[4] 5(1)/(2)times (7)/(11)times 4div (1)/(3)

To solve the expression \(5\frac{1}{2} \times \frac{7}{11} \times 4 \div \frac{1}{3}\), we can follow these steps:<br /><br />1. Convert the mixed number \(5\frac{1}{2}\) to an improper fraction:<br /> \[<br /> 5\frac{1}{2} = \frac{11}{2}<br /> \]<br /><br />2. Rewrite the division as multiplication by the reciprocal:<br /> \[<br /> 4 \div \frac{1}{3} = 4 \times 3 = 12<br /> \]<br /><br />3. Now multiply all the fractions together:<br /> \[<br /> \frac{11}{2} \times \frac{7}{11} \times 12<br /> \]<br /><br />4. Simplify the fractions:<br /> \[<br /> \frac{11}{2} \times \frac{7}{11} = \frac{11 \times 7}{2 \times 11} = \frac{7}{2}<br /> \]<br /><br />5. Multiply the result by 12:<br /> \[<br /> \frac{7}{2} \times 12 = \frac{7 \times 12}{2} = \frac{84}{2} = 42<br /> \]<br /><br />Therefore, the correct answer is \(42\).