Solve the following. \( \frac{5}{6} \div \frac{2}{3} \)

To solve the division of two fractions \(\frac{5}{6} \div \frac{2}{3}\), follow these steps: 1. **Recall the Rule for Dividing Fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. In other words: \[ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \] 2. **Apply the Rule to the Given Problem:** \[ \frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} \] 3. **Multiply the Numerators and the Denominators:** - **Numerators:** \(5 \times 3 = 15\) - **Denominators:** \(6 \times 2 = 12\) So, \[ \frac{5}{6} \times \frac{3}{2} = \frac{15}{12} \] 4. **Simplify the Fraction:** Both the numerator and the denominator can be divided by 3: \[ \frac{15 \div 3}{12 \div 3} = \frac{5}{4} \] Alternatively, \(\frac{5}{4}\) can be expressed as a mixed number: \[ 1 \frac{1}{4} \] Or as a decimal: \[ 1.25 \] **Final Answer:** \[ \frac{5}{6} \div \frac{2}{3} = \frac{5}{4} \quad \text{or} \quad 1 \frac{1}{4} \quad \text{or} \quad 1.25 \]