|(4)/(7) div (2)/(3)-| (5)/(7)

To solve the expression \( \left|\frac{4}{7} \div \frac{2}{3} - \frac{5}{7}\right| \), we need to follow the order of operations (PEMDAS/BODMAS) and simplify step by step.<br /><br />1. **Division**: First, perform the division inside the absolute value.<br /> \[<br /> \frac{4}{7} \div \frac{2}{3} = \frac{4}{7} \times \frac{3}{2} = \frac{4 \times 3}{7 \times 2} = \frac{12}{14} = \frac{6}{7}<br /> \]<br /><br />2. **Subtraction**: Next, subtract \(\frac{5}{7}\) from \(\frac{6}{7}\).<br /> \[<br /> \frac{6}{7} - \frac{5}{7} = \frac{6 - 5}{7} = \frac{1}{7}<br /> \]<br /><br />3. **Absolute Value**: Finally, take the absolute value of the result.<br /> \[<br /> \left|\frac{1}{7}\right| = \frac{1}{7}<br /> \]<br /><br />Therefore, the correct answer is:<br />\[<br />\boxed{\frac{1}{7}}<br />\]