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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.

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

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The above statement is not true!-3/4 is a fraction which is less than 1. Its reciprocal is -4/3 which is also less than 1, NOT greater.

A positive fraction that is less than one is known as a proper fraction. In a proper fraction, the denominator is greater than the numerator. A reciprocal fraction would have a numerator greater than the denominator. Such a fraction is known as an improper fraction. Improper fractions are greater than one.

That is why it is called an improper fraction because a proper or a common fraction always has its numerator less than its denominator.

When a number is a fraction, the reciprocal will always be greater than the original number. When the original number is a whole number, the reciprocal will be a fraction, which is less than a whole number.

What is the question ? This is often referred to as an "improper" fraction. It can always be re-written as an integer (whole number) plus a proper fraction (a fraction less than one).

Where is the fraction? 37 is less than 710.

If the denominator is positive and the numerator is less than the denominator then the fraction is less than 1. If the denominator is positive and the numerator is greater than the denominator then the fraction is greater than 1.

TRUE. A proper fraction is always less than 1 and a mixed number is always greater than 1

True.

... less than the original fraction.

the numerator always has to be less than the denominator and if its equal like 5 to 5 that is 1

No. Every proper fraction is less than 1, but improper fraction will be greater than 1.

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