What is the value of 4/9 divided by a common denominator of 45?

To determine the value of ( \frac{4}{9} ) divided by a common denominator of 45, we begin by converting ( \frac{4}{9} ) so that it has this common denominator.

To find the equivalent fraction of ( \frac{4}{9} ) with a denominator of 45, we need to find out what to multiply the denominator 9 by to get 45. This is done by calculating ( 45 \div 9 = 5 ). Consequently, we must multiply both the numerator and the denominator of ( \frac{4}{9} ) by 5:

[

\frac{4 \times 5}{9 \times 5} = \frac{20}{45}

]

Next, we need to perform the actual division of ( \frac{20}{45} ) by 45. This can be simplified as follows:

[

\frac{20}{45} \div 45 = \frac{20}{45} \times \frac{1}{45} = \frac{20}{2025}

]

Now we can simplify ( \frac{20}{2025} ):

First, we divide the