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Find three rational numbers between -6 and -5

Answer 1:

We havwe a rational number between -3 and -4.

                                =  space space space space fraction numerator left parenthesis negative 3 right parenthesis plus left parenthesis negative 4 right parenthesis over denominator 2 end fraction space equals space fraction numerator negative 7 over denominator 2 end fraction

A rational number between (-3) and space space fraction numerator negative 7 over denominator 2 end fraction

                                 = space space space open square brackets open parentheses negative 3 close parentheses plus open parentheses fraction numerator negative 7 over denominator 2 end fraction close parentheses close square brackets plus 2

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                                 =  space space space space space space fraction numerator negative 13 over denominator 2 end fraction cross times 1 half space equals space fraction numerator negative 13 over denominator 4 end fraction

A rational number between space space open parentheses fraction numerator negative 7 over denominator 2 end fraction close parentheses space and space left parenthesis negative 4 right parenthesis

                                     = space space space open square brackets fraction numerator negative 7 over denominator 2 end fraction plus left parenthesis negative 4 right parenthesis close square brackets space plus 2

                                     =  space space space space open square brackets fraction numerator negative 7 plus open parentheses negative 8 close parentheses over denominator 2 end fraction close square brackets plus 2

                                     =     space space space fraction numerator negative 15 over denominator 2 end fraction cross times 1 half space equals space fraction numerator negative 15 over denominator 4 end fraction


Thus, the three rational number  space space open parentheses fraction numerator negative 72 minus over denominator 2 end fraction close parentheses comma space open parentheses fraction numerator negative 13 over denominator 4 end fraction close parentheses space and space open parentheses fraction numerator negative 15 over denominator 4 end fraction close parentheses  are between (-3) and (-4).