Question

Simplify the following complex fraction.


1/2/5/8 + 1/4
A.
4/7




B.
4/13




C.
7/16




D.
7/4

Answer 1

To simplify the complex fraction \( \frac{1/2}{5/8} + \frac{1}{4} \), we can follow these steps:

1. **Simplify the complex fraction \( \frac{1/2}{5/8} \)**:
- When dividing fractions, we multiply by the reciprocal. Thus,
\[
\frac{1/2}{5/8} = \frac{1}{2} \times \frac{8}{5} = \frac{1 \times 8}{2 \times 5} = \frac{8}{10} = \frac{4}{5}
\]

2. **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:
\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\]

3. **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!