Many people think of arithmetic and mathematics as the same thing. Arithmetic, however, is defined as the most basic and fundamental category of mathematics. It includes computations that involve adding, subtracting, dividing, and multiplying numbers that are real, rational, and complex. This differs from mathematics, which involves studying number, shape, and quantity relationships. Mathematics also includes the use of not only signs and symbols, but also proofs.
When a person studies arithmetic, he learns how to work with numbers and do basic calculations. For example, he learns how to recognize and name quantities as well as how to add numbers together and subtract them. He also learns how to multiply numbers and divide them. This basic study typically provides a foundation students can use for calculation in everyday life as well as in preparation for more complicated work with numbers, such as in algebra and calculus.
Though arithmetic is considered a basic form of math, it is widely used. Typically, people use it in the course of everyday life. For example, they use it when counting, making purchases, preparing budgets, and balancing their checkbooks. It is also used by businesses that have to make accounting calculations. It often has a place in some higherlevel scientific calculations as well.
Addition is one of the basic types of arithmetic. It essentially involves combining numbers, which are referred to as addends, to get a total, which is called the sum. Subtraction is another basic operation of this type of math. It is the opposite of addition and involves finding the difference between numbers. The original number in a subtraction problem is called the minuend while the number that is subtracted is called the subtrahend.
Multiplication is another arithmetic operation; it involves adding numbers in a quick way. For example, a multiplication problem that involves multiplying two times four is basically adding two plus two plus two plus two—quickly. The numbers that are multiplied in this type of problem are called factors, and the answer is called the product. Division is the opposite of multiplication and involves splitting a number or quantity into equal parts. The original number is called the dividend, the number a person divides by is called the divisor, and the answer to a division problem is called the quotient.
Sometimes the word arithmetic is used to mean number theory. This, however, differs from the form of elementary math most people mean when they talk about arithmetic. Number theory involves the study of the properties of numbers.
SarahSon Post 6 
Arithmetic was something that never came easy for my son. We spent hours working with him on his multiplication tables. I think it is always helpful for someone to be able to perform basic arithmetic in their head.
When working with my son, I would even make up arithmetic games to help him with his skills. Even now he will always use a calculator over adding or multiplying something in his head.

miriam98 Post 5 
@oasis11  I spent four years teaching in Asia, and I suppose everyone knows that Asian students do better in arithmetic than American students do.
If you want to know my honest opinion about why that is, I can think of two things that I observed. Teachers there expose them early on to arithmetic, and they drill, drill, drill.
Unfortunately the drill approach has been mocked by some American educational professionals as the “drill and kill” approach, and has therefore largely been abandoned.
In its place American educators focus more on contextual approaches to learning. They may have their benefits, but I still see drills as the best way to reinforce the material. 
Charred Post 4 
@David09  I think that what you’re describing are logic arithmetic operations. We studied these in college too; they were basically known as truth tables, which had two values, True or False.
You combine these values to get different results. True and True would equal True, for example. True and False would equal False. Those concepts were implemented into computer programming because they were so elementary. 
David09 Post 3 
I completely agree that arithmetic, while thought of as basic, is fundamental; you never get away from it, even if you do advanced math.
This even holds true for computers, which we think capable of performing advanced mathematical concepts and functions. At its core, a computer processor just adds, subtracts, multiplies and divides, for every operation that you perform.
It does this through a process called binary arithmetic which is just a sequences of ones and zeros. These numbers act like switches which can turn each other on and off and represent different numeric values.
With these simple switches the computer performs operations that form the basis of the simplest math operations or the most demanding, graphics intensive calculations. 
cafe41 Post 2 
@Oasis11  Good for you. That is great that your kids are so good at arithmetic. My problem was that I was sort of a math phobic. I did okay in my arithmetic lessons when I was in elementary school, but in high school I struggled. I needed arithmetic help when I got to high school and had trouble with algebra. I never felt comfortable with math so maybe I just did not have a strong enough foundation in arithmetic.

oasis11 Post 1 
I think that arithmetic lessons are among the most important lessons that kids get from their math class. In fact, I have both of my children enrolled in a supplemental education program that focuses strictly on math computation.
The founders of the program realized that addition, subtraction, multiplication and division were the cornerstones of most mathematical operations.
If you have a solid foundation in these areas you should really have no problems with any type of arithmetic lesson. My children have been doing arithmetic worksheets daily for the last five years and they are not only great at math, but they are also very confident and always get a perfect scores in their math computation exercises and tests that they take in school. 