Since the magnitude is greater than 1, you cannot make it into a proper fraction.
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(1/2) / (1/3) = 3/2 = 11/2, which is not a proper fraction.
An inverted improper fraction is named a 'proper fraction'. e.g. 3/2 is Improper Fraction (Some times and incorrectly it is called a 'top heavy' fraction. Inverting 2/3 is a proper fraction.
Since the decimal fraction is greater than 1, there can be no proper fraction which is equal.
There is no specific name. -3 is greater than -4 and (-3)/(-4) = 3/4 is a positive proper fraction. 3 is greater than -4 and 3/(-4) = -3/4 is a negative proper fraction. 3 is greater than -2 and 3/(-2) = -3/2 is a negative improper fraction. 4 is greater than 3 and 4/3 is a positive improper fraction. Thus, the fraction can be negative or positive, proper or improper.
There is no specific name. -3 is greater than -4 and (-3)/(-4) = 3/4 is a positive proper fraction. 3 is greater than -4 and 3/(-4) = -3/4 is a negative proper fraction. 3 is greater than -2 and 3/(-2) = -3/2 is a negative improper fraction. 4 is greater than 3 and 4/3 is a positive improper fraction. Thus, the fraction can be negative or positive, proper or improper.