3 Work these out. Give each answer as a mixed number in its lowest terms. Cancel before you do any calculations. \( \begin{array}{lll}\text { a } \frac{3}{4} \times 18 & \text { b } \frac{5}{6} \times 21 & \text { (c) } \frac{5}{8} \times 22\end{array} \)

**a)** We have \[ \frac{3}{4} \times 18 = \frac{3}{4} \times \frac{18}{1}. \] Cancel common factors before multiplying. Notice that 18 and 4 have a common factor of 2: \[ \frac{3}{\cancel{4}^{\,2}} \times \frac{\cancel{18}^{\,9}}{1} = \frac{3 \times 9}{2} = \frac{27}{2}. \] Now, convert to a mixed number: \[ 27 \div 2 = 13 \text{ remainder } 1 \quad \Longrightarrow \quad 13\frac{1}{2}. \] **b)** We have \[ \frac{5}{6} \times 21 = \frac{5}{6} \times \frac{21}{1}. \] Cancel common factors: 21 and 6 have a common factor of 3: \[ \frac{5}{\cancel{6}^{\,2}} \times \frac{\cancel{21}^{\,7}}{1} = \frac{5 \times 7}{2} = \frac{35}{2}. \] Converting to a mixed number: \[ 35 \div 2 = 17 \text{ remainder } 1 \quad \Longrightarrow \quad 17\frac{1}{2}. \] **c)** We have \[ \frac{5}{8} \times 22 = \frac{5}{8} \times \frac{22}{1}. \] Cancel common factors: 22 and 8 share a factor of 2: \[ \frac{5}{\cancel{8}^{\,4}} \times \frac{\cancel{22}^{\,11}}{1} = \frac{5 \times 11}{4} = \frac{55}{4}. \] Convert to a mixed number: \[ 55 \div 4 = 13 \text{ remainder } 3 \quad \Longrightarrow \quad 13\frac{3}{4}. \] **Final Answers:** a) \(13\frac{1}{2}\) b) \(17\frac{1}{2}\) c) \(13\frac{3}{4}\)