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Q: An integer minus three times its reciprocal equals twenty six thirds What is the integer?

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That has no integer solution. Three times an integer is another integer; if you subtract to integers, you get an integer again, not a fraction.

Yes.

16

Three thirds = 3/3 = 1. So three thirds of twenty is twenty.

2 thirds

Yes.But -22 (minus twenty two) IS an integer

The reciprocal of 7 1/3 is 3/22 or three twenty-secondths.

It is an integer.

14

16

14 and two thirds

21/23 = .913

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