The importance of arithmetic in math

Arithmetic is the ABC of math. Addition, subtraction, multiplication, and division are the basics of math and every math operation known to humankind. In one way or another, every equation, graph, and an enormous amount of other things can be broken down into the ABC's of math, the four basic operations. As people say, math is a language, and addition subtraction, multiplication, and division are its alphabet, along with the number line as well. The properties are basically, proven ways to apply the mechanics of arithmetic into certain situations. You can usually find these situations within an equation. Some properties are much more basic and common then others; consequently, they pop up more often then others. For example, the reflexive property of equality, probably the most basic property there is. This property simply states that a number equals itself (a=a). This property is so fundamental that every time you do anything with a number, you see this property come up.

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Multiplication and Division by Zero are Illogical ...

Multiplication

When solving a multiple step equation, the only way we can really know that a number, if left alone from one step to the next has stayed the same is because of the reflexive property. This property allows us to establish that 1=1 and anywhere that that specific number comes up, its value is equal to every other number written the same way, "1." This is connected to the mechanics of arithmetic in the sense that all arithmetic operations assume that every number labeled "1" has a value of one. If you multiply 1 with 2 the "1" has the same value, of one, as it does in any other operation done with that specific number, "1". This is the most simple, broken down, and basic concept of math, this property allows us to always make the assumption that...