To determine the part-to-whole ratio for students who prefer yellow athletic shoes, follow these steps:
1. Identify the total number of students surveyed:
The total number of 6th-grade students surveyed is provided in the question, which is 60.
2. Identify the number of students who prefer yellow shoes:
According to the table, 16 students prefer yellow shoes.
3. Write the part-to-whole ratio:
The part-to-whole ratio is written as the number of students who prefer yellow shoes (the part) compared to the total number of students surveyed (the whole).
So, the ratio is:
[tex]\[
\frac{\text{Number of students who prefer yellow shoes}}{\text{Total number of students surveyed}} = \frac{16}{60}
\][/tex]
4. Express the ratio with a colon:
This ratio can be expressed with a colon as:
[tex]\[
16:60
\][/tex]
Finally, the part-to-whole ratio for students who prefer yellow shoes, written with a colon, is:
[tex]\[
16:60
\][/tex]
Therefore, the correct answer is [tex]\( \boxed{16:60} \)[/tex].
