What is the result of dividing 4/5 by 2/6?

To determine the result of dividing 4/5 by 2/6, one must remember that dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, dividing 4/5 by 2/6 can be rewritten as:

[

\frac{4}{5} \div \frac{2}{6} = \frac{4}{5} \times \frac{6}{2}

]

Next, when multiplying fractions, you can multiply the numerators together and the denominators together. This gives:

[

\frac{4 \times 6}{5 \times 2} = \frac{24}{10}

]

Now, 24/10 can be simplified, but the answer as it stands is already a valid outcome of the original division. Therefore, 24/10 is indeed the result of dividing 4/5 by 2/6.

This calculation demonstrates how manipulating fractions through division and multiplication yields a valid answer that reflects the original question's intent.