1. **State the problem:** Write expressions for given descriptions and describe given expressions in words. 2. **Write expressions for each description:** i. One-half of $x$ add 8: $$\frac{1}{2}x + 8$$ ii. Three-quarters of $x$ subtract 12: $$\frac{3}{4}x - 12$$ iii. 7 add four-fifths of $x$: $$7 + \frac{4}{5}x$$ iv. 20 subtract five-ninths of $x$: $$20 - \frac{5}{9}x$$ 3. **Describe each expression in words:** i. $\frac{x}{6} + 2$ means "one-sixth of $x$ plus 2." ii. $\frac{5x}{7} - 4$ means "five-sevenths of $x$ minus 4." iii. $8 - \frac{2x}{3}$ means "8 minus two-thirds of $x$." iv. $3 + \frac{7x}{8}$ means "3 plus seven-eighths of $x$." 4. **Maya's rectangle problem:** The rectangle has height $$\frac{1}{3}$$ cm and width $$4b$$ cm. The area $$A$$ of a rectangle is given by $$A = \text{height} \times \text{width}$$. So, $$A = \frac{1}{3} \times 4b = \frac{4b}{3}$$ cm$^2$. **Final answers:** - Expressions: i. $$\frac{1}{2}x + 8$$ ii. $$\frac{3}{4}x - 12$$ iii. $$7 + \frac{4}{5}x$$ iv. $$20 - \frac{5}{9}x$$ - Descriptions: i. One-sixth of $x$ plus 2 ii. Five-sevenths of $x$ minus 4 iii. 8 minus two-thirds of $x$ iv. 3 plus seven-eighths of $x$ - Area of Maya's rectangle: $$\frac{4b}{3}$$ cm$^2$