Solution:
1. Given:
- Dividend: \frac{2}{3}
- Divisor: \frac{5}{6}
2. Divide \frac{2}{3} by \frac{5}{6}:
- Division of fractions involves multiplying by the reciprocal.
- Reciprocal of \frac{5}{6} is \frac{6}{5}.
3. Multiply:
* \frac{2}{3} \times \frac{6}{5}
4. Multiply the numerators and the denominators:
* Numerators: 2 \times 6 = 12
* Denominators: 3 \times 5 = 15
5. Result - Simplify the fraction:
* \frac{12}{15} can be simplified by dividing both the numerator and denominator by their GCD, which is 3.
* \frac{12 \div 3}{15 \div 3} = \frac{4}{5}.
6. The quotient is:
* \frac{4}{5}