#### Answer

The third person owns $\frac{1}{3}$ of the franchise.

#### Work Step by Step

A franchise is owned by 3 people. Person 1 owns $\frac{5}{12}$ of the franchise. Person 2 owns $\frac{1}{4}$ of the franchise. We need to find the fractional part of the franchise that Person 3 owns. To do this, we need to consider the franchise as one (1) whole unit. So that the amounts owned by each of the three owners add up to give us 1.
We can set up an equation:
Person 1 + Person 2 + Person 3 = 1
Let's let the amount owned by Person 3 = x.
Then, using the fractional parts given for Person 1 and Person 2, we have:
$\frac{5}{12}$ + $\frac{1}{4}$ + x = 1
We now need a common denominator for our fractions. The common denominator for the two fractions we have in our equation is 12 (because both 4 and 12 will divide evenly into 12). 12 will divide into 12 one time. One times the 5 in the numerator of the fraction $\frac{5}{12}$ is still 5. For the fraction $\frac{1}{4}$, four will divide into 12 three times. Three times One is 3. So $\frac{1}{4}$ = $\frac{3}{12}$.
Our equation now looks like this:
$\frac{5}{12}$ + $\frac{3}{12}$ + x = 1
We can add the two fractions on the left side of the equation. We have:
$\frac{8}{12}$ + x = 1
We can rewrite 1 as $\frac{12}{12}$ so that it is in the same "units" as the other fractions. This gives us: $\frac{8}{12}$ + x = $\frac{12}{12}$
We can subtract $\frac{8}{12}$ from both sides of the equation.
$\frac{8}{12}$ - $\frac{8}{12}$ + x = $\frac{12}{12}$ - $\frac{8}{12}$
FInishing the subtraction, we get: x = $\frac{4}{12}$ = $\frac{1}{3}$.
This gives us the fractional part of the franchise that Person 3 owns: $\frac{1}{3}$