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Branch of mathematics that deals with the properties of numbers and ways of combining them through addition, subtraction, multiplication, and division. Initially it dealt only with the counting numbers, but its definition has broadened to include all real numbers. The most important arithmetic properties (where a and b are real numbers) are the commutative laws of addition and multiplication, a + b = b + a and ab = ba; the associative laws of addition and multiplication, a + (b + c) = (a + b) + c and a(bc) = (ab)c; and the distributive law, which connects addition and multiplication, a(b + c) = ab + ac. These properties include subtraction (addition of a negative number) and division (multiplication by a fraction).
This entry comes from Encyclopædia Britannica Concise. For the full entry on arithmetic, visit Britannica.com.