Find the value for the given expression with a single variable, the given term is \[\dfrac{4}{9} = \dfrac{x}{{54}}\] ?

Hint:For getting the value of a variable in this kind of fraction form, you just need to simplify the fraction, if simplification is possible with the fraction term then first simplify it and then cross multiply and find the solution of the variable, if simplification is not possible then just simply put every term in one side of equation and the variable on the other side to get the solution.

Complete step by step answer:
The given expression with the single variable is \[\dfrac{4}{9} = \dfrac{x}{{54}}\]
For simplification steps needed to be done are follows:
Here we have to find the solution for the variable, now first we will check that any simplification is possible in the left side of the equation, on solving we get:
\[\dfrac{4}{9} = factor\,of\,4 = 1,2,4\,factors\,of\,9 = 1,3,9\]
Here for this fraction no further simplification can be done because the common factor is only one, and after simplifying by one we will obtain the same result.

Now we have to cross multiply and get the value for the variable, on solving we get:
\[\dfrac{4}{9} = \dfrac{x}{{54}} \\
\Rightarrow x = \dfrac{4}{9} \times 54\,\,(here\,54\,and\,9\,can\,be\,simplified) \\
\therefore x = 4 \times 6 = 24 \\ \]
Here we get the solution for the variable which is “x=24”.

Note:In this sort of question you can directly go through cross multiplication and get the answer, but this practice is good for smaller numbers, when you have to deal with the larger number then before cross multiplication you have to check for the further simplification if possible, because this step makes the process easy and accurate.