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Why is the recipical of A fraction less than one is always a fraction greater than one?

Mollywags11tw3860

Lvl 1
2016-02-05 04:54:21

Fractions that are less than one are known as proper fractions. Their denominators are greater than their numerators. Their reciprocals would have numerators greater than their denominators, making them improper. Improper fractions are greater than one.

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2016-02-05 04:54:21
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2015-03-06 13:09:50

First of all, the proposition is the question is not true.

Consider the fraction A = -1/2. It is a fraction that is less than zero and so certainly less than one. However, its reciprocal is -2 which is NOT greater than 1. The statement is true only for positive fractions (bit that was not stated in the question).

A positive fraction A is less than 1 if its numerator is less than its denominator (both being positive). The numerator of the reciprocal of A will be the denominator of A and the denominator of the reciprocal of A will be the numerator of A. Thus, the reciprocal of A will have a numerator which is greater than its denominator. Consequently, the fraction will be greater than 1.