Question

Santi paints different colored horizontal stripes on a fence post. The fence post is 5/6 yard tall, and each stripe is 1/18 yard thick. Which equation shows how to find how many stripes Santi can paint on the fence post?

Answer 1

Option d is the correct equation:

`(5)/(6)/(1)/(18)=15`

Step-by-step 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,

`n*(1)/(18)`

If he painted the complete height of the post, then this must be equal to 5/6 yards,

`n*(1)/(18)=(5)/(6)`

If we want to find n, the number of stripes, we have to divide both sides by 1/18,

`\begin{gathered} n*(1)/(18)/(1)/(18)=(5)/(6)/(1)/(18) \\ \\ n=(5)/(6)/(1)/(18) \end{gathered}`

To solve this, change the division sign into a multiplication sign and flip the second fraction,

`n=(5)/(6)*18`

18 is divisible by 6, so we can simplify this before multiplying,

`n=(5)/(6)*18=5*3=15`

Hence, the correct equation is,

`(5)/(6)/(1)/(18)=15`