Solve for Missing Denominator: 15b/? = 3b/4a Equation

Complete the corresponding expression for the denominator

$\frac{15b}{?}=\frac{3b}{4a}$

$$Examine the following problem:

$\frac{15b}{?}=\frac{3b}{4a}$

Remember the fraction reduction operation,

Begin with the numbers:

In order for the fraction on the left side to be reducible, we want all the terms in its denominator to have a common factor,

Additionally, we want to reduce the number 15 to obtain the number 3 in the fraction's numerator. Furthermore we also want the number 4 in the fraction's denominator.

For this purpose, we'll select the number 15 - which is in the numerator of the left side as a product of numbers where one of them is the number 3. Remember that the number which we multiply by 3 in order to obtain the number 15 is the number 5:

$$$\frac{15b}{?}=\frac{3b}{4a} \\ \downarrow\\ \frac{\textcolor{blue}{3}\cdot\textcolor{orange}{5}\cdot b}{?}=\frac{\textcolor{blue}{3}b}{4a}$

Now we want that after reduction only the number 3 remains in the numerator of the fraction on the left side. However in the fraction's denominator the number 4 remains, meaning - that the number 5 will be reduced, therefore the obvious choice is the number 20, due to the fact that:

$20=4\cdot\textcolor{orange}{5}$

Let's continue to the letters:

Examine the expression once again:

$\frac{15b}{?}=\frac{3b}{4a}$

$$We want the term $a$ in the denominator of the fraction on the right side. Note that this term is not found in the expression in the numerator of the fraction on the left side. Therefore for the letters we'll choose the expression:

$a$

In summary, for both the letters and numbers together we'll choose the expression:

$\boxed{20a}$

Let's verify that from this choice we obtain the expression on the right side:

$\frac{15b}{?}=\frac{3b}{4a} \\ \downarrow\\ \frac{15b}{\textcolor{red}{20a}}\stackrel{?}{= }\frac{3b}{4a} \\ \frac{3\cdot\textcolor{orange}{\not{5}}\cdot b}{4\cdot\textcolor{orange}{\not{5}}\cdot a}=\frac{3b}{4a} \\ \downarrow\\ \boxed{\frac{3b}{4a}\stackrel{!}{= }\frac{3b}{4a} }$

Therefore this choice is indeed correct.

That means - the correct answer is answer A.