6. Which expressions have a sum greater than or equal to 14 ? Select all the correct answers. (a) \( 7 \frac{1}{3}+6 \frac{4}{6} \) b) \( 2 \frac{5}{6}+11 \frac{5}{8} \) c) \( 7 \frac{5}{8}+6 \frac{1}{12} \) d) \( 5 \frac{11}{15}+8 \frac{4}{20} \) e) \( 10 \frac{1}{7}+3 \frac{3}{4} \)

1. For option \(a\): - Express \(7 \frac{1}{3}\) as \(7 + \frac{1}{3}\) and \(6 \frac{4}{6}\) as \(6 + \frac{4}{6}\). Notice that \(\frac{4}{6}\) simplifies to \(\frac{2}{3}\). - Thus, \[ 7 \frac{1}{3}+6 \frac{2}{3} = (7+6) + \left(\frac{1}{3}+\frac{2}{3}\right) = 13 + 1 = 14. \] - Since the sum is \(14\) (which is greater than or equal to \(14\)), option \(a\) qualifies. 2. For option \(b\): - Write \(2 \frac{5}{6}\) as \(2 + \frac{5}{6}\) and \(11 \frac{5}{8}\) as \(11 + \frac{5}{8}\). - Approximating, \[ 2 \frac{5}{6} \approx 2.8333 \quad \text{and} \quad 11 \frac{5}{8} \approx 11.625. \] - Thus, \[ 2.8333 + 11.625 \approx 14.4583. \] - Since the sum is greater than \(14\), option \(b\) qualifies. 3. For option \(c\): - Write \(7 \frac{5}{8}\) as \(7 + \frac{5}{8}\) and \(6 \frac{1}{12}\) as \(6 + \frac{1}{12}\). - Approximating, \[ 7 \frac{5}{8} \approx 7.625 \quad \text{and} \quad 6 \frac{1}{12} \approx 6.0833. \] - Thus, \[ 7.625 + 6.0833 \approx 13.7083. \] - Since the sum is less than \(14\), option \(c\) does not qualify. 4. For option \(d\): - Write \(5 \frac{11}{15}\) as \(5 + \frac{11}{15}\) and \(8 \frac{4}{20}\) as \(8 + \frac{4}{20}\). Notice \(\frac{4}{20}\) simplifies to \(\frac{1}{5}\). - Convert \(\frac{1}{5}\) to fifteenths: \(\frac{1}{5} = \frac{3}{15}\). - Now, \[ 5 \frac{11}{15} + 8 \frac{3}{15} = (5+8) + \left(\frac{11}{15}+\frac{3}{15}\right) = 13 + \frac{14}{15}. \] - Since \(13 + \frac{14}{15} \approx 13.9333 < 14\), option \(d\) does not qualify. 5. For option \(e\): - Write \(10 \frac{1}{7}\) as \(10 + \frac{1}{7}\) and \(3 \frac{3}{4}\) as \(3 + \frac{3}{4}\). - Approximating, \[ 10 \frac{1}{7} \approx 10.1429 \quad \text{and} \quad 3 \frac{3}{4} = 3.75. \] - Thus, \[ 10.1429 + 3.75 \approx 13.8929. \] - Since the sum is less than \(14\), option \(e\) does not qualify. The expressions that have a sum greater than or equal to \(14\) are: \(a)\) and \(b)\).