Proper and Improper fractions; Negative fractions

The definition of an improper fraction is two part:

  1. The absolute value of the numerator must be greater than or equal to the denominator.
  2. The absolute value of the denominator cannot be zero

Let's look at the fraction


We look at the absolute values of these numbers (ignore the signs): 5 over 9
The numerator is less than the denominator so this is NOT improper.
And as long as we are discussing this fraction with the student. We NEVER leave the negative sign on the denominator (bottom) of a fraction. We ALWAYS put the sign on the numerator or out in front of the fraction. So, this fraction should be written -5/9. But that doesn't change the answer because we only look at the absolute values of the number, not the sign.
So, when the fraction has a negative sign in the denominator, just place that sign on the numerator or out in front. Now, if BOTH numerator and denominator have a negative sign, remember that a negative number divided by a negative number is a positive number, so neither number would have a negative sign. It is as if the two negatives cancel each other out.