1. **Problem:** Find the value of $\frac{5}{6} - \frac{1}{3}$. 2. **Formula and rules:** To subtract fractions, they must have a common denominator. 3. **Step 1:** Find the least common denominator (LCD) of 6 and 3, which is 6. 4. **Step 2:** Convert $\frac{1}{3}$ to an equivalent fraction with denominator 6: $$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$$ 5. **Step 3:** Subtract the fractions: $$\frac{5}{6} - \frac{2}{6} = \frac{5 - 2}{6} = \frac{3}{6}$$ 6. **Step 4:** Simplify the fraction by dividing numerator and denominator by their greatest common divisor (3): $$\frac{\cancel{3}}{\cancel{6}} = \frac{1}{2}$$ 7. **Answer:** $\frac{5}{6} - \frac{1}{3} = \frac{1}{2}$. --- 1. **Problem:** Find the value of $\frac{3}{4} + \frac{1}{2} \times \frac{4}{6}$. 2. **Formula and rules:** Follow order of operations: multiply before adding. 3. **Step 1:** Multiply $\frac{1}{2} \times \frac{4}{6}$: $$\frac{1}{2} \times \frac{4}{6} = \frac{1 \times 4}{2 \times 6} = \frac{4}{12}$$ 4. **Step 2:** Simplify $\frac{4}{12}$ by dividing numerator and denominator by 4: $$\frac{\cancel{4}}{\cancel{12}} = \frac{1}{3}$$ 5. **Step 3:** Add $\frac{3}{4} + \frac{1}{3}$. 6. **Step 4:** Find the least common denominator (LCD) of 4 and 3, which is 12. 7. **Step 5:** Convert both fractions to have denominator 12: $$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$$ $$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$ 8. **Step 6:** Add the fractions: $$\frac{9}{12} + \frac{4}{12} = \frac{9 + 4}{12} = \frac{13}{12}$$ 9. **Step 7:** Express as a mixed number: $$\frac{13}{12} = 1 \frac{1}{12}$$ 10. **Answer:** $\frac{3}{4} + \frac{1}{2} \times \frac{4}{6} = 1 \frac{1}{12}$.