Chapter 5.1, Problem 73E

To determine

To prove: Thenumber which is not equivalent to $\frac{40}{66}$ .

Answer to Problem 73E

Thenumber not equivalent to $\frac{40}{66}$ is $0\cdot \overline{6}$ .

Explanation of Solution

Given: The number is $\frac{40}{66}$ .

Calculation:

Simplify the number $\frac{40}{66}$

  $\Rightarrow \frac{40}{66}=\frac{20}{33}$

$\Rightarrow$ option A, $\frac{20}{33}$ is equivalent to $\frac{40}{66}$

$\Rightarrow$ option B, $\frac{60}{99}=\frac{20}{33}$ is equivalent to $\frac{40}{66}$

$\Rightarrow$ option C, $0\cdot \overline{6}=\frac{6}{9}=\frac{2}{3}$ is not equivalent to $\frac{40}{66}$

$\Rightarrow$ option D, $0\cdot \overline{60}=\frac{60}{99}=\frac{20}{33}$ is equivalent to $\frac{40}{66}$

Conclusion:

Thus, option C, $0\cdot \overline{6}=\frac{6}{9}=\frac{2}{3}$ is not equivalent to $\frac{40}{66}$ .