There are a couple of ways to look at this question. One way is to think of this question as asking for a mixed number result. Another is to think of it as an improper fraction.
Let's start with just looking at the statement for a moment. We have a mixed number (#4 2/3#) that is being added to a whole number (112). What is this saying? If we talk in terms of pizzas, we have 4 pizza added to another pizza that is only #2/3# there and we're then adding another 112 pizzas. So really, we have three addition statements:
#4+2/3+112#
and being addition, we can add them together:
#4+2/3+112=116 2/3#
This is the mixed number form of the answer.
What if we want to know how many equal pieces of pizza there are? For instance, we know that one of our pizzas only has #2/3# left to it. We can say that the smallest "slice" we want to consider is one that is #1/3# of a pizza. To do that, we need to convert the 116 whole pizzas into a form that expresses how many "#1/3# of a pizza slices" they have.
Each whole pizza has 3 slices that are "#1/3# of a pizza" big, so we'll multiply 116 by 3 (#116*3=348#) for the number of slices and put that into the numerator of a fraction. But since we are no longer talking about whole pizzas, we'll need to have a 3 in the denominator to show we're talking about thirds of a pizza:
#116/1=116/1*3/3=348/3#
We can now add the whole thing up:
#348/3+2/3=350/3#
This is the improper fraction form.
