9-2½:3¾-(2½-1⅓)×3

To solve the expression \( 9 - 2\frac{1}{2} : 3\frac{3}{4} - (2\frac{1}{2} - 1\frac{1}{3}) \times 3 \), we will follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right). First, let's convert all mixed numbers into improper fractions: 1. Convert \( 2\frac{1}{2} \): \[ 2\frac{1}{2} = \frac{5}{2} \] 2. Convert \( 3\frac{3}{4} \): \[ 3\frac{3}{4} = \frac{15}{4} \] 3. Convert \( 1\frac{1}{3} \): \[ 1\frac{1}{3} = \frac{4}{3} \] Now we can rewrite the expression with these fractions: \[ 9 - \frac{5}{2} : \frac{15}{4} - \left(\frac{5}{2} - \frac{4}{3}\right) \times 3 \] Next, we need to evaluate \( \frac{5}{2} : \frac{15}{4} \): \[ \frac{5}{2} : \frac{15}{4} = \frac{5}{2} \times \frac{4}{15} = \frac{20}{30} = \frac{2}{3} \] Now we calculate \( \frac{5}{2} - \frac{4}{3} \). To do this, we need a common denominator, which is 6: \[ \frac{5}{2} = \frac{15}{6} \] \[ \frac{4}{3} = \frac{8}{6} \] Then, \[ \frac{5}{2} - \frac{4}{3} = \frac{15}{6} - \frac{8}{6} = \frac{7}{6} \] Now, multiply this result by 3: \[ \left(\frac{5}{2} - \frac{4}{3}\right) \times 3 = \frac{7}{6} \times 3 = \frac{21}{6} = \frac{7}{2} \] Now substitute back into the original expression: \[ 9 - \frac{2}{3} - \frac{7}{2} \] Next, we convert 9 into a fraction with a common denominator of 6: \[ 9 = \frac{54}{6} \] Now putting it all together: \[ \frac{54}{6} - \frac{4}{6} - \frac{21}{6} = \frac{54 - 4 - 21}{6} = \frac{54 - 25}{6} = \frac{29}{6} \] Thus, the final result is: \[ \boxed{\frac{29}{6}} \]