Answers

2015-08-26T22:54:47+05:30
First make the numerator of 1/7 and 1/8 as 15.

 \frac{1}{7} =  \frac{1 \times 15}{7 \times 15} =  \frac{15}{105} \\ \\ \frac{1}{8} =  \frac{1 \times 15}{8 \times 15} =  \frac{15}{120}

Now, you can pick any number between 105 and 120 to fill the blank. Don't choose 105 or 120 itself.
So you can fill it by 106 or 107 or 108 or 109...... 118 or 119.

So it can be  \frac{15}{106}
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2015-08-27T00:37:42+05:30

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                        \frac{1}{7} \  < \ \ \ \ \ \frac{15}{X}\ \ \ \ \ \ < \frac{1}{8}
Divide by 15
                        \frac{1}{105} \  < \ \frac{1}{X} \ \ \  < \ \ \ \frac{1}{120}

Hence  X can be any number between:  106 and 119.
Choose  106, 118, 115., 114.

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another way:

15 / X    is the fraction required.
  1/7   <   15 / X    <   1/8  

Multiply the fractions in the numerator and denominator by 15..
       15 / 105    <    15  / X   <    15 / 120

   the numerators are same.  So denominators,  105, X , 120.
 Choose any X that is in between 105 and 120.. for example:  106, 108, 109, 112, 115, 118, 119.       so  115  is  one   answer.
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