Do you have an example of a word problem you are struggling with? I'm afraid there isn't enough information here for me to help you with your specific difficulty, but I tried to give an example below.
Here's an example I got from Khan Academy: "Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/16 a gallon of paint. How many statues can she paint?"
When you are dividing, you are essentially trying to figure out how many parts you can make out of the whole. This is true even if you have a fraction or if what you are dividing is less than "1." In this case, you can pretend 7/8 is the whole (it is not a whole number, 8/8 equals 1, which would be a whole number. Fractions, by definition, cannot be whole numbers).
The question is asking how many times you can take 1/16 out of 7/8. While you could keep subtracting 1/16 from 7/8, division is much faster. So to solve the problem, you need to answer this: 7/8 ÷ 1/16. 7/8 is your dividend, 1/16 is your divisor.
The answer (quotient) is 14. You can check your answer by multiplying. 1/16 x 14 = 7/8. If you're unsure of your answer, multiply your quotient by your divisor. The result should be the same fraction as your dividend. Sometimes, depending on the problem, you may also have a remainder. If you're checking your answer, add the remainder after you've multiplied the quotient and divisor.
If I haven't answered your question thoroughly enough, please feel free to ask follow-up questions. Be sure to add details to the question.
To comply with Wyzant's academic integrity policy and Khan Academy's copyright specification, here is the link to the exercise I got the example from: https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-div-fractions-word-problems/e/dividing-fractions-by-fractions-word-problems
"NOTE: All Khan Academy content is available for free at www.khanacademy.org" (I neither intend to endorse Khan Academy nor imply that they endorse Wyzant or myself, use of their materials requires specific attribution verbiage.)