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The sum of the largest and smallest fractions among \(\frac{6}{7}\), \(2\frac{3}{5}\), \(\frac{3}{8}\) and \(2\frac{8}{15}\) is :

  • A.\(2\frac{9}{35}\)
  • B.\(2\frac{37}{40}\)
  • C.\(2\frac{7}{35}\)
  • D.\(2\frac{39}{40}\)

Answer: D

The sum is \(2\frac{39}{40}\).

Compare the four values: \(\frac{6}{7} \approx 0.857\), \(2\frac{3}{5} = 2.6\), \(\frac{3}{8} = 0.375\) and \(2\frac{8}{15} \approx 2.533\). The largest is \(2\frac{3}{5}\) and the smallest \(\frac{3}{8}\):

\[ \begin{aligned} 2\frac{3}{5} + \frac{3}{8} &= 2 + \frac{24}{40} + \frac{15}{40} \\ &= 2\frac{39}{40} \end{aligned} \]

Taking \(2\frac{8}{15}\) as the largest, or \(\frac{6}{7}\) as the smallest, gives the other options.

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