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THE five? There are far more than five rational numbers between 1/2 and 2/3; in fact there are an INFINITE number of rational numbers between them. If you just want five, try (3/6 + 4/6) / 2 = 7/12, which is halfway between the two numbers; 13/24, which is halfway between 1/2 and 7/12; 25/48, which is halfway between 1/2 and 13/24; 49/96, which is halfway between 1/2 and 25/48; and 97/192, which is halfway between 1/2 and 49/96. Obviously I could continue forever finding the number that is halfway between 1/2 and the previous number calculated. All such numbers are between 1/2 and 2/3. And that doesn’t even include the number halfway between 7/12 and 2/3.
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