c \( 13-\left(\frac{5}{6}+7 \div \frac{2}{3}\right) \)

To simplify the expression \( c \left( 13 - \left( \frac{5}{6} + 7 \div \frac{2}{3} \right) \right) \), we will follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right). 1. **Calculate \( 7 \div \frac{2}{3} \)**: \[ 7 \div \frac{2}{3} = 7 \times \frac{3}{2} = \frac{21}{2} \] 2. **Now substitute this back into the expression**: \[ 13 - \left( \frac{5}{6} + \frac{21}{2} \right) \] 3. **Find a common denominator to add \( \frac{5}{6} \) and \( \frac{21}{2} \)**. The least common multiple of 6 and 2 is 6. Convert \( \frac{21}{2} \) to sixths: \[ \frac{21}{2} = \frac{21 \times 3}{2 \times 3} = \frac{63}{6} \] 4. **Now add \( \frac{5}{6} \) and \( \frac{63}{6} \)**: \[ \frac{5}{6} + \frac{63}{6} = \frac{5 + 63}{6} = \frac{68}{6} = \frac{34}{3} \] 5. **Substitute this back into the expression**: \[ 13 - \frac{34}{3} \] 6. **Convert 13 to a fraction with a denominator of 3**: \[ 13 = \frac{39}{3} \] 7. **Now perform the subtraction**: \[ \frac{39}{3} - \frac{34}{3} = \frac{39 - 34}{3} = \frac{5}{3} \] 8. **Finally, multiply by \( c \)**: \[ c \left( 13 - \left( \frac{5}{6} + 7 \div \frac{2}{3} \right) \right) = c \left( \frac{5}{3} \right) = \frac{5c}{3} \] Thus, the simplified expression is: \[ \frac{5c}{3} \]