1. **Problem 1: Find angle $n$ given that $n$ and $47^\circ$ are adjacent angles on a straight line.** 2. Angles on a straight line add up to $180^\circ$. This is called the supplementary angles rule. 3. Using the formula: $$n + 47^\circ = 180^\circ$$ 4. Solve for $n$: $$n = 180^\circ - 47^\circ = 133^\circ$$ 5. **Answer:** $n = 133^\circ$ 6. **Problem 2: Subtract $2$ from the mixed number $4 \frac{8}{9}$ and express the answer as a mixed number in simplest form.** 7. Convert the mixed number to an improper fraction: $$4 \frac{8}{9} = \frac{4 \times 9 + 8}{9} = \frac{36 + 8}{9} = \frac{44}{9}$$ 8. Subtract $2$ (which is $\frac{18}{9}$) from $\frac{44}{9}$: $$\frac{44}{9} - \frac{18}{9} = \frac{44 - 18}{9} = \frac{26}{9}$$ 9. Convert $\frac{26}{9}$ back to a mixed number: $$26 \div 9 = 2 \text{ remainder } 8$$ So, $$\frac{26}{9} = 2 \frac{8}{9}$$ 10. **Answer:** $2 \frac{8}{9}$ 11. **Problem 3: Find the missing numerator in the proportion $\frac{?}{5} = \frac{6}{10}$.** 12. Cross multiply to solve for the missing numerator $x$: $$x \times 10 = 6 \times 5$$ $$10x = 30$$ 13. Divide both sides by 10: $$x = \frac{30}{10} = 3$$ 14. **Answer:** The missing numerator is $3$. 15. **Problem 4: Convert $\frac{14}{9}$ to a mixed number in simplest form.** 16. Divide 14 by 9: $$14 \div 9 = 1 \text{ remainder } 5$$ 17. So, $$\frac{14}{9} = 1 \frac{5}{9}$$ 18. The fraction $\frac{5}{9}$ is already in simplest form. 19. **Answer:** $1 \frac{5}{9}$