1. The problem is to convert and understand the relationships between fractions, decimals, and percentages given in the table. 2. Let's analyze the first row: "gekürzter Bruch" (reduced fraction) 3/20. 3. To convert 3/20 to a decimal, divide numerator by denominator: $$\frac{3}{20} = 0.15$$ 4. To convert the decimal 0.15 to a percentage, multiply by 100: $$0.15 \times 100 = 15\%$$ 5. Check the second row: "Hundertstel Bruch" (hundredths fraction) 25/100. 6. 25/100 as a decimal is: $$\frac{25}{100} = 0.25$$ 7. As a percentage: $$0.25 \times 100 = 25\%$$ 8. Third row: "Dezimalbruch" (decimal fraction) 0,4 (which is 0.4 in English notation). 9. Convert decimal 0.4 to fraction: $$0.4 = \frac{4}{10} = \frac{2}{5}$$ (after simplification) 10. Convert decimal 0.4 to percentage: $$0.4 \times 100 = 40\%$$ 11. Fourth row: 4,25 (4.25 in English notation) as decimal. 12. Convert 4.25 to fraction: $$4.25 = 4 + 0.25 = 4 + \frac{1}{4} = \frac{17}{4}$$ 13. Convert 4.25 to percentage: $$4.25 \times 100 = 425\%$$ 14. Fifth row: 126% as percentage. 15. Convert 126% to decimal: $$126\% = \frac{126}{100} = 1.26$$ 16. Convert decimal 1.26 to fraction: $$1.26 = \frac{126}{100} = \frac{63}{50}$$ (simplified by dividing numerator and denominator by 2) 17. Sixth row: 1,5% (1.5%) as percentage. 18. Convert 1.5% to decimal: $$1.5\% = \frac{1.5}{100} = 0.015$$ 19. Convert decimal 0.015 to fraction: $$0.015 = \frac{15}{1000} = \frac{3}{200}$$ (simplified by dividing numerator and denominator by 5) 20. Seventh row: 200 as a number. 21. Convert 200 to decimal (already decimal), fraction: $$200 = \frac{200}{1}$$ 22. Convert 200 to percentage: $$200 \times 100 = 20000\%$$ Summary: - Fractions, decimals, and percentages are interconvertible by dividing, multiplying by 100, and simplifying. - Use the formulas: - Decimal = Numerator / Denominator - Percentage = Decimal \times 100 - Fraction from decimal: write decimal as fraction and simplify This completes the conversions for the first problem in the table.