Arithmetic or arithmetics (from the Greek word ἀριθμός, arithmos "number") is the oldest and most elementary branch of mathematics, used very popularly, for tasks ranging from simple day-to-day counting to advanced science and business calculations. 

An example of visual subtraction of natural numbers. image: wikipedia

It involves the study of quantity, especially as the result of operations that combine numbers. 

In common usage, it refers to the simpler properties when using the traditional operations of:

  • addition, 
  • subtraction, 
  • multiplication and 
  • division with smaller values of numbers. 

Professional mathematicians sometimes use the term (higher) arithmetic  when referring to more advanced results related to number theory, but this should not be confused with elementary arithmetic.