Answer
$\displaystyle \frac{30}{40}-\frac{3}{4} < \frac{14}{15}\cdot\frac{15}{14} \quad $ fill the box with $ < .$
Work Step by Step
$LHS:$
$\displaystyle \frac{30}{40}-\frac{3}{4}=\qquad$... reduce $\displaystyle \frac{30}{40}=\frac{30\div 10}{40\div 10}=\frac{3}{4}$
$LHS=\displaystyle \frac{3}{4}-\frac{3}{4}$
$LHS=0$
$RHS:$
the product of reciprocals is 1,
$RHS=1$
So
$0 < 1$
$LHS < RHS$
$\displaystyle \frac{30}{40}-\frac{3}{4} < \frac{14}{15}\cdot\frac{15}{14} $ fill the box with $ < .$
