To convert the mixed number \(5 \frac{3}{4}\) into an improper fraction, we can use the following steps:
- Multiply the whole number part (5) by the denominator of the fractional part (4).
- Add the numerator of the fractional part (3) to the result from step 1.
- The result will be the new numerator, while the denominator will remain the same (4).
Following these steps:
- \(5 \times 4 = 20\)
- \(20 + 3 = 23\)
Thus, \(5 \frac{3}{4}\) can be written as an improper fraction:
\[ \frac{23}{4} \]
Now, let's compare \( \frac{23}{4} \) with the options provided:
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\( \frac{46}{8} \) can be simplified: \[ \frac{46 \div 2}{8 \div 2} = \frac{23}{4} \]
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\( \frac{23}{3} \) is not equivalent since the denominators differ.
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\( \frac{46}{4} \) simplifies to: \[ \frac{46 \div 2}{4 \div 2} = \frac{23}{2} \]
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\( \frac{34}{8} \) can be simplified: \[ \frac{34 \div 2}{8 \div 2} = \frac{17}{4} \]
From these comparisons, we see that \( \frac{46}{8} \) is equivalent to \( \frac{23}{4} \).
Therefore, the improper fraction equivalent to \( 5 \frac{3}{4} \) is:
\[ \boxed{\frac{46}{8}} \]
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