1. **Problem 1: Write 17/3 as a mixed number in simplest form.** 2. To convert an improper fraction to a mixed number, divide the numerator by the denominator. 3. Divide 17 by 3: $$17 \div 3 = 5 \text{ remainder } 2$$ 4. The mixed number is the quotient plus the remainder over the original denominator: $$5 \frac{2}{3}$$ 5. **Problem 2: Work out $\frac{9}{10} - \frac{1}{5}$ in simplest form.** 6. Find a common denominator. The denominators are 10 and 5; the least common denominator is 10. 7. Convert $\frac{1}{5}$ to tenths: $$\frac{1}{5} = \frac{2}{10}$$ 8. Subtract: $$\frac{9}{10} - \frac{2}{10} = \frac{7}{10}$$ 9. **Problem 3: Work out the size of angle $x$ in a triangle with angles 43°, 75°, and $x$.** 10. The sum of angles in a triangle is 180°. 11. Calculate $x$: $$x = 180° - 43° - 75° = 62°$$ 12. **Problem 4: Find the missing number in the proportion $\frac{8}{20} = \frac{?}{5}$.** 13. Cross multiply: $$8 \times 5 = 20 \times ?$$ 14. Simplify: $$40 = 20?$$ 15. Solve for $?$: $$? = \frac{40}{20} = 2$$ 16. **Problem 5: Simplify $\frac{12}{16}$ to lowest terms.** 17. Find the greatest common divisor (GCD) of 12 and 16, which is 4. 18. Divide numerator and denominator by 4: $$\frac{12}{16} = \frac{3}{4}$$ 19. **Problem 6: Convert mixed number $2 \frac{3}{7}$ to an improper fraction in lowest terms.** 20. Multiply whole number by denominator and add numerator: $$2 \times 7 + 3 = 14 + 3 = 17$$ 21. Write as improper fraction: $$\frac{17}{7}$$ 22. **Problem 7: Find size of angle $p$ where angles 70°, 50°, and $p$ form a straight line.** 23. Sum of angles on a straight line is 180°. 24. Calculate $p$: $$p = 180° - 70° - 50° = 60°$$ 25. **Problem 8: Work out $\frac{5}{9} + \frac{4}{9}$ in simplest form.** 26. Denominators are the same, add numerators: $$\frac{5+4}{9} = \frac{9}{9} = 1$$ 27. **Problem 9: Work out $\frac{1}{14} + \frac{1}{7}$ in simplest form.** 28. Find common denominator: 14. 29. Convert $\frac{1}{7}$ to fourteenths: $$\frac{1}{7} = \frac{2}{14}$$ 30. Add: $$\frac{1}{14} + \frac{2}{14} = \frac{3}{14}$$ 31. **Problem 10: Find missing number in $\frac{3}{20} = \frac{?}{100}$.** 32. Cross multiply: $$3 \times 100 = 20 \times ?$$ 33. Simplify: $$300 = 20?$$ 34. Solve for $?$: $$? = \frac{300}{20} = 15$$ 35. **Problem 11: Work out size of angle $c$ in a right triangle with one angle 30°.** 36. Sum of angles in triangle is 180°, right angle is 90°. 37. Calculate $c$: $$c = 180° - 90° - 30° = 60°$$ 38. **Problem 12: Fraction of shape shaded if 4 out of 6 sectors are shaded.** 39. Fraction shaded: $$\frac{4}{6}$$ 40. Simplify by dividing numerator and denominator by 2: $$\frac{2}{3}$$ 41. **Problem 13: Convert mixed number $2 \frac{1}{9}$ to improper fraction in simplest form.** 42. Multiply whole number by denominator and add numerator: $$2 \times 9 + 1 = 18 + 1 = 19$$ 43. Write as improper fraction: $$\frac{19}{9}$$ 44. **Problem 14: Work out $\frac{7}{9} - \frac{7}{9}$.** 45. Subtract numerators: $$\frac{7-7}{9} = \frac{0}{9} = 0$$ 46. **Problem 15: Sum of angles $w$, $f$, and $c$ on a straight line.** 47. Sum of angles on a straight line is 180°. 48. **Problem 16: Work out $4 \frac{5}{7} - \frac{2}{7}$ as a mixed number in simplest form.** 49. Convert mixed number to improper fraction: $$4 \frac{5}{7} = \frac{33}{7}$$ 50. Subtract: $$\frac{33}{7} - \frac{2}{7} = \frac{31}{7}$$ 51. Convert back to mixed number: $$31 \div 7 = 4 \text{ remainder } 3$$ 52. Final answer: $$4 \frac{3}{7}$$ 53. **Problem 17: Which shapes are $\frac{3}{4}$ shaded?** 54. Shape C: 3 out of 4 squares shaded = $\frac{3}{4}$. 55. Shape E: 6 out of 8 squares shaded = $\frac{6}{8} = \frac{3}{4}$. **Final answers:** - 17/3 as mixed number: $5 \frac{2}{3}$ - $\frac{9}{10} - \frac{1}{5} = \frac{7}{10}$ - Angle $x = 62°$ - Missing number in $\frac{8}{20} = \frac{?}{5}$ is 2 - $\frac{12}{16}$ simplified is $\frac{3}{4}$ - $2 \frac{3}{7}$ as improper fraction is $\frac{17}{7}$ - Angle $p = 60°$ - $\frac{5}{9} + \frac{4}{9} = 1$ - $\frac{1}{14} + \frac{1}{7} = \frac{3}{14}$ - Missing number in $\frac{3}{20} = \frac{?}{100}$ is 15 - Angle $c = 60°$ - Fraction shaded is $\frac{2}{3}$ - $2 \frac{1}{9}$ as improper fraction is $\frac{19}{9}$ - $\frac{7}{9} - \frac{7}{9} = 0$ - Angles $w + f + c = 180°$ - $4 \frac{5}{7} - \frac{2}{7} = 4 \frac{3}{7}$ - Shapes C and E are $\frac{3}{4}$ shaded.