20 divided by 2/3
Understand the Problem
The question is asking for the result of dividing 20 by the fraction 2/3. To solve this, we can multiply 20 by the reciprocal of 2/3, which is 3/2.
Answer
30
Answer for screen readers
The final result of dividing 20 by the fraction $\frac{2}{3}$ is 30.
Steps to Solve

Recall the operation of dividing by a fraction
When you divide by a fraction, you can multiply by its reciprocal. The reciprocal of the fraction $\frac{2}{3}$ is $\frac{3}{2}$. 
Set up the multiplication
Now, we will multiply 20 by the reciprocal of $\frac{2}{3}$: $$ 20 \times \frac{3}{2} $$ 
Perform the multiplication
To compute this, first multiply 20 by 3, then divide by 2: $$ 20 \times 3 = 60 $$
Now divide 60 by 2: $$ \frac{60}{2} = 30 $$
The final result of dividing 20 by the fraction $\frac{2}{3}$ is 30.
More Information
Dividing by a fraction is essentially scaling the other number by the factor represented by the reciprocal. This concept is often used in situations where you need to find how many times a fraction fits into a whole number.
Tips
 Forgetting to take the reciprocal of the fraction before multiplying is a common mistake. Always remember that division by a fraction is the same as multiplication by its reciprocal.