How do you add $\dfrac{1}{3} + \dfrac{1}{9}$ ?

Hint: Take the larger of the two numbers in the denominator and then use addition for each term.

Complete step by step answer:
Find the least common denominator or LCM of the two denominator:
LCM of $3$ and $9$ is $9$
For the first fraction since $3 \times 3 = 9$
$\dfrac{1}{3} = \dfrac{{1 \times 3}}{{3 \times 3}} = \dfrac{3}{9}$
Add the two fraction
$\dfrac{3}{9} + \dfrac{1}{9} = \dfrac{{3 + 1}}{9} = \dfrac{4}{9}$

So, $\dfrac{1}{3} + \dfrac{1}{9} = \dfrac{4}{9}$.

Note: If the denominators are not the same, then you have to use an equivalent fraction that does have a common denominator. To do this, you need to find the least common multiple (LCM) of the two denominators.
To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify.
Fact one: We cannot directly add or subtract fractions’ top numbers (numerators) unless the bottom numbers (denominators) are the same.
Consider:
$\dfrac{{numerator}}{{deno\min ator}} \to \dfrac{{count}}{{size\, indicator\, of\, what\, we\, are\, counting}}$
$\dfrac{1}{2}$ we have a count of $1$ but it takes $2$ of what you are counting
to make a whole of something (all of it).
$\dfrac{2}{5}$ we have a count of $2$ but it takes $5$ of what you are counting
to make a whole of something (all of it).
Fact second: Multiply by $1$ and we do not change the intrinsic value.
Multiply by $1$ in another form and we can change the way a fraction looks without changing its intrinsic value.