ANSWER
Option d is the correct equation:
[tex]\frac{5}{6}\div\frac{1}{18}=15[/tex]
EXPLANATION
Let's say that Santi painted "n" stripes. If each stripe is 1/18 yard thick, then the total thickness of all n stripes is,
[tex]n\times\frac{1}{18}[/tex]
If he painted the complete height of the post, then this must be equal to 5/6 yards,
[tex]n\times\frac{1}{18}=\frac{5}{6}[/tex]
If we want to find n, the number of stripes, we have to divide both sides by 1/18,
[tex]\begin{gathered} n\times\frac{1}{18}\div\frac{1}{18}=\frac{5}{6}\div\frac{1}{18} \\ \\ n=\frac{5}{6}\div\frac{1}{18} \end{gathered}[/tex]
To solve this, change the division sign into a multiplication sign and flip the second fraction,
[tex]n=\frac{5}{6}\times18[/tex]
18 is divisible by 6, so we can simplify this before multiplying,
[tex]n=\frac{5}{6}\times18=5\times3=15[/tex]
Hence, the correct equation is,
[tex]\frac{5}{6}\div\frac{1}{18}=15[/tex]
