What is the missing number in the box? 21 : 18 = [ ? ] : 12 There are $\frac{4}{5}$ as many male workers as female workers in a factory. What is the ratio of the number of female workers to the total number of workers in the factory?

1. Simplify the given ratio

The given ratio is $21 : 18$. Dividing both sides by their greatest common divisor, $3$, we get:
$21 : 18 = 7 : 6$

2. Find the equivalent ratio with the consequent 12

We need to find the missing number in $[ ? ] : 12$ such that it is equivalent to $7 : 6$.
Since $12 = 6 \times 2$, we multiply the antecedent by $2$:
$7 \times 2 = 14$
So, $21 : 18 = 14 : 12$.

1. Translate the given fraction into a ratio of units

Since there are $\frac{4}{5}$ as many male workers as female workers, we can represent the number of male workers as $4$ units and the number of female workers as $5$ units.
Male : Female = $4 : 5$

2. Find the total number of units

Total units = $4 + 5 = 9$ units

3. State the required ratio

Ratio of female workers to total workers = $5 : 9$