5/6 part of 18 means divide 18 into 6 equal parts and take 5 of the equal parts with you.
Thus, 5/6 of 18 = (5/6)*18 = 5*(18/6) = 5*3 = 15
There are other ways to solve this problem. One way would be to convert 5/6 into decimal. When dividing numerator by denominator, the decimal is .833 and then multiply this by 18, and you would get 15. Another way would be to use manipulatives and show a fraction bar of sixths. If you applied this to your whole of 18 and then portioned it off into sixths, five sixths pieces would cover 15 of the total 18. In a more manipulative sense, give the fourth grader 18 Starburst candies, or any candy in smaller parts. Then, ask them to divide this total into groups of sixths. Finally, tell them that they can keep 5 of these sixths and they should be able to, after trial and error, determine that they get 15 total.
You can answer this question by multiplying the two numbers together:
5/6 x 18 = 15
so 15 is 5/6 of 18
To see why this is so, consider the two ratios:
5/6 = N/18
so N = 18 x 5/6
All you have to do here is to multiply. You are going to multiply 5/6 by 18. To do that, the best way is to make 18 into a fraction -- that is, write it as 18/1. From there, you know what to do. When you multiply two fractions, you multiply top numbers by top numbers, bottom numbers by bottom numbers.
So here, you would multiply 5 by 18 and 6 by 1. That would get you 90/6. So 5/6 of 18 is 90/6.
If you like, you can divide that to simplify and you get 15.
Another way to do it is to divide 18 by 6 which gets you 3. Then you know that 3 is 1/6 of 18. From there, you multiply by 5 and get 15.