To add the fractions \( \frac{1}{2} \) and \( \frac{5}{7} \), we first need to find a common denominator. The least common multiple of 2 and 7 is 14.
Next, we convert each fraction to have a denominator of 14:
For \( \frac{1}{2} \): \[ \frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14} \]
For \( \frac{5}{7} \): \[ \frac{5}{7} = \frac{5 \times 2}{7 \times 2} = \frac{10}{14} \]
Now we can add the two fractions: \[ \frac{7}{14} + \frac{10}{14} = \frac{7 + 10}{14} = \frac{17}{14} \]
Thus, \( 1/2 + 5/7 = \frac{17}{14} \).
In the notation you provided, this corresponds to: \[ [17] [14] \]
So the answer is: \[ [17] [14]/[14] \]