You can then abstract counting and numbers 2 and 3 as common to all those fields. Moreover, once you’ve done counting, you can deal with counts alone, not even thinking where they come from. You conclude that 2 + 3 = 5 no matter what you have been counting. That's why math can take off as a separate discipline, called pure math (not that applied math is dirty!). Pure means that suddenly we are not interested where the quantities, counts, numbers come from, we are specifically and only interested in the numbers, counts properties.
When you see a person writing down 2 + 3 =... you don't know what objects she has on her mind, what objects she is adding! But you know the result will be 5! That's, actually, pure math! You see, a person is writing down 2 + 3 =… Now, let's say it again, you don’t know what that person has in mind, which objects she was counting. But, you know that the result will be 5! You abstracted the counts and counting from objects being counted. That’s, so called, pure math. Even, probably, without knowing it, you did a great job abstracting numbers, and operations on them, from real world situations. It is important to note how you dealt here with counts only, and not with particular objects. But, if you keep, on a separate sheet, what objects you are counting, you can transfer the result back to the real world.
Once you are aware that you can work with numbers, counts only, you are in position to investigate properties of these counts, without considering at all where they come from. You may now want to continue to develop math as a separate discipline! Make more examples, think of more numbers, operations on them! 5 + 3 = 8. 3 x 4 = 12. 8 - 5 = 3. You can say now, that if you have 7 and you add 8 you will get 15, just by dealing with numbers, no matter what objects and rules about them were involved. You realize that you can work with numbers only! And operations you have at your disposal, addition, subtraction, division, multiplication. Now, be sure, there are no other operations in math. These four are sufficient to define all "kinds" of numbers and all mathematics. Other, so called, more complex operations (although they are not so complex, in many cases) are just different sequences of these basic four, +, -, x, /, it’s just that mathematicians like give them exotic names, that's all.
This is probably the most important step you have made in learning math so far.
You can play with other numbers and math operations (addition, subtraction, division, multiplication) on them and be sure they will be common and be in intersection of other fields (outside math). Mathematics could have been also called Countology, a science about counts. Or even Setology, a science about sets, because sets are fundamental objects in mathematics. Calling math Setology or Countology is emphasizing the fact that no matter which "fancy" names mathematicians use inside math, those names always represent sets, or counts, or sets of counts, or sets of pairs of counts, sums, or some other relationships between them!
One important note about math and applied math. Looking at 2 + 3 it is impossible to say to which objects these numbers are referring to. Of course, you can try to find examples from real life for the counts 2 and 3 and their addition, but, again, going the other way, from math to real world, just looking at 2 and 3 you can not say what you have counted. That' pure math. You can add 2 and 3 and then you can return the result to the real world, to the objects you have been counted. So, if you counted apples, it will be 5 apples, if you counted cars, it will be 5 cars. Note how math result can be reused for many different objects you have counted. In this "re-usability" lies the value of math. But, on the other hand, since you can deal with numbers only, you can investigate properties of pure numbers, their relationships, their magnitudes, you can investigate operations on them, different sets of counts, i.e. numbers. Result may be applicable to some real world scenario, and frequently is.
Real world reasoning will tell you what to count and with which mathematical operations you will start with. Mathematics will accept these starting points, but will see only numbers and operations, and not what is counted or measured. An example can be any physical law. In each formula, which is within physics, is important what you measure or count, and relationships between the objects or concepts, like mass, speed, electrical charge, distance. But when you start calculations, you will deal with pure math, counts, numbers, keeping aside what is counted (kilograms, meters, seconds, temperature, etc). For instance, in finance, buying or selling is not part of the math. That's part of financial domain. It's separate logic. When you count how much you have sold or bought, those numbers, or counts are actual mathematics. It is YOU who will have to keep track who "buys" and who "sells", while math will keep track of counts and give you results in them.
There are two parts of an applied math problem. 1) Correctly establish relations between non-mathematical objects 2) Solve newly defined numerical, i.e. mathematical problem. The first action will require the knowledge of the real world domain, which is, in most cases, extraneous to mathematics, and, in many cases you will deal with relations and definitions that has little to do with math. For instance, when you "buy" or "sell" something and in certain quantity, buying and selling are not mathematical objects. In Physics, object moving through space, or water going through turbine, are not mathematical relations nor objects. They are non mathematical things whose actions can be quantified, that's all. But these things themselves or their actions are not mathematical objects, they are physical objects. In economics, you will have demand for 500 cars, and supply of 470 cars. But, demand and supply are not mathematical objects, and their relations are not mathematical. Their relations are defined by human will, decision making, sociological laws, and specific logic associated with it. Only when we start quantifying them, keeping track which numbers are "demand" and which numbers are "supply" we enter mathematical world. Note that without keeping track what we have counted, we would not know to which objects the numbers 500 and 470 belong too.
Once we established what needs to be calculated, we can deal with numbers only, with mathematics only. And that's the second part of problem solving. Given these initial conditions from the world of economics or physics or trading, we now deal with calculations, perhaps solving some equations, which is pure math, and knowledge of pure math can be very beneficial at this point. Once the calculations are done (of course, we should keep, all along, track of units) we go back to the real world domain and use the newly obtained solution and results.
One answer to the question how math can be applied to so many different fields is because so many things can be quantified. But even before that, we have to make decision to quantify something. The very fact that we can distinguish different objects through our psychological, cognitive, abstraction, categorization capacities and abilities gives a rise to an important choice of action - to count what we can distinguish. The very fact that we can distinguish so many objects means that we can put them in sets, and count them is the core reason why mathematics can be applicable to so many real world situations.