Perform the operation and simplify the answer fully.

To perform the operation ( frac{1}{5} div frac{2}{9} ), you can rewrite the division as multiplication by the reciprocal. Here’s how to do it step-by-step:

1. Write the division as multiplication:

[

frac{1}{5} div frac{2}{9} = frac{1}{5} times frac{9}{2}

]

2. Multiply the numerators and the denominators:

[

= frac{1 times 9}{5 times 2} = frac{9}{10}

]

3. Simplification: The fraction ( frac{9}{10} ) is already in its simplest form since 9 and 10 have no common factors.

The final answer is:

[

frac{9}{10}

]

Great job working through this problem! If you need any more assistance, feel free to ask.

To perform the operation ( frac{1}{5} div frac{2}{9} ), you can multiply by the reciprocal of the second fraction.

1. Find the reciprocal of ( frac{2}{9} ), which is ( frac{9}{2} ).
2. Multiply the first fraction by this reciprocal:

[

frac{1}{5} times frac{9}{2} = frac{1 times 9}{5 times 2} = frac{9}{10}

]

So, the simplified answer is ( frac{9}{10} ).

If you have more questions or need further help, feel free to ask!