r [3] 1(3)/(6)div 5(2)/(5)times (1)/(2)times 8

To solve the expression $1\frac {3}{6}\div 5\frac {2}{5}\times \frac {1}{2}\times 8$, we first need to simplify the mixed numbers and then perform the operations step by step.<br /><br />Step 1: Simplify the mixed numbers.<br />$1\frac {3}{6}$ can be simplified to $1\frac {1}{2}$ since $\frac {3}{6}$ is equivalent to $\frac {1}{2}$.<br />$5\frac {2}{5}$ is already in its simplest form.<br /><br />Step 2: Perform the division.<br />Divide $1\frac {1}{2}$ by $5\frac {2}{5}$.<br />To divide mixed numbers, we convert them to improper fractions.<br />$1\frac {1}{2}$ is equivalent to $\frac {3}{2}$.<br />$5\frac {2}{5}$ is equivalent to $\frac {27}{5}$.<br /><br />Now, divide $\frac {3}{2}$ by $\frac {27}{5}$.<br />To divide fractions, we multiply by the reciprocal of the second fraction.<br />$\frac {3}{2} \div \frac {27}{5} = \frac {3}{2} \times \frac {5}{27}$.<br /><br />Step 3: Perform the multiplication.<br />Multiply $\frac {3}{2}$ by $\frac {5}{27}$.<br />$\frac {3}{2} \times \frac {5}{27} = \frac {15}{54}$.<br /><br />Step 4: Simplify the fraction.<br />Simplify $\frac {15}{54}$ by dividing both the numerator and denominator by their greatest common divisor, which is 3.<br />$\frac {15}{54} = \frac {5}{18}$.<br /><br />Step 5: Perform the remaining operations.<br />Multiply $\frac {5}{18}$ by $\frac {1}{2}$.<br />$\frac {5}{18} \times \frac {1}{2} = \frac {5}{36}$.<br /><br />Finally, multiply $\frac {5}{36}$ by 8.<br />$\frac {5}{36} \times 8 = \frac {40}{36}$.<br /><br />Step 6: Simplify the final fraction.<br />Simplify $\frac {40}{36}$ by dividing both the numerator and denominator by their greatest common divisor, which is 4.<br />$\frac {40}{36} = \frac {10}{9}$.<br /><br />Therefore, the final answer is $\frac {10}{9}$ or approximately 1.11.