## Elementary Algebra

($\frac{5}{6}$) ($\frac{8}{12}$) $\lt$ ($\frac{3}{7}$)($\frac{14}{15}$) To check whether this inequality is true or false, we simplify it. ($\frac{5}{6}$) $\times$ ($\frac{8}{12}$) $\lt$ ($\frac{3}{7}$) $\times$ ($\frac{14}{15}$) $\frac{5\ \times\ 8}{6\ \times\ 12}$ $\lt$ $\frac{3\ \times\ 14}{7\ \times\ 15}$ $\frac{40}{72}$ $\lt$ $\frac{42}{105}$ 0.555555 $\lt$ 0.4 Because it is not true that 0.55555 is less than 0.4, this inequality is false.