Simplify. Write your answer as a proper or improper fraction in simplest form. (frac (31)/(10))((31)/(35))=(square )/(square )

To simplify the given expression, we need to divide the fraction $\frac{31}{10}$ by the fraction $\frac{31}{35}$.<br /><br />To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and denominator.<br /><br />So, the reciprocal of $\frac{31}{35}$ is $\frac{35}{31}$.<br /><br />Now, we can rewrite the expression as:<br />$\frac{\frac{31}{10}}{\frac{31}{35}} = \frac{31}{10} \times \frac{35}{31}$<br /><br />Next, we can simplify the expression by canceling out the common factors in the numerator and denominator.<br /><br />In this case, the common factor is 31.<br /><br />So, we can cancel out the 31 in the numerator and denominator:<br />$\frac{31}{10} \times \frac{35}{31} = \frac{1}{10} \times \frac{35}{1}$<br /><br />Now, we can multiply the fractions:<br />$\frac{1}{10} \times \frac{35}{1} = \frac{35}{10}$<br /><br />Therefore, the simplified form of the given expression is $\frac{35}{10}$.<br /><br />So, the answer is $\frac{35}{10}$.