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... less than the original fraction.

Q: The square of a fraction less than one will always be?

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That is true.

Yes, ALWAYS. Think of it this way... If you had 1/2 a pie and you wanted just a FRACTION of it, that's less than the 1/2 you started with.

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.

Yes, if it is a whole number but not if it is a fraction

Yes, a fraction less than 1 will always have a numerator that is less than its denominator. This is because the value of a fraction decreases as the numerator gets smaller in relation to the denominator. For example, 1/2 is smaller than 3/2 or 4/2.

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That is true.

(3 and any fraction less than 1) is always bigger than (1 and any fraction less than 1).

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.

Yes, ALWAYS. Think of it this way... If you had 1/2 a pie and you wanted just a FRACTION of it, that's less than the 1/2 you started with.

No. The product of a mixed number between 4 and 5 and a fraction between 0 and 1 is always less than 5, but is not always less than 4.

You mean a proper fraction (less than 1). Multiply anything by less than 1 and you will make it smaller. Therefore the square root of your result is bigger than the start value. For numbers bigger than one it's the other way round.

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

Yes it is - any proper fraction is always less than one !

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.

Yes, if it is a whole number but not if it is a fraction

Yes, a fraction less than 1 will always have a numerator that is less than its denominator. This is because the value of a fraction decreases as the numerator gets smaller in relation to the denominator. For example, 1/2 is smaller than 3/2 or 4/2.