Question

Which improper fraction is equivalent to 5 3/4 A 23 / 3 B 46/8 C 46 / 4 D 34/8

Answer 1

To convert the mixed number \(5 \frac{3}{4}\) into an improper fraction, you can follow these steps:

1. Multiply the whole number part (5) by the denominator of the fractional part (4):
\[
5 \times 4 = 20
\]

2. Add the numerator of the fractional part (3) to this product:
\[
20 + 3 = 23
\]

3. Place this sum over the original denominator (4):
\[
5 \frac{3}{4} = \frac{23}{4}
\]

Now, let's check if this improper fraction is equivalent to any of the given options:

A. \( \frac{23}{3} \) - Not equivalent to \( \frac{23}{4} \)
B. \( \frac{46}{8} \) - To simplify \( \frac{46}{8} \), divide both the numerator and denominator by 2:
\[
\frac{46 \div 2}{8 \div 2} = \frac{23}{4} \quad \text{(this is equivalent)}
\]
C. \( \frac{46}{4} \) - Not equivalent to \( \frac{23}{4} \)
D. \( \frac{34}{8} \) - To simplify \( \frac{34}{8} \), divide both the numerator and denominator by 2:
\[
\frac{34 \div 2}{8 \div 2} = \frac{17}{4} \quad \text{(not equivalent)}
\]

Thus, the answer is \( \boxed{B} \) \( \frac{46}{8} \), which simplifies to \( \frac{23}{4} \).