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Q: What is a fraction less than two thirds but greater than one half?

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If two times the numerator is less than the denominator, the fraction is less than half. If two times the numerator is equal to the denominator, the fraction is equal to a half. If two times the numerator is greater than the denominator, the fraction is greater than half.

Every negative fraction, and every positive fraction whose numerator is half of its denominator or less, is not greater than one half.

greater

greater than

7/3 is greater than 1/2

less, if it is a fraction of a half, it cannt be a whole

If the fraction is less than half, round down. If the fraction is half or greater, round up.

If the numerator is greater than or less than one half of the denominator. For example, 7/16 is less because 7 is less than half of 16.

5/8

5/8

2/5

There are infinitely many of them: 41/97 is one such.

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