What should be added to \[\dfrac{1}{4}\] to get \[\dfrac{4}{9}\] ?

Hint:The question which is given can be found out by using the way the required number can be determined by subtracting the given number from the sum. That is by considering an unknown number as \[x\] and finding the value of it using the simple addition and subtraction process.

Complete step by step answer:
As per the question, let \[x\] be the required number. With that as of the remainder the equation is formed as, \[\dfrac{1}{4}\] is the number needed to be added with another number that is the unknown number \[x\] and give the solution as \[\dfrac{4}{9}\].
\[\dfrac{1}{4} + x = \dfrac{4}{9}\]
or we can write in another way as
\[\dfrac{{1 + 4x}}{4} = \dfrac{4}{9}\]
And in the another simplifying form as
\[1 + 4x = \dfrac{{16}}{9}\]
And hence with the required equation obtained simplifying as,
\[4x = \dfrac{{16}}{9} - 1\]
Taking LCM on the RHS side, then
\[4x = \dfrac{{16 - 9}}{9}\]
\[\Rightarrow 4x = \dfrac{7}{9}\]
Thus, for finding the value of \[x\] need of the RHS to get multiplied by the reciprocal of LHS
\[x = \dfrac{7}{9} \times \dfrac{1}{4}\]
\[\therefore x = \dfrac{7}{{36}}\]

So, \[\dfrac{7}{{36}}\] must be added to \[\dfrac{1}{4}\] to get the solution as \[\dfrac{4}{9}\].

Note:A fact family is a group of math facts or a set of numbers formed using the same set of numbers in math. The fact family depicts the connections between the three integers. There are four addition and subtraction sentences formed utilizing three integers in an addition and subtraction fact family.