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There are a lot of fractions bigger than 2/3 and less than 3/4. There are an infinite number, in fact. Let's convert the fractions into something that will allow us to compare them. 2/3 = 4/6 = 8/12 = 16/24 = 32/48 [We just doubled the numerator and denominator progressively.] 3/4 = 9/12 = 18/24 = 36/48 [We trippled numerator and denominator first, then doubled them progressively.] Look at 32/48 and 36/48. The fractions 33/48, 34/48 (which is 17/24), and 35/48 all fall between 2/3 and 3/4 as was asked. We could keep going, too.

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Q: What fraction is bigger than two thirds but less than three quarters?
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