1. **State the problem:** Calculate $1 \frac{7}{10} - \frac{5}{6}$. 2. **Convert mixed number to improper fraction:** $$1 \frac{7}{10} = \frac{10 \times 1 + 7}{10} = \frac{17}{10}$$ 3. **Find common denominator:** The denominators are 10 and 6. The least common denominator (LCD) is 30. 4. **Convert fractions to have the LCD:** $$\frac{17}{10} = \frac{17 \times 3}{10 \times 3} = \frac{51}{30}$$ $$\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}$$ 5. **Subtract the fractions:** $$\frac{51}{30} - \frac{25}{30} = \frac{51 - 25}{30} = \frac{26}{30}$$ 6. **Simplify the fraction:** $$\frac{26}{30} = \frac{\cancel{26}^{13}}{\cancel{30}^{15}} = \frac{13}{15}$$ 7. **Final answer:** $$1 \frac{7}{10} - \frac{5}{6} = \frac{13}{15}$$