Question: will the reciprocal of a proper fraction be a proper fraction

Answer: No, The reciprocal of a fraction is another fraction with the numerator and denominator exchanged. The reciprocal of 3 7 (\displaystyle (\tfrac (3)(7))) , for instance, is 7 3 (\displaystyle (\tfrac (7)(3))) . The product of a fraction and its reciprocal is 1, hence the reciprocal is the multiplicative inverse of a fraction. The reciprocal of a proper fraction is improper, and the reciprocal of an improper fraction not equal to 1, that is, numerator and denominator are not equal, is a proper fraction.