There is no difference in value between "equal" fractions: the difference is zero.
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An integer is a whole number. There are lots of other numbers, such as fractions or rationals, and irrational numbers (such as the square root of 2)
The GCF refers to integers, not fractions.
Well, darling, between 5 and 6, there are infinity fractions. Fractions are like rabbits, they just keep multiplying. So, if you want an exact number, tough luck, because you'll be counting those fractions until the cows come home.
Proper and improper fractions are alike in that they both represent parts of a whole. Both types of fractions have a numerator (the top number) and a denominator (the bottom number). The relationship between the numerator and denominator determines the value of the fraction. The main difference between proper and improper fractions is that in a proper fraction, the numerator is smaller than the denominator, while in an improper fraction, the numerator is equal to or larger than the denominator.
As the denominator increases the fraction will be smaller but there is no limit to how tiny that fraction can be. So between any two numbers on the number line, you can have an infinite number of fractions.