Question

Which improper fraction is equivalent to 5 3/4? Is it 46/8, 23/3, 46/4, 34/8.

Answer 1

To convert the mixed number \(5 \frac{3}{4}\) into an improper fraction, we can use the following steps:

1. Multiply the whole number part (5) by the denominator of the fractional part (4).
2. Add the numerator of the fractional part (3) to the result from step 1.
3. The result will be the new numerator, while the denominator will remain the same (4).

Following these steps:

1. \(5 \times 4 = 20\)
2. \(20 + 3 = 23\)

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:

- \( \frac{46}{8} \) can be simplified:
\[
\frac{46 \div 2}{8 \div 2} = \frac{23}{4}
\]

- \( \frac{23}{3} \) is not equivalent since the denominators differ.
- \( \frac{46}{4} \) simplifies to:
\[
\frac{46 \div 2}{4 \div 2} = \frac{23}{2}
\]

- \( \frac{34}{8} \) 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:

\[
\boxed{\frac{46}{8}}
\]