Simplify each expression. Homework Help \( \begin{array}{lll}\text { a. } 18 \div \frac{3}{4} & \text { b. } \frac{2}{3}(9-6)+40 & \text { c. } 15 \div 5+\frac{1}{2} \cdot\left(-\frac{4}{7}\right) \\ \text { d. }-\frac{7}{10}+\left(-\frac{5}{12}\right)-\left(\frac{1}{4}\right) & \text { e. } 4.25-7.06 & \text { f. } \frac{7}{8}-\left(-\frac{1}{10}\right)+\left(-\frac{3}{18}\right)\end{array} \)

For \( a. \) \( 18 \div \frac{3}{4} = 18 \times \frac{4}{3} = 24 \). For \( b. \) \( \frac{2}{3}(9-6)+40 = \frac{2}{3} \cdot 3 + 40 = 2 + 40 = 42 \). For \( c. \) \( 15 \div 5+\frac{1}{2} \cdot\left(-\frac{4}{7}\right) = 3 - \frac{2}{7} = \frac{21}{7} - \frac{2}{7} = \frac{19}{7} \) or approximately \( 2.71 \). For \( d. \) \( -\frac{7}{10}+\left(-\frac{5}{12}\right)-\left(\frac{1}{4}\right) = -\frac{42}{60}-\frac{25}{60}-\frac{15}{60} = -\frac{82}{60} = -\frac{41}{30} \) or approximately \( -1.37 \). For \( e. \) \( 4.25-7.06 = -2.81 \). For \( f. \) \( \frac{7}{8}-\left(-\frac{1}{10}\right)+\left(-\frac{3}{18}\right) = \frac{7}{8} + \frac{1}{10} - \frac{1}{6} \). Finding a common denominator (120), we get: \( \frac{105}{120} + \frac{12}{120} - \frac{20}{120} = \frac{97}{120} \) or approximately \( 0.81 \).