1. Estimate the sum of $\frac{2}{3} + \frac{6}{9}$. Simplify $\frac{6}{9} = \frac{2}{3}$. Sum: $\frac{2}{3} + \frac{2}{3} = \frac{4}{3} \approx 1.33$. 2. Estimate $\frac{3}{20} + \frac{3}{8}$. Find common denominator 40: $\frac{3}{20} = \frac{6}{40}$, $\frac{3}{8} = \frac{15}{40}$. Sum: $\frac{6}{40} + \frac{15}{40} = \frac{21}{40} = 0.525$. 3. Estimate $\frac{7}{12} + \frac{8}{15}$. Common denominator 60: $\frac{7}{12} = \frac{35}{60}$, $\frac{8}{15} = \frac{32}{60}$. Sum: $\frac{67}{60} \approx 1.12$. 4. Estimate $\frac{3}{10} + \frac{4}{7}$. Common denominator 70: $\frac{3}{10} = \frac{21}{70}$, $\frac{4}{7} = \frac{40}{70}$. Sum: $\frac{61}{70} \approx 0.87$. 5. Estimate $\frac{7}{10} + 2 + \frac{13}{20}$. Convert to fractions: $\frac{6}{3} = 2$. Common denominator 20: $\frac{7}{10} = \frac{14}{20}$. Sum: $\frac{14}{20} + 2 + \frac{13}{20} = \frac{27}{20} + 2 = 1.35 + 2 = 3.35$. 6. Estimate $\frac{9}{11} + \frac{6}{7} + \frac{1}{9}$. Approximate decimals: $0.82 + 0.86 + 0.11 = 1.79$. 7. Estimate $\frac{3}{4} + \frac{2}{8} + \frac{6}{15}$. Convert: $\frac{2}{8} = \frac{1}{4}$. Approximate decimals: $0.75 + 0.25 + 0.4 = 1.4$. 8. Estimate $\frac{5}{12} + \frac{2}{11} + \frac{4}{9}$. Approximate decimals: $0.42 + 0.18 + 0.44 = 1.04$. 9. Estimate $\frac{4}{5} + \frac{2}{9} + \frac{7}{16} + \frac{9}{10}$. Approximate decimals: $0.8 + 0.22 + 0.44 + 0.9 = 2.36$. 10. Estimate $\frac{11}{12} + \frac{5}{6} + \frac{1}{10} + \frac{17}{20}$. Approximate decimals: $0.92 + 0.83 + 0.1 + 0.85 = 2.7$. 11. Estimate $\frac{5}{6} + \frac{1}{8} + \frac{4}{9} + \frac{4}{10}$. Approximate decimals: $0.83 + 0.13 + 0.44 + 0.4 = 1.8$. 12. Which sums are between 1 and 2? - $\frac{3}{7} + \frac{5}{8} + \frac{9}{20} \approx 0.429 + 0.625 + 0.45 = 1.504$ (yes). - $\frac{2}{11} + \frac{1}{8} + \frac{3}{9} \approx 0.182 + 0.125 + 0.333 = 0.64$ (no). - $\frac{4}{5} + \frac{7}{12} + \frac{6}{7} \approx 0.8 + 0.58 + 0.857 = 2.24$ (no). - $\frac{9}{11} + \frac{5}{9} + \frac{2}{7} \approx 0.82 + 0.56 + 0.29 = 1.67$ (yes). - $\frac{7}{15} + \frac{2}{8} + \frac{17}{20} \approx 0.467 + 0.25 + 0.85 = 1.57$ (yes). - $\frac{7}{8} + 1\frac{1}{5} + \frac{4}{7}$ is more than 2 since $1\frac{1}{5} = 1.2$, sum $0.875 + 1.2 + 0.571 = 2.65$ (no). Final answers summarized: 1) 1.33 2) 0.53 3) 1.12 4) 0.87 5) 3.35 6) 1.79 7) 1.4 8) 1.04 9) 2.36 10) 2.7 11) 1.8 12) Which sums between 1 and 2: Problems 1, 3, 6, 7, 8, 11 and from part 12 problem options: 1,4,5