Which improper fraction is equivalent to 5(3/4)?

Question

Responses

34/8
34 eighths - no response given

46/8
46 eighths - not selected, this is the correct answer

46/4
46 fourths - no response given

23/3
23 thirds - incorrect

Answer 1

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

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

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

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

So, \(5\frac{3}{4}\) is equivalent to \(\frac{23}{4}\).

Now, if you are to express this as an equivalent improper fraction with a denominator of 8, you would convert as follows:

1. Since \(4\) can be converted to \(8\) by multiplying by \(2\), you can represent \(\frac{23}{4}\) as: \[ \frac{23 \times 2}{4 \times 2} = \frac{46}{8} \]

Thus, the improper fraction equivalent to \(5\frac{3}{4}\) is \(\frac{46}{8}\).

So the correct response is indeed 46/8.