Combine and simplify \( \frac{5}{7}-\frac{1}{2} \)

To combine and simplify the expression \( \frac{5}{7} - \frac{1}{2} \), follow these steps: 1. **Find a Common Denominator:** The denominators are 7 and 2. The least common denominator (LCD) is the smallest number that both denominators divide into, which is 14. 2. **Convert Each Fraction:** - For \( \frac{5}{7} \): \[ \frac{5}{7} = \frac{5 \times 2}{7 \times 2} = \frac{10}{14} \] - For \( \frac{1}{2} \): \[ \frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14} \] 3. **Subtract the Fractions:** Now that both fractions have the same denominator, subtract the numerators: \[ \frac{10}{14} - \frac{7}{14} = \frac{10 - 7}{14} = \frac{3}{14} \] **Final Answer:** \[ \frac{5}{7} - \frac{1}{2} = \frac{3}{14} \]