What is the result of dividing 3/5 by 2/9?

To divide the fraction 3/5 by the fraction 2/9, you can use the rule that states dividing by a fraction is the same as multiplying by its reciprocal. Thus, you first take the reciprocal of 2/9, which is 9/2.

Now, the operation changes from division to multiplication:

(3/5) ÷ (2/9) is the same as (3/5) × (9/2).

Next, you multiply the numerators together and the denominators together:

Numerator: 3 × 9 = 27

Denominator: 5 × 2 = 10

So, the result of the multiplication is 27/10. This fraction is in its simplest form, and thus, the correct answer is 27/10.

This operation highlights how to handle fractional division effectively, reinforcing the process of multiplying by the reciprocal to arrive at the final answer.