To solve \( 23 \div 35 \), we can express the division as a fraction:
\[ \frac{23}{35} \]
This fraction is already in its simplest form because 23 is a prime number and does not divide evenly into 35.
To get a decimal approximation, you can perform the division:
\[ 23 \div 35 \approx 0.6571 \]
Now, let's check the provided answers to see which one matches \( \frac{23}{35} \) or its decimal approximation.
The options given are:
- 615
- 56 over 15
- 585 eighths
- 9159 over 15
- 109
It looks like option 2, which is \( \frac{56}{15} \), is the closest as a fraction form. To simplify further, we can convert \( \frac{23}{35} \) to a similar format:
Let's check \( \frac{56}{15} \):
Calculating the decimal of \( \frac{56}{15} \):
\[ \frac{56}{15} \approx 3.7333 \]
This doesn't match with \( 0.6571 \).
Now let's check the rest:
- 615 seems like a whole number.
- 585 eighths would convert to \( \frac{585}{8} = 73.125 \).
- 9159 over 15 gives \( \frac{9159}{15} = 610.6 \).
- 109 doesn't make sense without context.
Thus, it appears that none of the provided options correctly represent \( 23 \div 35 \) or its proper decimal representation of approximately \( 0.6571 \).
If I had to choose the best representation based strictly on the forms provided, option 2 might seem more plausible but does not equal \( 23 \div 35 \). So, it appears there are no correct answers based on available options.