1 Work these out. \( \begin{array}{lll}\text { a) } 14 \div \frac{1}{2} & \text { (i) } 16 \div \frac{2}{3} & \text { c) } 18 \div \frac{3}{5} \\ 2 \text { Work these out. Give each answer as a mixed number i } \\ \text { In all parts, cancel before you do any calculations. } \\ \begin{array}{lll}\text { a) } 22 \div \frac{4}{7} & \text { b) } 10 \div \frac{4}{5} & \text { (d) } 21 \div \frac{14}{31}\end{array}\end{array}> \)

**1. Work these out.** **a)** We have \[ 14 \div \frac{1}{2} = 14 \times \frac{1}{\frac{1}{2}} = 14 \times 2 = 28. \] **(i)** We have \[ 16 \div \frac{2}{3} = 16 \times \frac{3}{2}. \] Before multiplying, note that \[ 16 \times \frac{3}{2} = \frac{16 \times 3}{2} = \frac{48}{2} = 24. \] **c)** We have \[ 18 \div \frac{3}{5} = 18 \times \frac{5}{3}. \] Simplify by canceling common factors before multiplying: \[ 18 \times \frac{5}{3} = \frac{18 \times 5}{3} = \frac{90}{3} = 30. \] --- **2. Work these out. Give each answer as a mixed number. In all parts, cancel before you do any calculations.** **a)** We have \[ 22 \div \frac{4}{7} = 22 \times \frac{7}{4}. \] Multiply: \[ 22 \times \frac{7}{4} = \frac{154}{4}. \] Simplify by dividing numerator and denominator by 2: \[ \frac{154}{4} = \frac{77}{2}. \] Convert to a mixed number: \[ \frac{77}{2} = 38 \frac{1}{2}. \] **b)** We have \[ 10 \div \frac{4}{5} = 10 \times \frac{5}{4}. \] Multiply: \[ 10 \times \frac{5}{4} = \frac{50}{4}. \] Simplify by dividing numerator and denominator by 2: \[ \frac{50}{4} = \frac{25}{2}. \] Convert to a mixed number: \[ \frac{25}{2} = 12 \frac{1}{2}. \] **(d)** We have \[ 21 \div \frac{14}{31} = 21 \times \frac{31}{14}. \] Before multiplying, cancel common factors. Factorize: \[ 21 = 3 \times 7 \quad \text{and} \quad 14 = 2 \times 7. \] Cancel the common factor \(7\): \[ 21 \times \frac{31}{14} = \frac{3 \times 7 \times 31}{2 \times 7} = \frac{3 \times 31}{2} = \frac{93}{2}. \] Convert to a mixed number: \[ \frac{93}{2} = 46 \frac{1}{2}. \]