17. \( \frac{2}{10}+\left(\frac{6}{10}+\frac{1}{7}\right) \)

To simplify the expression \( \frac{2}{10}+\left(\frac{6}{10}+\frac{1}{7}\right) \), start by working on the parentheses: 1. First, we need a common denominator for \( \frac{6}{10} \) and \( \frac{1}{7} \). The least common multiple of 10 and 7 is 70. 2. Convert \( \frac{6}{10} \) to a fraction with a denominator of 70: \[ \frac{6}{10} = \frac{6 \times 7}{10 \times 7} = \frac{42}{70} \] 3. Convert \( \frac{1}{7} \) to a fraction with a denominator of 70: \[ \frac{1}{7} = \frac{1 \times 10}{7 \times 10} = \frac{10}{70} \] 4. Now add \( \frac{42}{70} \) and \( \frac{10}{70} \): \[ \frac{42}{70} + \frac{10}{70} = \frac{42 + 10}{70} = \frac{52}{70} \] 5. Next, simplify \( \frac{52}{70} \) by dividing by their greatest common divisor, which is 26: \[ \frac{52 \div 26}{70 \div 26} = \frac{2}{5} \] 6. Now, go back to the whole expression: \[ \frac{2}{10} + \frac{2}{5} \] 7. Convert \( \frac{2}{10} \) to have a common denominator with \( \frac{2}{5} \): \[ \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \] 8. Finally, add \( \frac{2}{10} + \frac{4}{10} \): \[ \frac{2 + 4}{10} = \frac{6}{10} \] 9. Simplifying \( \frac{6}{10} \): \[ \frac{6 \div 2}{10 \div 2} = \frac{3}{5} \] Thus, the final result is \( \frac{3}{5} \).