`(13)/(48)` is equal to

Options

A. `(1)/(3 + (1)/(1 + (1)/(16)))`
B. `(1)/(2 + (1)/(1 + (1)/(8)))`
C. `(1)/(3 + (1)/(1 + (1)/(1 + (1)/(8))))`
D. `(1)/(3 + (1)/(1 + (1)/(2 + (1)/(4))))`

Answer

To solve the question `(13)/(48)` and find its equivalent form, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Fraction**: We start with the fraction \( \frac{13}{48} \). Our goal is to express this fraction in a different form.

2. **Finding a Common Denominator**: We can express \( \frac{13}{48} \) in terms of a mixed number or another fraction. To do this, we can look for fractions that have a denominator that is a factor of 48.

3. **Testing Options**: We will check several options to see which one is equivalent to \( \frac{13}{48} \).

- **Option A**: \( 1 + \frac{1}{16} \)
- Calculate: \( 1 + \frac{1}{16} = \frac{16}{16} + \frac{1}{16} = \frac{17}{16} \)
- Find the reciprocal: \( \frac{1}{\frac{17}{16}} = \frac{16}{17} \)
- This does not equal \( \frac{13}{48} \).

- **Option B**: \( 1 + \frac{1}{8} \)
- Calculate: \( 1 + \frac{1}{8} = \frac{8}{8} + \frac{1}{8} = \frac{9}{8} \)
- Find the reciprocal: \( \frac{1}{\frac{9}{8}} = \frac{8}{9} \)
- This does not equal \( \frac{13}{48} \).

- **Option C**: \( 1 + \frac{1}{8} \) again (as per the transcript, it seems to repeat)
- This has already been calculated and does not equal \( \frac{13}{48} \).

- **Option D**: \( 2 + \frac{1}{4} \)
- Calculate: \( 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \)
- Find the reciprocal: \( \frac{1}{\frac{9}{4}} = \frac{4}{9} \)
- Now calculate \( 1 + \frac{4}{9} = \frac{9}{9} + \frac{4}{9} = \frac{13}{9} \)
- Find the reciprocal: \( \frac{1}{\frac{13}{9}} = \frac{9}{13} \)

4. **Final Check**: We need to check if any of these options can be manipulated to equal \( \frac{13}{48} \).

- After checking all options, we find that none of them equal \( \frac{13}{48} \) directly. However, through manipulation and checking, we can confirm that \( \frac{13}{48} \) can be expressed in terms of other fractions, but none of the options provided in the question were equivalent.

### Conclusion:
The fraction \( \frac{13}{48} \) does not equal any of the options provided in the question.