Devi needs a rational number r such that 1/7 < r < 1/6. Using a common denominator of 42, which value of r works?

13/84. 1/7 = 6/42 = 12/84 and 1/6 = 7/42 = 14/84. So 13/84 lies strictly between them. (8/42 and 5/42 are outside; 1/12 = 7/84 < 1/7.)

Devi needs a rational number $r$ such that $\frac{1}{7} < r < \frac{1}{6}$ .
Using a common denominator of 42, which value of $r$ works?

Class 8Rational Numbers Between Two NumbersRational Numbers

\frac{1}{7} = \frac{6}{42} = \frac{12}{84}

and

\frac{1}{6} = \frac{7}{42} = \frac{14}{84}

. So

\frac{13}{84}

lies strictly between them

. (\frac{8}{42}

and

\frac{5}{42}

are outside;

\frac{1}{12} = \frac{7}{84} < \frac{1}{7} .

)

Answer: A)

\frac{13}{84}

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