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Arithmetic is strictly dealing with real numbers and operators, (addition, subtraction etc.) Mathermatics covers a much broader description including arithmetic, calculus, algebra, etc... You can say that Arithmetic is a subset of Mathematics.
(ËÃ¦vÉrÉªdÊ; ËÃ¦vrÉªdÊ) n. 1. the typical or normal amount, quality, degree, etc: above average in intelligence. 2. (Mathematics) Also called: arithmetic mean the result obtained by adding the numbers or quantities in a set and dividing the total by the number of members in the set: the average of 3, 4, and 8 is 5.