Fraction in-between
Consider the fractions \( \dfrac{5}{29} \) and \( \dfrac{1}{2} \).
Adding tops and bottoms produces a number in between, so \( \dfrac{6}{31}\) is in between \( \dfrac{5}{29} \) and \( \dfrac{1}{2} \).
But \(\dfrac{6}{31} \) is less than half, so it must be \( \dfrac{5}{29} < \dfrac{6}{31} < \dfrac{1}{2} \).
FB reminded me of this argument for why 5/29 is less than 6/31 from five years ago...Consider the fractions 5/29 and 1/2. Adding tops and bottoms produces a number in between, so 6/31 is in between 5/29 and 1/2. But 6/31 is less than half, so it must be 5/29 < 6/31 < 1/2.
— David Butler (@DavidKButlerUoA) September 23, 2020
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