. The least common denominator (LCD) of 5 and 4 is 20.
- Convert \( \frac{4}{5} \) to a fraction with a denominator of 20: \[ \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20} \]
- Convert \( \frac{1}{4} \) to a fraction with a denominator of 20: \[ \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20} \]
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Now add the two fractions: \[ \frac{16}{20} + \frac{5}{20} = \frac{16 + 5}{20} = \frac{21}{20} \]
Thus, the simplified result is: \[ \frac{21}{20} = 1.05 \]
However, this simplified fraction does not match any of the given answer choices (A through D). Please double-check the options provided, or clarify if there was a mistake in the original expression or the options presented!