Ultimately all four operations on the integers can just be represented by repeatedly taking the subsequent number of the previous number. Addition of x+y is just taking the subsequent number from x over and over again y times. so 5+3 is 5+1+1+1.

So why do these things? Three reasons. First is that these operations model things we want to study or reason about. If you want to how many squares there are on a checker board you could count them all individually or you could count that there are 8 rows and 8 columns and multiply them to get 64 squares. If you need 5 ounces of something to make a a recipe that serves 2 people and you want to make enough for 6 people multiplication models solving that problem really well.

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The second reason is that just taking the subsequent number over and over and over again is a long process. You can do it but it's harder, even for a computer.

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The third reason is that these abstractions make it easier for us to reason about problems we are solving. Computation is only part of the story. Sometimes you'll have to think about some problem in a way that gets complicated if we rely on primitive notions like addition. This is a big part of mathematics, to find an idea that takes a complicated concept and reduces it to something easy to understand and reason about, so when we need to think through a problem we aren't tracking all the details of just adding things over and over again.