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Insert three fractions between \(1/4\) and \(1/3\) so the five fractions form an arithmetic sequence. What is the sum, expressed as a common fraction, of these three new fractions?

 May 22, 2022
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The difference between 1/3 and 1/4 is 1/12. On a number line, there should be four sections each seperated from each other by 1 fraction. The distance between each fraction therefore should be 1/(12*4)=1/48. Then our new fractions can be found as 13/48,14/48, and 15/48. (13+14+15)/48=42/48=7/8

 May 22, 2022

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