The easiest division problems are the ones that involve two positive integers. A fun way to teach students about dividing positive integers is by adding a little bit of English to the exercise. Create a list of 50 simple division problems and have students complete it. Make sure each answer is a number between 1 through 26 so it corresponds with a letter of the alphabet. When they finish, have them use the answers to spell a certain word or phrase, and make sure they have to get every answer correct in order to figure out the puzzle.
When you divide two negative integers the answer is always a positive number, so you can have them correspond to the alphabet and play a word puzzle again. Instead of simply having students answer division problems ( ex. -10/-5 = _), have them fill in the blanks this time (ex. -10/_ = 2). This will keep their mind actively thinking, instead of simply repeating.
When you divide a positive and negative integer, the answer is always a negative number. Create a worksheet with 50 or so division problems, and make sure each problem has one positive and one negative number. You can also mix in some fill-in-the-blank questions. Have students add up all their answers and divide by the number of questions in order to get the average answer. They'll need to get all the answers correct to get the correct average.
When students get into the rhythm of repeating, their brains use less energy. It's easy to do 50 of the same problem, then 50 of another type of problem and get them all correct. You don't know if they remember that a positive divided by a negative equals a negative and a negative divided by a negative equals a positive, or if it's just memorization. Create a worksheet of division problems and throw in everything you've taught (fill-ins, negative/negative, positive/positive, negative/positive). When they're done, have them add all their answers together; the sum should equal a designated number.